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Title : Saturn and its system : containing discussions of the motions (real and apparent) and telescopic appearance of the planet saturn, its satellites, and rings, the nature of the rings, the great inequality of saturn and jupiter, and the habitability of saturn / by Richard A. Proctor,...

Author : Proctor, Richard Anthony (1837-1888). Auteur du texte

Publisher : (London)

Publication date : 1865

Subject : Saturne (planète)

Relationship : http://catalogue.bnf.fr/ark:/12148/cb37277456j

Type : text

Type : monographie imprimée

Language : english

Language : English

Format : 1 vol. (252 p.) : ill.

Format : Nombre total de vues : 317

Description : Contient une table des matières

Rights : Consultable en ligne

Rights : Public domain

Identifier : ark:/12148/bpt6k95020n

Source : Université Paris Sud, B3-70

Provenance : Bibliothèque nationale de France

Online date : 15/10/2007

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S AT UR N.


LOMDOJf

l'UlNTED J'Y SPOTTISWOOr)]! A!fD CO. KEW-SME~TS~n~tm





SATURN AND ITS SYSTEM CONTAINING DISCUSSIONS OF

THE MOTIONS (REAL AND APPARENT) AND TELESCOPIC APPEARANCE OF THE PLANET SATURN, ITS SATELLITES, AND RINGS; THE NATURE OF THE RINGS; THE 'GREAT INEQUALITY' OF SATURN AND JUPITER; AND THE HABITABILITY OF SATURN.

TO wnicn Atu': ArrENDHt)

NOTES ON CHALM3AN ASTRONOMY, LAPLACE'S NEBULAR THEORY. AND THE HABITABILITY OF THE MOON; A SERIES OF TABLES WITH EXPLANATORY NOTES; AND EXPLANATIONS OF ASTRONOMICAL TERMS.

t6r nn

~î!~SJ~

BY -1..1\:1 J.

BY ~'r'$~$y'~

RICHARD A. PROCTOR, B.A. ~Êï~~

Z~< c/ ~H'~ College, C~ a~ ~< College, ~x.

ILLUSTRATED BY FOURTEEN ENCRAVINCS <N STEEL AND COPPER.

THU nEAVEXS DECLAM THE GMHY Ot' GOn, -niR FmMAAtEXT SHO~VTTtt !!M HAXDYWOTtK.

LONDON:

LONGMAN, GREEN, LONGMAN, ROBERTS, GREEN.

18G5.


Hea.v'n

la as the book of God before m- set,

Wherein to read His wondrous works, and leam

His seasons, hours, or days, or months, or years.

MiLTON.

This I say, and would wish all men. to know and lay to heart, that he who discerns nothing but Mechanism in thé Universe, bas in thé fatalleat way misaed the Secret of the Universe altogether. CARLYLE.


I HAVE endeavoured in this work to give a complète account of thé phenomena presented by thé planet Saturn and its system. It might appear, at first sight, that a single planet, however interesting or elaborate thé scheme of which it is thé centre, should rather be made the subject of a chapter than of a volume, even of the moderate dimensions of the present. It will be found, however, that much that is contained in these pages, is applicable, with suitable changes in matters of detail, to ail the members of the solar system. The inquiry into the nature of thé rings, in Chapter V., deals with a subject not uninteresting, I think, on its own account, but which gathers an additional interest from its bearing on the speculations of Laplace. It is not altogether impossible that in thé variations perceptibly proceeding in thé Saturnian ring-system a key may one day be found to thé law of development under which thé solar system bas reached its present condition.

Certain points of resemblance between thé relations of Saturn and our earth, as respects thé variations of their seasons, have induced me to dévote somewhat more space to thé considération of the celestial phenomena presented to the Saturnians than thé nature of thé subject might appear to warrant. Thèse featnres of resemblance–singular in

PREFACE.


planets that differ so widely m ail other respects–may bc thus presented

The vernal equinoxes of the northern hemispheres of Saturn and the earth occur when thé heliocentric longitudes of tbose planets are respectively 171° 43' 35"'l, and 180° the axes of Saturn and the earth are inclined 26° 49' 27"'87 and 23° 27' 24~-69, respectively, to thé respective orbital planes of thé two planets and the north pole of thé Saturnian celestial sphère is separated by an arc of only 7° 7'24" from thé north pole of our heavens again, the longitudes of the perihelia of thé orbits of Saturn and thé earth are respectively 90° 23' 36~4, and 100° 38' f-8; and Saturn and the earth are in perihelion after passing over 98° 40' 1~-3 and 100° 38' 1"'8, respectively, in longitude, from the autumnal equinoxes of their respective northern hémisphères.

Thus the variations in the Saturnian seasons more directly illustrate the corresponding variations in those of the earth than might, at first sight, be supposed. It will be seen from the note on page 117 that even thé exanunation of thé appearance of thé rings to thé Saturnians is not without its bearing on terrestrial phenomena.

Thé connection between the subjects treated of in thé notes fbrming Appendix I., and the main subject of thé work, will appear on perusal. The reader is reminded tliat thèse are notes, not essays they contain merely the heads of arguments supporting opinions expressed in the body of thé work.

The Tables numbered Vil., VIII., X. and XI. now appear for thé first time: parts of the other tables, also, are original. Thé sources from which the tables have been derived, or thé formulas from which they have been calculated, are given in thé explanations of thé Tables, which I have endeavoured


to make as complete as possible. The expirations of astronomical terms extend oniy to terms actually used in thé present work.

In thé body of the work I have adopted for thé sun'n equatorial horizontal solar paraiïax (the carth at her mean distance) Professer Hansen's détermination, namely, 8~-9159. More than ten years have elapsed since M. Hansen nrst pointed out that thé solar parallax (8~-5776) deduced by.Encke from thé transits of Venus in 1761 and 1769, requires to be increased, to correspond with the observed extent of thé moon's parallactic inequality. Thé above value, M Hansen's later calculation, corresponds very closely with thé results obtained by Leverrier and others. In thé tables of Appendix II., two values are given (corresponding to thé above values of thé solar parallax) of every élément whose détermination depends upon thé sun's distance.

I have endeavoured to make thé engravings represent as accurately as possible what they are meant -to illustrate. This is to be understood of all thé figures throughout thé work, unless it is expressly statcd in the text that général principles only are illustrated (as in thé first six ngurcs of Plate X.) or'that a part of any figure is purposely- exaggerated (as the rings in ng. 1, Plate VIII.)

In thé figures of Plate I., thé outlines of thé planet and .rings, and of their shadows, have been determined A'om calculations founded on thé dimensions of thé planet and rings adopted in Tables III. and IV. such détails hâve then been introduced as hav e been noted by thé best observers. Thé slope of thé figures is, to à-certain extent, a matter of indiSerence, since it varies with the hour of observation but to preserve uniformityl have adopted thé following rule Thé horizontal line through thé centre of thé dise in the


figures of Plates I., VII., IX., and XIII. represents the planet's heliocentricpatb, the direction of the planet's motion being from left to right in the figures of Plate I. (which are supposed to be seen through an inverting telescope), and from right to left in ail the other figures.

The star-maps in Plates II. and III. are on the gnomonic projection.* The stars in Plate III. have been taken (with a correction for precession) from the niaps of the Society for the Diffusion of Usefui Knowledge. The positions of thé stars in Plate II. have been corrected for the precession of the equinoxes, but not for the proper motions, since we have no means of learning whether the proper motions of the stars are constant for long periods. The path of Saturn in Plate III. has been taken from the ~Nautical Almanacs' for the years 1859-1866 the path in Plate II. has been calculated for an unclisturbed elliptic orbit, corrected from Saturn's present orbit for variations in the position of the nodal line and perihelion thus the minor irregularities in thé path on Plate III. (chiefly due to the disturbing attractions of Jupiter) are wanting in Plate II. The figures of the constellations have been slightly altered from thé Society's maps.

The gnomonic projection seems thé natural mode of projection for star-maps, since the eye of an observer vicwing tho celestial sphere actually occupies the point of sight' ofthe projection-that is thé centre of the sphere. The object to bo sought in all star-maps, is that the greatest portion possible of the celestial sphere should be visible at a single view with as little distortion as possible. In the Society's maps, the celestial sphere is projëcted from thc centre upon the circumseribing cube thus forming six maps considerably distorted near the angles. I am preparing a series of star-maps on a plan which appears to offer greater advantages. The celestial sphere is projected from the centre npon the circumseribing dodccahedron thus forming twelve pentagonal maps much less distorted near tho angles than the Society's maps and further, by presenting the six maps of each hémisphère in a single plate in thcir proper relative positions-that is, as Sre pentagons upon the five sides of thé polar pentagonal map-the relative positions of thé northern or of the southern constellations are seen at a glance. A slight addition to thé outer maps brings the whole length of thc equator into cach sextuple map.


The orbit of Nysa in fig. 3, Plate VI., bas been cleri.vecl from the elements given in NichoPs Cyclopsedia of thc Physical Sciences,' and Mitchel's Popular Astronomy 1 (both published in 1860). 1 think it little probable that these elements are even approximately correct. The direction of the planetary motions is indicated in this figure, in fig. 1, Plate VIII., and in ng. 7, Plate X., by the Zodiacal signs outside the orbit of Saturn that is, the motions are supposed in these figures to take place in a direction contrary to that in which thé hands of a watch move. The dimensions of the satellites Mimas, Enceladus, and Hyperion, in fig. 1, Plate VII., are slightly exaggerated. These satellites would scai~cely be visible on the scale of that figure..

Thé figures of Plate XIV. are derived from woodents in Layard's 'Nineveh and Babylon' and Nineveh and its Remains.'

Collingwood Villas, Stoke, De'von 3/ 1865.


CONTENTS.

-+-

CHAPTEK I.

DISCOVERY OF SATURN–THE SIMPLER ELEMENTS 0F IIIS OMIT.

l'AO-M

Probable Order in which tho Planets wcre diseo\'<;red 1 Discovery of Saturn–how eQected 2 Apparent Motions of a Superior Planet expiai ned 5 Application to Satarn's Motions. 7 Saturn's Distance and Sidereal Period determined-

From his Arc and Period of Retrogression 8 From bis Motion in Quadrature .11 From the Interval in which hc returns to thc apparent Place ho had occupied -whon in Opposition 12 From bis Synodical Period 1-i From the Interval in which he apparontly completes the Circle of thé Zodiac 15 Saturn's Distance determined from his Sidereal Period and his Motion between his Stations 16 Discordant Results 18 The Plane ofSaturn'aOrbitinclinedto the Ecliptic .19 Line of Nodes of Saturn's Orbit on the Ecliptie-how determined 20 Inclination of Saturn's Orbit to thé Ecliptic-how measured 21 S:).turn'8 looped and twisted apparent Path on thé Celeatial Sphore explained 23 CHAPTER II.

FALS)-: SYSTEMS–MODERN ASTRONOMY––ELEMENTS OF SATURAS ELLIPTIC ORDIT.

Problem set themscivea by thé Epicyelians 27 How solved 28 Distances of the Planets not determinable if thc Earth the Contre of their Motions 29 Astrology 31 Alchemy 33 Copernicus and his System 31 Kepler discovers his two first Laws 35 Illustrated by Satum's Motions 36 Kepler discovcrs his third Law 39 Illustrated by Relations bctwcen the Orbits of S~tum and the Earth ib. Newton investigates Kepler's Laws 40 Discovers tho Law of Universal Gravitntion 41 Characters of Copernicus, Kepler, and Newton, compared 42 Aberration of Light -1-i


CHAPTERHI.

TELESCOPIC DISCOVERIES.

r~GE

Galileo announees that Saturn is triform 4ô Perplexed by Satarn's Changes of Form 46 Hevelius explanatory 47 Huyge~s discovers Saturn's Ring 48 And Titan 49 Bail and Cassini discover thé Division in the Ring .&. Cassini discovers Japetus .< Variatiuns of Brilliancy observed in this Satellite ôO Cassini discovers Rhea, Tethys, and Dione .51 Huygens and others determine thé Elements of the Orbits of Five Satellitt-s 52 Maradi détecta Irregularities in Saturn's Rings .53 Herschel examines the gréât Division 54 Discovers Enceladus and Mimas 55 Examines Belts on Satum's Surface 57 Determines Sa.tuni's Period of Rotation ib. Determines Period of Rotation of Outer Ring ï6Measures thé Planet and Rings 58 Examines the Rings when their Edge is turned to thé Earth 59 Detects Traces of un Atmosphère surrounding Satum ?'&. Bond and others detect Traces of Divisions in thé Rings .61 1 Bond and Lassell discover Hyperion G2 Bond, Lassell, and Dawes discover thé Dark Ring 0 63 Dark Spacfs observed on thé Inner Bright Ring 64 Wray and 0. Struve discover Nebulous Appendages 65 Observations by Carpenter and Dawes 67 Dimensions of Saturn's Globe and Rings 68 Compression of Saturn's Globe. 69 Thickness of the Rings 70 0 Saturn's Mass determined from the Motions of Titan .71 1 Saturn's Volume undDensity 74 .t Relative Dimensions of thc varions ~'mbers of thé Solar System, and of thcir Orbits !7/. Telescopic Powcrs neeessary to ~Lsprvf' the varions Phf-nomena prcsentcd by

S:'turn's System '76 5

~rturns, 'îv

CHAPTER IV.

THE PERIODIC CHANGES IN THE APPEARANCp OF SATURN'S SYSTEM. Direction of Saturn's Axis unchangcd during his Révolution about thé Sun 77 ï Position of thé Ring's Plane with respect to the'Ecliptie and to Saturn's Orbit 7S S Changes of Appearance tbaf. would be presented to an ohj-erver supposed to be placed- at the Sun's centre during a complete Révolution (/f Saturn 79 9 Actual Changes observed from thé Earth 81 Eneet of thé Inclination of Saturn's Orbit to the Erliptic 83 DisappparMCCS and Rcappearanc'-s of t]u' Ring c'xphtincd 85


FAùt!

Thc Shadow of thé Rings on the Planet, aud of thé Phuiet on thc Rings 91 ConstructionofaSaturnianOrrery 9o Changes in thc Figures of thc Saturnian Belts explained SatumneverGibbous 99 Eclipses, Occultations, and Transits of Saturn's Satellites, 100 CHAPTER V.

NATUttE OF THE K!NGS.

Speculations of Maupcrtius, Buffon, and Mamtn 105 Objections to the Solidity of Saturn's Rings, drawn from–

The variable Traces of Division 106 The Appeartmce of the Dtirk Ring 108 'fhe Dimensions of the Rings 109 The Increase in the Breadth of the System 110 Laptacoprovesthat the Rings must Rotate 112 AndatdIBcrentR&tes ib. ThatthoRingsifsolidarenotuniform 113 SuggMtsthattheymaybenon-unIform8olIdsf-ccentricaMyphic<?d .114 Piercca.nd Maxwell provethat'thé Rings eannotbeSohd. 116 Nor Fluid Instances of Rings of disconnected Bodies in the Universe .117 Difficulties before considered disappear on the Hypothesis that Saturn's Rings aresoconstitutpd 118 Elliptical Shading of thé Rings explained ib. Appearances observed by Wray and 0. Struve explained .121 Problem of thé Motions of Rings of Satellites too complex for exact Solution 122 Such Rings safe from sudden Destruetion .123 Extra-planar DIsturbances and their ESecta ?~. Wavcs of Concentration and Dispersion, and their Eiïects 124 Collisions among thé Satellites and their Effects 125 Observed Changes in the Ring. correspond with th- Results of Anal)"ti 126 C'HAPTER VI.

TIΠC):EAT !~EQUAHTY OF S.U'CRX AXD JUt'tTEi!.

Irregularities in thc ~lotions of Saturn and Jupiter 128 Variable Elejnents of thé PIanetary Oi-bits ..120 Effects of Normal Disturbing Forces .131 Effects of Perpendicnlar Disturbing Forces 13S Effects of Tangcntial Disturbing Forces 133 These Forces generally combine their Effects .134 Examination of the Motions of an inferior distm-bed by a superior PIanet–(i) Orbits of both Planets circular .135 (il) Orbit of inferior Planet. (alêne) Elliptie 137 (iii)OrbitofsnpprIoi'Pianet(alone)EUiptic 139 (iv) Orbits of both Planets Elliptie 140


l'A(J~

Results are diruetly applicable to thé c'asc of .t. supcrior disturbed by an iafenor

Planct. 1.12

Approaeh to a Simple Rotation of Commonsurability bctwcc-n thc Penods of Saturnand Jupiter · zl''

More exact Examination uf thé Motions of thé. two Planets 1-11 Disturbing Eiïects due to–

Tho Forma and Positions of the two Orbits 148 The varying latervals between successive Conjunetioiis ~J The variable Distance between the two Planets at successive Conjuactions 150 The variable Motions of the two Planets Thé varying Intervals between successive Triple Conjonctions The-varyingPcriodaofthetwoPlaneta 151 Thé Inclination of thé Flânes of their Orbits Thé Variations in thé I~dial aud Perpcndicular Forces Results uf thé Analytical Examination of these Distu).'ba.nc';s lo2 CycIcofDisturbimccs Distnrbanecs caused by t.he other Mombers of thc Sular System 1<~ Variations in the Ececntrieity and Inclination of Saturn's Orbit .15-1 La.grange'aLa\s i/I.

CHAPTER ~H.

HAHITABILITY OF SATURN.

Saturnprobablyinhabited Variation of Gravity on Sttturn's Globe .1~7 Density of Matcrials composing Satnrn's Globe not necessarily ttu- sanLe :t.s thc mean Density of the Globe lo8 Océans on Saturn's Surface not necessarily colleeted in one .Mcmisplu-rc ih. Heat and Light received on Satum'a Globe .160 ThoSaturnianSpasons Rapid Apparent Motions ofCelestialObjects .164 Effects of the long Saturnian Year 16o Effects of thé Eccentricity of Saturn's Orbit ï~. Electrical Conditions ofS~tuin as yetunknown .168 Parts of Saturn's Surface from which tho different Rings an' visible .160 Apparent Ontlines of the Rings viewcd from différent pai't~ of Satnrn's Surface 171 Rings not always Visible, and variable in Brilliancy 17C Motion of the Shadow of.thc Planctacross thé Rings-how Variable ..177 Eclipses of Saturn's Surface by the Rings 179 Showntolastmanyyears in somo Latitudes .181 Examined by tho Method of Projection ib. Eclipses of thé Outor Satellite by the Rings 183 Seven Inner Satellites cannot be eclipsed by the Rings, except for places near Saturn'sEquator ib. Satellites vary in apparent Magnitude as thcy traverse tho Saturnian Sky Jupiter and Uranus,onlyPlancts visible from Saturn 18-1 Conclusion


CONTENTS.

XV

APPENDIX I.

NOTE A.–CRALD~EAN ASTRONOMY.

PAGR

Eastern Systems of Astronomy not derived from the Egyptians, Chinese, Indigos, PersiansorBabylonians 189 BaiUy's'Atlantides' 190 Chaldaeans not originally settled in Mesopotamia ib. Bailly's Objections to the Chaldaean Origin of Astronomy considered 191 Fabulous Accounts of Chaldaean Astronomical System 192 Real Discoveries effected by thé Chddœans ib. Chaldaeans probably acquainted with True System of the Universe .193 Opinions attributedbyFhilolaustoPythagoras–howprobablydcrived 194 Chaldaeans not acquainted with Gravity 19.5 Mechanical Skill of the Assyrians ib. Astronomical Observations–howrecordedby the Chaldseans Assyrians acquainted with the Laws of Optics 196 Mythological System of the Assyrians ï~. Mylitta and Bel–how represented .197 Attributes of Nisroch, the Time-God .198 Nisroch represented within a Ring .199 Figure of a Ring commonly met with in cngraved Tablets ï~. NOTE B.-LAPLACE'S NEBULAR THEORY.

PhenomenaonwhichtheTheoryisfoundpd .201 l These may be ascribed to a. Law of Development, since God works nothing in Nature but by Second Causes' ib. The Nebular Theory 202 How the Theory must be modified to correspond witb modern Scientific Discoveries ib. Notions of the Satellites of Uranus and Neptune--how reconcilabic with Laplace's Theory 203 Laplace Theory reconcilable with thé Scripture Account of Création 204 Changes going on in Saturn's Ring-System correspond with the Processes conceived by Laplace 206 NOTE C.-HABITABILITY OF THE MOON.

Physical Condition of the Moon veiy different from that of the Earth 207 Arguments against thé Existence of a Lunar Atmosphere ib. OpposingArgT.iments 208 Attempt td reconcile thèse Arguments by Considerations drawnfrom the Moon's Figure 209 Improbable that all Traces of a Lunar Atmosphère should be concealed in thé mannersuggested 210 Colour of the Moon not such as thé Earth would présent at the Moon's distance 211 Effects of Diminution of Température Oceans on the Moon's Surface probably Frozen, and Gases once enveloping the MooncondcnsedtutheLiquidorSolidForms a


APPENDIX II.

Table PA&K I.–CertainSolarElements 215 II.–Certain Eléments of the Earth, January Ist, 1865. III.–Eléments of Saturn, January lst, 1865 216 IV.-Elements of Saturn's Rings, January Ist, 1865 .217 V.-Elements of Saturn's Satellites 219 VI. -Elements of thé Planets ib. VII.–For Determining the Appearance of Saturn's Rings, &c. 220 VIII.–For Calculating the Elevation of the Sun above the Plane of the Rings, &c. 221 IX.-Great Inequality of Saturn and Jupiter 222 X.-Passages of the Ring's Plane through the Sun between the years 1600 and2000 223 XI.–For Determining the Sun's Diurnal Path on the Saturnian Heavens at the Saturnian Solstices and Equinoxes, the Appearance of the Rings,

and the Ee]ipses of the Sun by the Rings, for different Latitudes

on Saturn's Globe 224 JEr~~a~oMo/eT~M~ 227 .Ecp~M~t'oM of ~roMo~ca~ Terms 237


LIST OF ILLUSTRATIONS.

PLATE PAGH I.–Three Figures of Saturn and his Rings, &c. F~o~t'~t'cce. II.–Saturn's apparent Path about 4000 years ago < !'o j~tcc eacA o~e~\ 2 and 3 III.–Saturn's apparent Path during years 1859-1866 1 &e~'e<~jp6~M J 2 und 3 IV.–Dntgra.nis !'o./ace~~e ô V.–Diagrams lo VI.–Diagrams. Part of Solar System 27 VII.–Two Figures of Saturn and his System 4o VIII.–Orbits of Saturn and the Earth. Diagrams. Saturnian Qrrery 77 IX.–Figures ofS.tturn and his Rings, &G. 105 X.–Diagrams. Orbits of Jupiter andSaturn 131 XI.–Diagrams 163 XII.–Shadowof the Planet on the Rings) other pages 178 and XIII.–Shadow of the Rings on thé Planet <oy~ce McA oi'~ oe~MM ~~M 178 <ZKM 179 XIV. -Assyrian Déifies. Tablet stamped from an Assyrian Cylinder–~o ./hce ~c 197



ERRATA.

h, T.tb!<- M-, p~g'- 2't, h~ading of first row; in page -23-t, ~in~ 19 .md in pa~c -~o, line 1, for ~M~ r~d .M~ m's~nding ~c word in sensc corresponding to that of the word ~/it~~ in the expression ~o~< ~/t7~f~.

In p~e 243, lines 18-24, the first parts uf t.he d~nitiors .<d. correct; th. p~rts from 'm .~r.T words tu thé end must. he intereh~ngt'd.



SATUEN AND ITS SYSTEM.

CHAPTER I.

DISOOVERY 0F SATURN–THE SIMPLER ELEMENTS OF HIS ORBIT. No ACCOUNT, historical or traditional, has been handed down to us of the discovery of thé planet Saturn. Though he is included in the list of wandering stars in the earliest astronomical systems whose records have reached us, there can be little doubt that Venus, Jupiter, and Mars were discovered long before Saturnthe most distant planet known to the ancients. The two first, surpassing in splendour the brightest of the fixed stars, must at a very early period have attracted the notice of astronomical observers, who could not fail soon to perceive that those orbs were changing their positions on the celestial sphere. Mars, in like manner, with his ruddy but brilliant light, and swift motions amongst the fixed stars, was probably recognised as a wandering orb at a very remote period. Mercury, on thé other hand, twinkling like a fixed star, and never visible but when near the horizon, and when his lustre is dimmed by the glory of the rising or setting sun, probahly escaped the notice of astronomers, or was at least not recognised as a planet* till long after even Saturn's dull orb had been discovered, and his slow movements traced upon the celestial sphere.

Let us consider in what manner the astronomers of old must have attained to the discovery of Saturne planetary nature, and Mercury, though probably the ln.st-d!seovcrcd planet of 'the ancient system of astronomy, was included in thé stellar worship practised under the Lachmites by the Asedites.

7!


to the knowledge of the various facts respecting him with which we learn that they were acquainted. The time thus spent in retreading the paths by which past generations attained to knowledge would not be altogether wasted if we only learnt thence the lessons of patience and watcbfLLiness. But such an inquiry bas, in fact, a closer connection with modern science than might at first be supposed. In the brief paragraphs that announce each year the discoveries of new asteroids or of telescopic cornets, we see the records of the same patient observation applied in the same manner as of old. It is true that the powerful and delicate instruments now used, and the application of modern methods of mathematical l analysis, enable the astronomer to obtain in a few weeks résulta tbat formerly a life would have been insunicient to compass. An air of mystery, also, surrounds his researches, lying, as they do, chiefly in depths to which the far-seeing eye of thé telescope alone penetrates. Yet the modern astronomer, like thé observer of old, seeks among the celestial bodies the signs of change and motion, and when he has detected these, he tracks the wandering orb and calculates the extent and character of its orbit. To this work he must apply–besides his tel.escopes and his analyses-the oldfashioned instruments, patience, energy, and watchfulness. At a very early period the ancients separated the stars into constellations. In all probability this arrangement was soon followed by the construction of rough maps, on which the positions of the principal stars were noted down. They marked, no doubt, with special care, the stars in the zodiac-that belt of the celestial sphere within which the sun, moon, and planets were observed to move. Let us consider how this process must have led to the discovery of Saturn.

Shining with a dull yellow light, and traveiling amongst the fixed stars with a scarcely perceptible motion, the planetary nature of Saturn remains for a long time unnoticed. But bis path on the celestial sphere brings him into very close (apparent) proximity with some of thé brightest of the fixed st:ars, and astronomers must at length have become too well acquainted with the général configuration of thé zoadical constellations not to notice the presence of a strange star in such a position. Once observed,




though they might remain in doubt for a few days as to his planetary nature, these doubts would soon be set at rest by obvious alterations in bis bearing with respect to the neighbouring fixed stars.

Let us suppose, by way of illiistration, that Saturn is describing that part of his orbit indicated in Plate II., and that he is first observed when in opposition near the bright star Regulus.* The time then is mid-winter.f The heavens–in the eastern clime of those nrst astronomers–are sparkling as if set with myriads of varied gems. The greater Lion, with the brilliant stars Deneb and Régula is in the south-east, slowly rising to the meridian. Near Regulus, about a degree and a half to the north, a strange star is seen, whose dull yellow light contrasta strangely with the dazzling white of the fixed star. As they rise together to culmination, and then sink towards the south-western horizon, thé closest observation can detect no change in their relative positions. On the following night the stranger is again seen close to Regulus. But now its position seems slightly changed :-it is no longer due north of Regulus, but has moved slightly westward. The change of position is, however, so small as to be scarcely perceptible. It is not until several days hâve elapsed that the wandering nature of the stranger is certainly established. It passes to the north-west of Regulns, and continues to move slowly westward.

As Mars and Jupiter both appear to move from east to west when in opposition, though their real motion is from west to east, it remains doubti'ul whether the new planet moves from east to west, as he appears to do, or, like the other planets, from west to east. Careful observation soon shows that Saturn's westward motion is gradually diminishing yet, when six weeks (the time Thé bright star below thé zodiac, near the centre of the map.

t Regulus now souths at miduight in the middic of Mfn'ch. Four thousn.ud years ago he passed thé meridian at midnight two months earlicr. The position of thé ecliptic was also dIËerent.. Regulus, now nearly half a degreo to tho north, was then south of thé eeliptic. Sa.turn's path on thé celestinl sphère lias, in likû manncr, undergone several changes for Instance, thé positions of the nodes and of thé perihelion, and tho inclination of thé orbit to the ecliptic, hâve varied, and other changes have taken place which need not at present be dweit upon.

B 2


in which Mars retrogrades after opposition) have passed, Saturn is still moving westward, nor bas his retrograde motion ceased when two months (the corresponding period of Jupiter's retrogression) have elapsed. For yet anotber fortnight he retr ogrades, and then begins to move slowly along 'his advancing arc. Although be bas thus been retrograding for nearly two montbs and a half from opposition, he bas passed over an arc of ouly three degrees on the celestial sphere.

Saturn's progressive motion, slow at nrst, gradually increases as he approaches conjunction, when, becoming an evening star, his light is dimmed, and finally lost, in the light of the sun. About a month after conj unction, he again becomes visible as a morning star. His apparent motion is still progressive, but gradually decreases until he becomes stationary. He then slowly rétrogrades for nearly five months, passing through opposition; becomes stationary again, then advances, and so on continually, advancing during seven montbs and a half and retrograding during five, but on the whole slowly traversing the zodiac from west to east, or in the order of the signs.

Having ascertained that the strange orb is a planet, let us see how the ancient astronomers could approximately determine the distance and period of the new planet from its apparent motions. We may proceed on the supposition that they were acquainted with the true system of the world. It would obviously be awaste of time to consider, at any length, methods belonging to a false system tbere are also good reasons for supposing that thé true system was actually known to ancient astronomers.* For thé sake of simplicity, the paths of Saturn and the earth are supposed to lie in thé same plane, and to be circles about the sun as centre.

In the first place, what inferences may be deduced from Saturn's slow retrograde motion when in opposition, his long period of retrogression, and the small arc passed over by him in that period? To answer these questions it will be necessary to recall to the reader's mind the cause of the retrograde motion of a planet in opposition.

See Note A, Appendix I., Chaidgeati Astronomy.



Let s (fig. 1, Plate IV.) represent the sun, EE'E~the earth'a orbit, p p'p~ part of the orbit of a superior planet. When the earth is at E let the planet be at r, so that (SEP being a straight line) the planet is in opposition when at p. Starting from these positions, suppose that the earth and the planet, in the same interval of time, pass respectively over the arcs E E' and PP', EE' being greater tlian PP'. Then it is obvions that the line E'p' is inclined to the line EP, and that if thèse two Unes are produced tbey will meet beyond P. Let them be produced, beyond their point of intersection o, to K and x' respectively. Now the observer on the earth sees the planet in the direction E K when the earth is at E, and in the direction when tbe earth is at E' thus tbe planet appears to have moved in the direction KK/, while it bas actually moved in the contrary direction, namely, from p to p~. The amount of thé planet's retrograde motion during the interval is measured by the angle contained between the lines E P, E'p', that is, by the angle EOE' or KOE/; and, vice ~c~, if the retrograde arc passed over by the planet on the celestial sphere be measured, the angle E o E~ becornes known witb. an exactness proportioned to the accuracy of the instruments used in effecting the measurement and the skill of the observer employing tbem. Let us now carry thé earth and planet forward in their orbits. It is obvious that tite path of the earth becomes more and more inclined to the line of sight to the planet the farther thé earth is carried on in the arc EE'E"; thus if E", P", and E~, P~, be respectively contemporaneous positions of the earth and planet, the angle between the line E~P~ and the arc E~E" is less than the angle between thé line E~p" and the arc E~E', and this angle again is less than the angle between the line E~ and the arc E'E. Hence the effect of the earth's superior velocity, so far as it operates in changing the direction of the line of sight to the planet, gradually diminishes, until at length the earth reaches a position, as at E", such that the effect of tbe direction of its motion exactly counterbalances its superior velocity, andthe planet appears to be stationary. If E~E~ and p~p~~ a.re smaU arcs passed over by the eM'th and planet in the same time at tbis period, tbe line E~p~ is parallel to thé line E~P", the superiority in length of the arc E~' over


the arc p~p" being compensated by the smallness of the angle at which E~E~ is inclined to the line of sight E~p' compared witb thé inclination of p~p~~ to the same line. Tbus thé planet is seen in the same direction at the end of this interval as at the beginning, or is stationary.*

After this, it is plain that the planet will appear to advance for at first the earth's path becomes inclined at a smaller angle to the line of sight to the planet, till it coincides with that line and afterwards, as the earth passes on to conjunction, its motion (considered with reference to the line of sight at any instant) is in a contrary direction to that Qf the planet, and therefore adds to the planet's apparent motion on the celestial sphere.

If the planet were visible when in conjunction, its motion would appear swifter then than at any other time. Thus let es~ be the line along which conjunction takes place, the earth beingat e and the planet atp and e', p' the positions of the earth and planet after a short interval of time then e~) is the direction in which the planet would be seen when in conjunction, that in which it would be seen at the end of the interval of time. Now 6j9 and 6V meet witbin the orbit of the planet at o; the angle 60~ or ~o~measures the arc on the celestial sphere passed over by the planet, and the wbole motions both of the planet and thé earth conspire to increase this ang-le whereas in any other positions, either the difference of these motions, or only parts of them, affect the angle between the lines of sight at the beginning and end of any corresponding interval of time. And although the angle is diminished when a superior planet is in conjunction through the effect of increased distance (e~ plainly exceeding Ep by twice the radius of the earth's orbit, or by twice s E\°yet under the actual relations of the velocities and distances of the planets.f increase prevails over decrease, and a superior planet, if It must be remembered that thé arcs j~ and ~p~~ are supposed to be veiy small. A planet is not actuaïïy stationary during any finite period of time retrograde motion merges into progressive progressive into retrograde,.at a definite instant, before which (by howerer smal] an interval of time) thé motion is of one kind, after~rds of the contrary; it is oniy~ that instant that there is no motion, progressive or retrograde. f &

t If 0!, D be respectively thé mean distances of thé earth and of a superior planet


visible, would appear to move more rapidly wben in conjunction than at any other time. A planet is, however, always invisible when at or near conjunction, since it then occupies the same region of the celestial sphere as thé sun, and is tberefore lost in his superior light. When the planet next becomes visible, however, the effect of its swifter motion in conjunction is seen in the change of its position among the zodiacal constellations.

Passing from conjunction to opposition, thé planet goes through the saine changes in a reverse order. Its progressive motion gradually diminishes till it becomes stationary thence it rétrogrades tbrough opposition to its next station; and so on continua] ly, the total result of its motion in each synodical révolution being a progression from east to west, or in the order of the signs of the zodiac.

Let us now consider what inferences may be drawn from the nature of Saturn's apparent motions on the celestial sphere. The nrst point to be noticed is the slowness of his retrogression when in opposition. Now, referring to fig. I, Plate IV., it becomes clear that tbis must arise from one of two causes. If r F~ were very nearly equal to E E', E'r' would be very nearly parallel to E~, or, in other words, thé angle E o E~ would be very small. Hence the slowness of Saturn's retrogression arise from his velocity being very nearly equal to that of the eartb. But again, from thé s-un p, p thcir respective periods; v, v their respective mean angular velocities about the sim. We have from Kepler's third law-

3 3

P f~ D~

D 1 1

but v

p D~

l i 1 l

h l A~ 1 l

therefore v v v + v D~ D2 + 1

now, on the supposition of circular orbits, thé retrograde velocity of a superior planet in opposition would be proportional to and the progressive velocity in conjunetion would be proportional to but from thé proportion deduced above, it follows

D + d

that

that is, (smce (n~+~)~ = D+~ + 2D"c~, or is greater than D+<) thé apparent velocity in conjunction is grcatcr than the apparent Tplocity in opposition.


if (the l'est of thé figure remaining uncbanged) we make the orbit r p'p" very large, and suppose the planet's velocity in this large orbit to be no greater than in the smaller one, the angle EOE~ would obviously becorne very small, for thé fartber P p' is removed from E E~ thé more nearly will E~P~ and E r approach to parallelism. Thus, then, Saturn's slow motion in opposition ?m~ arise from the fact tbat his orbit M very large compared with tbat of the eartb. Hence, within a week of Saturn's discovery, enough might be known to show that either bis velocity in his orbit is very nearly equal to that of the earth in hers, or that he must move at an immense distance from the earth. Anotber fact revealed by observation points to the true cause of Saturn's slow retrograde motion. After opposition he retrogrades for nearly two months and a half. In this time the earth bas completed nearly a quarteT of her orbit, and therefore her path bas become inclined at a very small angle to the line of sight to Saturn. Since, then, it is only when the earth's path is thus inelined that her superior velocity is so far compensated by inclination tbat Saturn appears to be stati'onary~ it is clear that the earth's motion must be much swifter than Saturn's. Hence we have only one possible explanation left of the slowness of Saturn's retrograde motion namely, that it is due to bis vast distance from the eartb.

Having arrived at this conclusion, let us see how the ancient astronomers might apply the results of observations of thé new planet (even those taken during only tbe first few months after discovery) to obtain more definite notions of his distance, and thence to determine bis period.

Let a small circle E E'E~ (ng. 2, Plate IV.) be described to represent the orbit of the earth about s the sun; and with the same centre let p p~ part of a large circle, be described to represent Saturn's orbit, of which as yet notbing is supposed to be known but that it is large compared with thé earth's orbit. LetE,? be the positions of the earth, and Saturn when the latter is in opposition) so tbat s E p is a straight line. Let E~ be the position of the earth when Saturn is stationary, that is, two months and a half after opposition; thus ESE~ is an angle of


about 75°. Through E' let the straight line E'P' be drawn, inclined to s F at an angle containing the sarne number of degrees, minutes, and seconds, as the arc on thé celestial sphere through which Saturn has been observed to move during the two months and a half following opposition thus E'K' is the line of sight from the earth to the planet when the earth is at E'; and p', the point in which E'E/ meets the planet's orbit, must be the position of the planet at that time. Produce P'E' to a convenient distance from E', to B; through B draw BA in a direction perpendicular to s P, and draw E'A touching the circle E E'E" in E'. We have, then, the following facts to guide us :-the earth and Saturn both lie in the line B K/ the earth is leaving this line in the direction E'A Saturn is leaving it in the direction of the tangent to PP'P" atp', a direction approximately parallel to BA.* Now the planet appears stationary when at P'–in other words, the rates of departure of Saturn and the earth from thé line E~ are exactly equal. If, then, we suppose a point to move from B in direction B A (which is parallel to Saturn's line of motion at p') witb Saturn's velocity, and another point to start from E' at thé same moment in direction with the earth's velocity, then, since the rates of departure of these two points from the line B E' are exactly equal, they would arrive at the point A at the same instant. Hence the velocities of these moving pointa–wbich velocities are, by our supposition~ the velocities of Saturn and the earth respecti.vely-are respectively proportional to B A, E'A, the spaces they pass over in equal times. We arrive, then, at the important result, that Saturn's velocity in bis orbit the earth's velocity in hers the line B A the line E'A, very approximately. If the figure is constructed with proper care, we have only to measure thé lines B A and E~A to determine the value of tbis proportion or we can employ a very simple trigonometrical calculation for this purpose. t Either method leads to the resuit The tangent at p is pa.ra.llcl to BA since, then, the arc rp" is very small, the tangent at p~, which is perpendicular to sp~, is inclined at a -very small angle to the tangent at P, and is therefore very nearly parallel to D A, and for our pnrpose may be considered as actually parallel to B A.

t In the triangle ABE' the angle HAJ-/ is pqual to thcknown angle ESE~, and thc angle AE'D is the complement of thé angle BE~s, which is the sum of two known angles viz.


tbat A E' is about 3~ times as large as B A, or SaturD's velocity is to that of thé earth in the proportion of 11 to 34, very nearly. We can now determine Saturn's distance in either of two ways. Thé orbit r p~p", assigned to Saturn in the above investigation, was simply a circle, large compared with E E'E~ and it is to be observed that thé dimensions of this circle had nothing to do with thé formation of the triangle A B E~, on which the determination of Saturne velocity was made to depend except that, knowing thé planet's orbit to be large, we were able to assert that the direction of its motion at p' was very nearly parallel to BA. But we can apply the result just obtained to see whether pp'p~ correctly represents Saturn's orbit. For the arc p p~ passed over by Saturn should bear to the arc E E' passed over, in thé same time, by the earth, thé proportion, above determined, of 11 to 34. In our figure r r' does not bear this proportion to E E', being too large. The radius s r is therefore too small, and we must select snch a radius in place of sp that thé arc intercepted between s r and E'p' may be of the requisite Jength, viz. ~ths of EE'. It will be found that for this purpose s r should be about 9~ times as great as s E.

We may confirm the correctness of this resuit by applying a second method to determine Saturn's distance. Observation shows that, when near opposition, Saturn retrogrades daily over an arc of about 4' 43" on thé celestial sphere. Now Saturn is advancing from r with -ths of the velocity with which the earth advances from E. Therefore Saturn's motion, as observed from the earth, is the same as if he were retrograding with ~ths of the earth's velocity. If, tben, he were at the same distance from the earth as thé sun is, he would appear to pass daily over an arc equal to -~ths of the arc passed over daily by the sun, since the sun's apparent motion is due to the ~A(~6 of the earth's motion. Now the sun passes daily over an arc of about 59' 8'~ Thus Saturn; if he were at the sun's distance, would paas over nearly 40~ 0~ daily. But Satnrn actually passes over 4' 43", or about ~-tbs thé angle E s E' and thé angle of jncHnation of B'r' to s p. Thua the proportion that B A. be:u's to A B' can be df'termined.

The arc passed over daily by the sun is of 3600 approximately.


of thé arc he would pass over if he were at thé same distance as t.he sun from the earth. Hence Lis distance from the earth when in opposition must be greater than thé sun's distance from the earth in the proportion of 17 2 that is, EP is 8~ times as great as s E and therefore s p is 9~ times as great as s E.

Having thus ascertained Saturn's distance approximately, another figure may be constructed (as ng. 3, Plate IV.) in the same manner, in which thé orbits of Saturn and the earth are more correctly proportioned, and a new triangle A D E' may be drawn, in wbich BA, instead of being at right angles to sr, is parallel to the tangent at p'. The proportion that D A bears to AE'in this triangle will more correctly represent thé proportion that Saturn's velocity bears to the velocity of the earth than the corresponding proportion in the original triangle. Thence we can arrive at a new and more exact determination of Saturn's distance. This might be again applied to correct the triangle A D E'; but the repetition of this approximative process would be useless after a second or third construction, since thé errors of observation, and tbose due to the supposition of circular orbits, are far more important than thé corrections that would be obtained from a fourth or fifth construction.

Having determined the proportion that the distance of Saturn from the sun, and his velocity in his orbit, bear to the distance and velocity respectively of the earth, Saturn's period follows at once. Thé path he describes in completing one revolution round thé sun is 9- times as gréât as the corresponding path of the earth, while his velocity is only -ths of the earth's velocity therefore the time he occupies in completing a revolution the corresponding time occupied by the earth (that is, ayear) as- x 1, or as 29~- I, veiy nearly. Thus Saturn's year contains about 29~- of our years.

Soon after passing his stationary point, Saturn arrives at another important position. When in opposition, he passes thé meridian at midnight-that is, twelve hours after the sun. After this he souths earlier every night–until, when nearly three months have elapsed, he passes thé meridian six hours after midday in other words, Saturn in opposition was 180" from the sun, but is now


90° from the sun.~ Let ng. 4, Plate II., represent the sun, Saturn, and the earth, in this position at s, p', and E~ respectively. The angle p~E~ is a right angle, and the angle E s E'' very nearly a right angle, E E~ being the arc passed over by the earth in three days less than a quarter of a year. Now P~E~ is a tangent to the circle E E~E~, since it is at right angles to s E~. Hence the earth when at E~ is moving directly from Saturn at p~, and the earth's motion therefore produces no modifying effect whatever upon Saturn's apparent motions on the celestial sphere these are due to Saturn's own motion only. It is easily seen that, under these circumstances., Saturn's motion, viewed from the earth at E~ is exactly the same in amount as it would appear if viewed from the sun at s. For though E~ is less than SP~ and Saturn's path at p~ not inclined at a right angle to E~j/ as it is to s p~j yet the two errors introduced by these causes act in opposite ways, and, being exactly equal, destroy each other. For if Saturn were viewed from s at a distance E~p~ his motion would be greater than it would appear at a distance s p~ in the proportion of s P' to ~p~ and again, if Saturn's motion were inclined to s p at the angle in which it is inclined to E p\ that motion would appear ~as than it would if at right angles to s p', in the proportion of E~ to s p~f hence Saturn's actual motion, when at pl, is exactly the same in amount, whether viewed from E~ or from s. Now it is found that Saturn's apparent daily motion at this time is slightly greater than 2'. His daily motion about the sun is therefore also slightly in excess of 2~ so that he completes his orbit about the sun in rather less than 360 x 30 or 10,800 days.t

Owing to a cause presently to be explained, Saturn does not in his progressive path exactly retrace his former retrograde path on the celestial sphere. In thé instance selected as an illustration of bis movements, his advancing arc lies at first slightly to the south of his former retrograde patb (see Plate II.) but in about four months and a baïf from opposition he returhs almost to the exact 'When thus situated, a planet is sa~d to be in quartile, or ~cf~c to the sun. t The sine of the angle B~F~ is the ratio in this case but the angle B'p~ is tho complement of the angle R~s, and is therefore equnl to thé a.ngle E~sp', and thé sine of E's P' is equal to the ratio of E~ to s F'.

The true period is 10,759~ days.


place he had occupied when in opposition (his advancing arc afterwards lying to the north of his former retrograde arc). In. 6g. 4, Plate IV., let p, E be the positions of Saturn and the earth respectively, when Saturn is in opposition p", E" their respective positions four months and a half afterwards then, since Saturn is seen from thé earth at E" in the same direction as when he was in opposition to the sun (neglecting his northerly deviation, which corresponds to a very slight élévation above the plane of the paper on which the figure is drawn), K~ must be parallel to E P. Now, since E E" is the arc passed over by thé earth in four months and a half, ESE" is an angle of about 135°; thus the point E' is known. We have then only to measure the arcs E E'E~ and rP" passed over by the earth and Saturn, in the same time, to determine their relative rates of motion. The result confirms those already obtained. It may be mentioned that this method is independent of the two first, for it is not necessary (in applying it to determine Saturn's velocity) that sp should be even approximately known. Ail that is required to be known is the fact that Saturn's orbit is large compared with the earth's; this being the case, it is easily seen that the arc PP~ does not differ greatly from SA, thé perpendicular on E~p~. Having determined Satur n's velocity, his distance may be determined, as before, from his rate of motion in opposition. The construction may then be repeated, using this result to represent s p more correctly. In this way the ratio of Saturn's velocity to the earth's may be obtained with greater exactness than by the two former methods for, in the first, it is necessary that thé angle between E~ and E P should be very accurately measured, a slight error in this measurement having an important effect in vitiating the construction or calculation for determining Saturn's velocity. In the second method, Saturn's daily motion is too small to be accurately measured, except by very delicate and trustworthy instruments, very skillfully used. His rate of motion is also increasing each day, when he is in quartile after opposition, and the determination of the exact instant in which he assumes this aspect is not very easy. The third method, on the other hand, is founded on an observation of the simplest nature, and thé arcs E E~ and r p~ may be easily measured or calculated.


The results, however, of the first few months' observations of thé distant stranger could, of course, be viewed only as rough approximations, to be corrected as time enabled the astronomer to apply more exact and trustworthy methods of investigation. When a year had passed from the time at which Saturn was in opposition, the celestial sphère had apparently made a complete revolution round the earth, so tbat each star rose, culminated, and set at the same hours at the end as at the beginning of that interval. But Saturn had been slowly advancing in his orbit during that period-that is, he had been moving from west to east; and since the apparent annual revolution of the celestial sphère (like its apparent daily motion) is from east to west, Saturn had not yet reacbed opposition when thé year was completed, but was to be found at midnigbt somewhat to the east of the meridian. Twelve days and three quarters elapse before he is in opposition, or has completed a synodical revolution, as it is termed, about the earth. If the exact moments at which Saturn was in opposition, or the beginning and end of a complete synodical revolution, had been accurately noted, his period could have been at once determined, on the supposition, at least, that both Saturn and thé earth move in uniform circular orbits. It is not, however, probable that the ancient astronomers could accurately détermine the moment at which a planet arrived at opposition-an operation of some difficulty. After a few years, however, Saturn's average synodical

y

period was no doubt determined with considerable accuracy. As already mentioned, this period exceeds a year by twelve days and three quarters. Let us consider how this result maybe applied to détermine Saturn's period of revolution in bis orbit, or his sidereal period.

Let s (fig. 1, Plate V.) be thé sun, E,p the positions of the earth and Saturn in their orbits when Saturn is in opposition at thé beginning- of a synodical period, E~, r' their respective positions when Saturn is next in opposition-that is, at the end of thé synodical period. Thus SEP and s~E'P~ are straight line.; the arc r r' is passed over by Saturn in a year, twelve days, and about eighteen bours, or in rather more than 378 days and dnring this time the earth bas performed a complete révolution, and in addition




thé arc Ei~. Thus thé earth bas passed over thé arc EE~ in 12~ days. Hence, since Saturn and the earth pass over thé arcs p i~ and EE'' in 378 and 12~ days respectively; and since, further, thé arc p p~ bears the same proportion to Saturn's complete orbit that the arc E E~ does to the earth's orbit; the times in which Saturn and the earth perform their complete orbits are to each other in the proportion of 378 to 12~–that is, of 1512 to 51. But thé earth performs her complete orbit in a year; hence Saturn's period is -L~-}-s- years, or rather more than 29~ years.

From careful observations of each return of the planet to opposition, Saturn's synodical period became still more accurately ascertained, and thus his sidereal period was more correctly determined. This period is 10759-21. {)7106 days. When this interval had elapsed from the time of bis first discovery, Saturn had completed a revolution about the sun. It is not, however, so simple a matter as it might at first sigbt appear to determine frorn Saturn's position on the celestial sphère the exact instant at which a sidereal period, commencing at any given moment, is completed. In a sidereal period Saturn completes very nearly 28t synodical révolutions thus Saturn is in ultogether different aspects with respect to thé sun at the beginning and at the end of such a period. For instance, if Saturn is in opposition at the commencement, he is very near conjunction at tbe end of a sidereal revolution, and is therefore not visible. On the other hand, if he is in quadrature p?~<?6c~wy opposition at the commencement, he is very near quadrature/o~c'~m~ opposition at the end of a sidereal period, and vice ~'s~. Now it follows, from what bas been already shown, that from conjunction to opposition Saturn appears in advance of his true position in his orbit, whereas from opposition to conjunction he is behind his true place. Hence, if Saturn is in quadrature preceding opposition, or apparently in advance of bis true position, at thé &6~?T/7M~/ of a sidereal period, then, at the 6?~ (when, of course, his true position is the same as at the beginning), he appears not to have Thé mim'bpr of synod!ca.l révolutions in a s!dere:d period is obtaincd by dividing 107o9-2197106 by 378-090: it is therefore 28-457 very nearly.

t That is, lus position in his orbit as it would appoa.r to un eye placcd n.t tho sun's centre; or, as it is tenned, his hplioccntric position.


reached his t.rue place, still less thé place he appeared to occupy at the commencement of the period. And in whatever aspect we suppose Saturn to be at the beginning of his sidereal period, the same difficulty presents itself. From the knowledge of Saturn's period and distance already obtained, the astronomer could correct the discrepancies due to this cause, and, if necessary, apply the period thus deduced (which would be more nearly correct tban his former results) to obtain a more accurate approximation. These results could be still further corrected by comparing the results obtained when different epochs are assumed from which the sidereal periods are supposed to commence and when Saturn had completed several complete revolutions about the sun from thé time of his nrst discovery, there can be little doubt that the length of his sidereal period had been very accurately determined by astronomers.

Sir John Herschel bas shown in his ~Outlines of Astronomy' tbat the distance of a superior planet whose period is known may be determined by observing its motion during a single day when in opposition. In the case of Saturn, however, this method would not be more exact than those already indicated, since Saturn's motion when in opposition is very slow,* and a very small error in thé determination of thé arc he daily traverses at this time would altogether vitiate the result of calculation or construction founded upon such determination. The following process is more trustworthy

Let the time in which Saturn passes from opposition to his stationary point, and the arc on the celestial sphere passed over by him in that time, be accurately noted. Then, knowing Saturn's When Saturn is near opposition he passes over a space on thé celestial sphère equ~ to the mean diameter of the moon's dise in a.bout 5~ days. It may bc mentioned, however, that this ia a much smaller space than might be supposed. The brilliancy of the moon deceives the unaided eye, and the impressicn is conveyed that the moon covers a larger space on the celestial sphere than it actually does, Thus the space between two neighbouring stars of the three (nearly equidistant) forming Orion's belt would be considered by the unaided eye as somewhat less than the moon's apparent diameter, which yet it exceeds in the proportion of three to one. The distance between the two stars Hizar and Alcor (the middle star in the tail of the greater Bear), which appearao close to thé naked eye, is equal to the moon's apparent semi. diameter.


period, we know also the arc of bis orbit he actually passes over in that time, on the supposition, at least, that his orbit is circular and his motion uniform; and we know, also, the arc of her orbit passed over by the earth in the same time. We can proceed, then, to the following construction

Draw the circle E"E E~ (hg. 2, Plate V.) to represent the earth's orbit about s, the Sun. Let s E K be the line on which the earth, Saturn, and the Sun are situated when Satura is in opposition. Let the angles KSI/ and K SEI be the angles swept out about the Sun by Satum and the earth, respectively, during the time in which Satum passes from opposition to his stationary point thus, when Saturn is stationary, the earth is at E~, and Saturn somewhere in the Une s i/. Again, through E' draw E~K~ inclined to s x in an angle containing as many degrees, minutes, and seconds, as the arc on the celestial sphere passed over by Saturn in the interval of time we are considering thus E'K~ is the line of sight from the earth to Saturn when he is stationary; so that at this time he must be somewhere in thé line E~:K/. But we have already seen that at thé same moment he is somewhere in the line s L'. Hence the point r~ in which the two lines E~K'' and s L' intersect, is Saturn's actual position at this moment. We bave, then, oniy to compare the lengths of the lines s P~ and s E by simple measurement, to determine the relation between the distances of Saturn and the earth from the sun or we can obtain the required relation by a very simple trigonometrical calculation.*

Instead of determining the interval of time and the arc passed over from the moment of opposition to the following station (a matter of some difficulty), the interval and arc between the station preceding and the station following opposition may be noted. If E~ and E~ be the positions of the earth at those epochs respectively, s r, bisecting the angle E~s E~, is the line of opposition. If, then, s r'i/ and s P~L~ are each inclined to s p in an angle equal to half that swept out by Saturn in his orbit, in the interval between Thus :-in thé triangle SE'p~ thé side 8B' is known; the angle B~sp', being thé difference of two known angles (E'sK and P~SK) is known and so aiso is the angle E'r~a, since it is thé sum of two known angles (P's K and the angle betweon the Unes E'J</ and s x) hence we can determine the remaining sides and angles of the triangle s E'p', and s p' becomes known.

C


the two stations, while E~'K~ and E~p~K~ are each inclined to s p in an angle corresponding to half the arc passed over by Saturn on the celestial sphère in the same interval, p' and p~ are both points on Saturn's orbit and the measurement of s r' or sr~, or the trigonometrical calculation of the length of either as compared to the length of SE, enables us to determine as before the relation between the distances of Saturn and the earth from the sun.

If thé orbits of Saturn and the earth were circular and in one plane, tbis method and those before described would be strictly exact. The results obtained would be affected only by errors of observation, of construction, or of calculation. To such errors, at nrst, the astronomers of old must have been inclined to attribute the discrepancies which appeared, not only between the results obtained by different methods, but between results obtained by the same method applied at different times. If the first three methods described be so applied, Saturn appears to be traversing an orbit at one time larger, at another smaller, than the orbit resulting as the average of a large number of observations while his velocity is less in the larger orbit, and greater in the smaller, than his mean velocity.. If, on the other hand, Saturn's sidereal period be assumed as the basis of calculation, there still appears a discrepancy in the magnitudes of the orbits determined at different epochs, but the velocities thence determined appear greater in the larger, and less in the smaller orbits. The ellipticity of Saturn's orbit and the variations in his velocity, to which thèse discrepancies are due, will be considered furth er on. In the case of Saturn, the resultin g irregularities, though not so marked as those of the Moon Mars, and Mercury, must have been sufficiently obvious to the carefui observer, even of old times, and their periodicity could hardly fail to attract his notice. Indeed, there are reasons for supposing that the early Chaldaean astronomers detected these irregularities in the planetary movements, and assigned them to their true cause.* Anotber circumstance in which Saturn's orbit differs from the uniform orbit we have imagined-an irregularity undoubtedly detected in very early times-remains to be considered. See Note A, Appendix.


If the orbits of Saturn and thé earth lay in one plane, i.t is evident that the line of sight from the earth to Saturn would always lie in this plane, and thus, whatever effect the motion of the earth might have on Saturn's apparent motions, hewouldaiways be seen on the circle in which this plane meets the celestial sphere; in other words, Saturn would always be seen on the ecliptic. Hence, in retrograding, he would appear to retrace part of his former progressive path and vice ~'s< His actual apparent movements are not of tbis nature. He follows a looped and twisted course, as shown in Plates II. and III. his retrogressive path lying sometimes above and sometimes below bis progressive patb, and vice ver8â. It is clear, then, that Saturn's orbit cannot lie in the same plane as thé earth's orbit.

The inclination of the plane of Saturne orbit to the ecliptic is small. Since both planes pass through the Sun's centre their line of intersection passes also through that point. This line is called the line of Saturn's nodes and when, in travelling along his orbit, he reaches this line he is said to be in C6 node. One half of his orbit lies to the north,* the other balf to the south of the ecliptic. When he is passing from the southern to the northern side of thé ecliptic he is said to be in hie ascending node and in. his <~esce~~o<~6 when he is passing from the northern to the southern side of the ecliptic.

Thus in fig. 3, Plate V., let Nr'r~ represent the northern half of Saturn's orbit (viewed in perspective), ~E ~E~ the earth's orbit, and Npjp~~the projection of Saturn's orbit on thé plane of the earth's orbit. Let N s N'' be the line of Saturn's nodes on this plane, and let s r' be at right angles to N s N', so tbat, when at r', Saturn is at his greatest distance from the ecliptic on the northern side. Then the angle P~Sj/ is the angle of inclination of the plane of Saturn's orbit to the ecliptic N is Saturn's ascending node, N' his descending node.

The ancient astronomers determined the positions of the nodes of the planets, and the inclinations of the planetary orbits to the ecliptic, with tolerable accuracy. The exact determination of these That is, on the same side of the ecliptic as the north pole of the earth. Strictly spe~king, the terms north, south, east, and west refer to the equinoctial oni~. c 2


éléments is not easy. Let us consider the methods applicable in the case of Saturn.

When Saturn is at a node, at N or N', it is clear that, wherever the earth may be, the line of sight to Saturn lies in the plane of the ecliptic. It is equally clear that when Saturn is at any other part of his orbit he is not seen on the ecliptic, for the line of sight from thé earth no longer coincides with thé plane of the ecliptic. Thus, if we can determine the exact moment at which Saturn appears to cross the ecliptic, we know that at that moment he is in a node. It does not, however, necessarily follow that the point at which Saturn appears to cross the ecliptic indicates the position of the node. Saturn, as we hâve already seen, may appear bebind, or in advance of bis true place, at the moment of passing his node. If the correction due to this cause were made, however, thé position of Saturn's node would become known from such an observation.

If the plane of Saturn's orbit were inclined at a considerable angle to the plane of the ecliptic, this method would be as accurate as it is simple. But the angle is so small in the case of Saturn (as of nearly all the planets) that it is difficult to determine the exact point at which he passes the ecliptic. For several degrees on either side of this point his distance from the ecliptic is scarcely appreciable. It must further be remembered that the determination of the exact position of the ecliptic itself upon the celestial sphere is a problem of no inconsiderable difficulty, and a very slight error in its solution would introduce a very important error in thé determination of the nodes of a planet whose orbital plane is inclined' at a very small angle to the ecliptic.

If it were not for the difficulty of determining the exact moment at which Saturn crosses the ecliptic, his period could be determined with far greater accuracy by successive observations of bis nodal passages than by any other method. For, in the first place, the interval between successive passages of his ascending node (or of his descending node) is constant, being in fact no other tban his sidereal period.* In the second place, the observation to be made Strictly speaking, this interval, which may be called Saturn's nodical penod, is neither constant nor equal to lus sidereal period but both errors must bo measurcd, not by days and honrs, but by minutes and seconds.


is simple, and the position of the earth in her orbit exercises no modifying influence on the resuit as in other methods. Let us next consider how the angle in which the plane of Saturn's orbit is inclined to the plane of the ecliptic may be determined. If it were not very small, all that would be necessary would be to observe the angle between Saturn's path and the ecliptic at the time of either nodal passage it is plain that this angle, Q~N or RN~, is the same as the angle p~sp', whose value is required. This method is inapplicable in the actual case, but a very simple method may still be employed. After passing a node Saturn moves farther and fartber from the ecliptic, through about 90° of his apparent path, and attaining here a maximum distance from the ecliptic, approacbes nearer and nearer to it, till he is again upon the ecliptic, or at a node. Now, if the observer were placed at the sun's centre these motions of separation and of approach would plainly be continuons, since Saturn and the earth would each appear to describe a great circle on the celestial sphere. Further, it is perfectly clear that the arc measuring Saturn's distance from the ecliptic, when he is fartbest from that great circle, contains as many degress, minutes, and seconds, as the angle between the planes in which Saturn and the earth are moving. If, then, the supposed spectator in the sun were to measure tbis arc on the celestial sphere, he would know the angle we are seeking. But to the actual observer'on earth Saturne apparent motions of separation from and approach towards the ecliptic are not continous or rather, though continuons, we cannot separate them into two periods, one of separation, the other of approach. Althougb, on the whole, Saturn's distance from the ecliptic appears to be increasing, tbrough about 90° of bis path from a node, his apparent path on the celestial sphere is twisted into loops of varying sbape, in his motion along which he moves alternately from and towards the ecliptic. His return to the ecliptic is effected in the same manner. The reason may easily be seen if Saturn is in any other part of his orbit except either node, thé line of sight from the observer on earth only lies in the plane of Saturn's orbit when the earth herself is in that plane; in other words, Saturn is only seen on his true or heliocentric path when the earth is on the line


of nodes, either at or n'. lu moving from through E to the earth is south of the plane of Saturne orbit, and Saturn tberefore appears north of his true path similarly, while the earth moves from ?~/ through E~ to n, Saturn appears south of his true place. Hence, if the earth is at any other part of her orbit but n or n' when Saturn attains his greatest distance from the ecliptic, a corresponding correction must be made on this account. A further slight correction is necessary on account of the difference between Saturn's distance from the earth at the moment of observation and his mean distance from the sun. The inclination of Saturn's orbit to the ecliptic may, however, be determined very approximately without attending to the first of these corrections. For when Saturn is describing the part p p"p~ of his orbit, his distance from the ecliptic varies very slowly. But during this time the earth describes ratber more than one complete revolution, and therefore passes both the points n and n' of her orbit. If the distance of Satum from the ecliptic be measured when the earth is at either of these points, and increased in the proportion of the distances of the earth and sun from Saturn at tbis time, then the required angle contains as many degrees, minutes, and seconds, as the arc thus determined, very approximately. The nearer Saturn is to the point F~, or to the opposite point of his orbit, when the earth is passing n or n', the more exact will be the determination of the angle required. In thé course of two or three revolutions of Saturn, one observation at least that is perfectly trustworthy may be effected.

It is found in this manner that Saturn's orbit is inclined to that of the earth at an angle of about 2~°. Owing to the causes mentioned in the preceding paragraph, his greatest departure from the ecliptic exceeds this angle by about a quarter of a degree. The arc of the celestial sphere, tben, that measures Saturn's greatest possible departure from the ecliptic is rather more than five times as great as the moon's mean apparent semi-diameter. The distance between the two stars commonly known as the Pointers is almost exactly double the arc we are considering.

Owing to causes which will be mentioned further on, both That is, a (Dubhe) and Ursse majoris.


the position of Saturn's line of nodes and the indination of his orbit to thé ecliptic are variable. The annual variation in the inclination is always very small; for long intervals it operates to increase, and for corresponding intervals to diminish, the angle of inclination so that this angle varies in an oseillatory manner, the period of oscillation being very great, and thé total amount of variation either way being very small. The line of nodes move. sometimes from east to west, sometimes from west to east, but the westerly motion prevails, sotbaton the whole thé line of nodes revolves in a retrograde direction, but so slowly that a complete revolution is not effected in less than 66,000 ye~

The looped nature of Saturne apparent path on the celestial sphere is due to the inclination of the plane of Saturn's orbit to the plane of the ecliptic. The varying forms assumed by the loop correspond to Saturn's varying positions in bis orbit. Wben he is near a node his path is twisted, but without a loop for instance, when he is near his ascending node his patb is as shown in Plate II. (where the path crosses the ecliptic). As be moves on in his orbit his path becomes looped, the loop lying to the north of his mean pathf in the case ~e are considering (tbat is, after thé passage of the ascending node), or on the side f~he.t from thé ecliptic. The loop gradually developes at first, the progressive path intersects the former retrograde path; in each successive loop the point of intersection falls farther and farther from the stationary point following opposition, till it reaches the stationary pI~pLding opposition-, after this, for several successive loops the point of intersection lies on the former progressive path, being hJway between the stationary points when Saturn reaches bis greatest distance from the ecliptic. From this point to the tables of the planetary elements the longitude ~L~~r~:

described as subject to an annual decrease of 1~J"v~. This is to be understood as re-

~r~ of the ascending node. Since the pre-

cession of the equinoxes is 50'1 yearly (in longitude), tho longitude of Saturn's

ascending node inereases annually by more than half Il minute of arc.

t That is, his Iceliocent~~ic path j in the maps forming Plates II. and 111., Saturn's

heliocentrie path would be representod by straight lines dmwn in the direction indi-

cated by the general direction of his geocentric path, in such a manner that Saturns

about equal. Seo the dotted linea in figures 4 and 6, Plate V.


descending node the loops undergo similar changes in a reverse order; the point of intersection passes to the station following opposition thence along the retrograde path to the station pre~ceding opposition (so that the opening between the loop and path, which before was towards the east, now lies towards the west) and finally, near thé descending node, the path, as at the ascending node, is twisted without a loop. In passing from his descending to his ascending node, Saturn's path is similarly varied, the loop being now south of the ecliptic, or still on thé side of Saturn's mean path farthest from the ecliptic.

The causes of these phenomena will be made sufficiently apparent if we consider Saturn's motion during a synodical revolution in each of two extreme cases-viz., first, when he is at a node, and secondly, when he is at his greatest distance from the ecliptic.

Suppose, then, first, that during a synodical revolution Saturn passes from Q to Q~ (fig. 3, Plate V.), and is in opposition when at his ascending node N. During this time the earth moves from a point slightly to the west of through rather more than one complete révolution, to a point slightly to the east of As the earth passes the point n' Saturn passes from the northern to the southern side of his heliocentric path. He remains to the south of that path as the earth moves from n' through E' to n. When the earth is at~ Saturn (in opposition at his ascending node) again crosses his heliocentric path and also the ecliptic, passing to the north of both these great circles of the'celestial sphere. While the earth moves from n through E to n' Saturn remains to the north of his heliocentric path, passing to the south as the earth passes the point n'.

If, then, we draw the line EN (fig. 4, Plate V.) to represent part of the ecliptic, and the dotted line SN s', inclined at an angle of 2~ to E E', to represent part of Saturn's heliocentric path, and combine the results of the preceding paragraph with thé knowledge already obtained of Saturn's progressions and retrogressions, it is easily seen that Saturn's apparent path on the celestial sphere, during the synodical revolution considered, is of


the form Q~N~; N and being the points at wbich he appears to cross his heliocentric path s 8~

Next let us consider the nature of Saturn's apparent path when he is at bis greatest distance from the ecliptic. Suppose that during a synodical revolution he passes from r to P~ (fig. 3, Plate V.), and is in opposition when at his greatest distance from the ecliptic at During this time the earth moves from a point slightly to the west of E~ through rather more than a complete revolution to a point slightly to the east of While the earth is moving to she is on the northern side of the plane of Saturn's orbit, and Satum is on the southern side of bis heliocentric path. He passes to the northern side as the earth passes the point n remains on the northern side of his heliocentric path as the earth moves~ from 7. through E to (attaining bis greatest departure from that path when in opposition at ~); crosses to the southern side as the earth passes the pointa; and remains on that side throughout the remainder of the synodical revolution ~e are considering. r

If, then, we draw EE~ ng. 5, Plate V., to represent part of the ecliptic, and the dotted line s n' 7~ (parallel to E E' and at a distance from that line corresponding to an arc of 2~ degrees on thé celestial sphere) to represent Saturn's heliocentric path, it is plain that Saturn's path during the synodical period is of the form p 7~ ~p~ and being the points at which he appears to cross his heliocentric path.f

There is no difficulty in applying similar methods to determine the form of Saturn's apparent path when he is in any other part of bis orbit. It will be found to vary in the manner While traversing parts of this path near Q ~d Saturn is not visible from thé earth being near conjunetion. If he were visible in thèse parts of his orbit, it would found tl~t at n and his departure from the ecliptic is greater than at any other moment during thé synodical revolution considered. These points are therefore and~ to indicate their correspondence with the points p and in the synodical revolution next considered.

t. While traversing parts of thé path ncar r and Saturn is not visible from the earth, being near conjunetion if he were visible in these parts of his orbit, it would be found that at p and the positions he occupies Menthe earth is at E', he attains his greatest southern departure from his heliocentric path-or approaches nearest to thé ecliptie-in the synodical revolution considered.


described above. The followmg consideration may assist the student:–

Since Saturn is seen on bis heliocentric path whenever the earth is at n or n', his geocentric path crosses his heliocentric path once in every six months; now, Saturn completes a synodical revolution in a period exceeding twelve months by twelve days and three quarters thus the points of intersection of his geocentric and heliocentric paths fall successively farther and farther back, in each successive synodical loop, by the space Saturn traverses in 6~ days they therefore occupy, successively, every part of Saturn's synodical loops.



CHAPTER II.

FALSE SYSTEMS–MODERN ASTRONOMY–ELEMENTS OF SATDRN'S ELLIPTIC ORBIT.

BEFORE turning to the consideration of the methods and discoveries of modern astronomy, a few words on the system which explained Saturn's motions (in common with those of the other planets) on the supposition that the earth is the centre of the universe, will not be out of place. This system, and the fanciful and superstitious dreams of the middle ages, may be considered as occupying a place midway between the simple systems and intelligent inquiries of the Chaldaean astronomers, on the one hand, and the analyses and discoveries of modern times on the other.

The difficulties connected with the Ptolemaic system are not due so much to the inherent error of the system itself, as to the fanciful hypotheses with which thé originators of the system perplexed themselves. Ail the varieties of the planetary motions, except a few irregularities only to be detected by the most exact instrumental observation, may be as exactly explained on the supposition that the earth is the centre of the system as on the true theory, and with almost equal simplicity. But the Epicyclians set themselves a problem of far greater complexity. They sought to explain the apparent motions of the heavenly bodies, not merely on thé supposition that the earth is the centre of the system, but with the additional hypotheses that aU the members of the system move in circular orbits and with uniform velocities. Bodies terrestrial, they argued, are gross, corrupt, and imperfect-therefore they move in imperfect orbits, with varying velocities bodies celestial are sublime, incorrupt, and perfect-therefore they move in perfect orbits with uniform velocities; the circle is the only perfect


figure-therefore the heavenly bodies move in circles; but the supposition of uniform motion in simple circular orbits is insufficient to account for the apparent motions of the heavenly bodies-therefore those motions must be explained by properly combining two or more sets of circular and uniform movements. Such was the problem they set tbemselves in what manner they solved it will appear by an illustration drawn from the motions of Saturn. Let E (fig. ï, Plate VI.) be the eartb, c c/c~ a circle a'bout E as centre. Then, clearly, Saturn's progressive and retrograde motions cannot possibly be explained by supposing him to move uniformly in the circle c c'c". Suppose, however, that Pp r'p~ is a smaller circle, whose centrée is on the circle c c'c"; and that while Saturn moves with uniform velocity round the circle rppy, thé centre of this circle moves uniformly round the circle c c/c~. Then it is clear that if Satum's velocity in the smaller circle is greater than the velocity with which the centre of that circle moves round the larger circle, bis apparent motion will be rétrograde when he is at or near and furtber, that by assigning suitable dimensions to the two circles, and a proper ratio between the velocities considered, Saturn's period of rétrocession and the length of his retrograde arc may be readily explained.~

We have seen that Saturn's distance from the earth, at opposition, is variable. These variations may be explained with tolerable accuracy by supposing that the earth occupies an eccentric position within the circle c c'c~ as at E~.

Saturn's looped and twisted path may also be easily explained. We have onlyto suppose the plane of the circle ppp' inclined at a small angle to that of the circle c cV or, instead of this, we may suppose both circles to lie in one plane which oscillates through a small angle about a fixed line through the earth at E'. Srnaller irregularities may be accounted for by supposing that Pp P'p' isnot~s' orbit, but the path of the centre of a smaller circle, s s s~, along wbose circumference Saturn moves uniformly. For this purpose the radius of the smaller circle rn~st bear to the radius of the larger circle the proportion that the radius of the earth's orbit t bears to that of Saturn again, Saturn must revolve once in a year round the smaller circle, whoso centre must revolve once in a Saturnian year round the earth.


Again, we may suppose that the circle c c/c~ is not the path of the ce~6 ofthe circle p~ r~ but of a point near the centre in other words, that the circle Pp P'p~ is eccentric as well as the circle c c/c~. We may extend this eccentricity to the circle s s s~, or introduce additional variety by supposing any or all of the circles to lie in different or in oscillating planes in fine, by a series of such suppositions, which may be carried on ad M~m, we may account for nearly every irregularity in Saturn's motion with a very close degree of approximation.

To explain how tbese motions were supposed to be impressed and maintained by a system of celestial spheres, and through the complicated effects attributed to their rotations, would be out of place. The whole system, with its

centrics and eccentrics scribbled o'er,

Cycle and epicycle, orb in orb,

bas been long since swept away, and its records merely remain a~ illustrations of perverted ingenuity.

One point, however, connected with the Ptolemaic system of the universe remains to be noticed. If the earth really occupied thé central place in our system, thé actual, and even the relative distances of the various members of that system must have remained for ever unknown. Let us consider, for a moment, how the geometer ascertains the distance of an inaccessible object. To effect this, he observes the directions in which the object is seen from two convenient points, the distance between which he measures. Then, either by geometrical construction, in which thèse relations are represented on a convenient scale, or, more exactly, by trigonometrical calculation, he determines thé distance of the inaccessible object from either point. That this determination may be depended upon, it is necessary, not only tbat the instruments with wbich the requisite data are obtained should be trustworthy, but that the distance between the two points should not bear too small a proportion to the distance of the inaccessible object. For instance, a base line of ten yards, with good instruments, would be sufficient for the determination of distances up to three or four bundred yards but it would obviously be altogether useless to


apply such a base to determine the exact distance of an object two or three miles off. The slightest error in the determination of either of the base angles would make a difference of a mile or two in thé result deduced by construction or calculation. Now the length of the earth's diameter being about one-thirtieth part of the moon's distance from the earth, this distance can be determined with tolerable accuracy from a base line whose extreme points lie on the earth's surface.* But the distances of the other members of our system (including the sun) from the earth are so vast that it would be altogether impossible to determine their actual distances by using any base line on thé earth. To obtain any notion of their relative distances would 'require the utmost perfection and power of modern instruments, and the highest skill of the modern astronomer. Even with these appliances, our ideas of the relative distances of the planets would be as vague and uncertain, if the earth were the centre of our system, as are our present ideas of the relative distances of the fixed stars from the earth.f Nor is there any point in the Epicyclic theory that would enable its supporters to form any conjectures regarding the relative distances of thé planets. It is plain that to an observer placed at E (fi g. 2, Plate VI.) the appearance of a planet revolving uniformly round the circle p p~r~, while the centre of that circle moved uniformly round the circle c (/c~ would be precisely the same as that of a planet revolving uniformlyround the circle pp~)~p~~ while Yet from the most trustworthy modern measurement it appears that the determination of the moon's distance hitherto adopted has been about twenty miles too great. t In the case of thé sun, as in that of the moon, our base line is limited by thé earth's dimensions and since the sun's distance is so vast compared with such a base line, we could expect to obtain no very close approximation to that distance. Accordingly, we find that before the discovery of the telescope the ideas of astronomers on the subject of the sun's distance were of the most vague and indefinite kind; and thé discovery lately made, that the modem détermination of the sun's distance is probably too great by three millions of miles or more, shows that even in the present advanced state of the science of astronomy the problem is no easy one. In the planets Mercury and Venus, however, we have two objecta, which serve, so to speak, as celestial instruments the sun's diac, at thé times of their transits, serving as an index-plate. Observers at different parts of the earth's surface, marking the different indications of this celestial theodolite, calculate thence the solar distance. At favourable parts of his orbit, Mars, though n superior planet, serves the same purpose in a somewhat dînèrent manner, the celestial sphere serving as an index-plate.


ASTROLOGY.

the centre of that circle moved uniformly round the circle c </c~ if the periods of revolution of the two planets and of their orbitcentres were respectively equal.

It appears, then, that if the Epicyclians merely trusted to the results of observation applied on the hypotheses which formed their system, they could have had no accurate notions, even of thé relative distances of the sun and planets from the earth, far less of their actual distances. For anything they could perceive to the contrary, Saturn might (after the moon) be the nearest of the heavenly bodies-Mars, Venus, or Mercury the most distant. Yet we learn that the order of the planetary distances was known to the ancients at a very remote period. In the fanciful scheme ascribed by Philolaus to Pythagoras, in which musical tones were supposed to be produced by the revolution of the spheres bearing the planets, the note assigned to the Satumian sphere was the /M/pû~6, or deepest tone, the note assigned to the moon's sphère thé neate, or highest tone of the celestial harmonies, the spheres of the other heavenly bodies being placed in their just order in tbe scale. It seems probable, therefore, that the Greek astronomers had derived part of their knowledge from nations to whom the true system of the universe was not unknown.

Before turning to the discoveries of modem astronomy, it may not be uninteresting to dwell for a moment on the superstitions fancies of the astrologer. The origin of the system which ascribed an influence on the fates of men and nations to the planetary phenomena is lost in the obscurity of a far antiquity. It was probably connected with the Sabaeanism of the ancient ChaldaBans and Arabians, a form of religious worship derived from a purer system, in which thé stars and planets were not themselves the objects of adoration, but simply regarded as types of the divine attributes. Astrology was gradually formed into a system showing few traces of the religions source from which it had been derived. Its complex and mystical cbaracter marks it as framed rather to deceive and impress the ignorant, than as possessing the confidence of its professors. Thus it became a weapon in the hands of the priesthood of Nineveh and Babylon, a weapon which might serve good or evil purposes, according to the character of him who wielded it,


but which was too often employed to subserve the evil designs of the despotic emperors under whose sway the priestly orders were subdued. It would be out of place to record here, at length, the details of the system itself, or to trace the graduai process by which astrology--deriving its origin from pure and lofty conceptions of the divine power, wisdom, and goodness-fell to the position it bas now so long occupied, and became the tool of cheats and charlatans. It may be mentioned, however, that the idea of physical influences exerted by the planets in their varying positions, bas been entertained by many who fully recognised the absurdity of the so-called astrological systems. Bacon (who was, however, but superficially acquainted with astronomy, and strongly prejudiced against the Copernican system) considered an inquiry into such influences likely to lead to valuable results. Astrology,' he wrote, < is so full of superstition, that scarce anything sound can be discovered in it; though we judge it sbould rather be purged than absolutely rejected.' He then propounded his 'Astrologia Sana,' wbich should contain inquiries into-(i.) the commixture of planetary rays in the different positions of the planets with respect to one another and on the zodiac (ii.) the zenith distances of the planets, or the planetary seasons (iii.) the influences of the planets at their apogées and périgées and (iv.) 'the other accidents of the planets' motions, their accelerations, retardations, courses, stations, retrogradations, distances from the sun, &c. for all these things affect thé rays of the planets, and cause them tô act either weaker or stronger, or in a different manner. The following lines of Chaucer present the gloomy and dismal ideas which astrologers naturally associated with Saturn's dull light and sluggish motions

My dere doughter Venus, quod Saturne, My cours, that bath so wide for to turne, Hath more power than wot any man.

Min is the drenching in the see so wan, Min is the prison in the derke cote,

Min is the strangel and hanging by tbe throte, The murmure, and the cherles rebelling, The groyning, and the prive empoysoning. 'Advuncement of Leaming,' Book iii. Chap. 4.


Another superstition, whose origin is equally obscure with that of astrology-the idea, namely, that the planets exerted influences (each on its respective metal) over the labours of the alchemist-is mentioned by the same poet in the Chanones Yemannes tale. He thus succinctly states the distribution of the metals among the planets-

No satisfactory explanation has.been given, so far as I know, of the distribution indicated above. That the two most valuable metals should be assigned to the sun and moon needs no explanation; tho silvery light of the moon, and thé yellow or red light of the sun whenever it can be viewed by thé naked eye, make the distribution still more appropriate. On a différent principle one can understand w.hy quicksilver should be assigned to Mercury, wbich is so difficult to detect, and whose motions are so rapid. On other principles the association of JMars and iron may bo explained for some resemblance can be imagined between thé colours of thé ruddy planet and of the red oxide of iron, or Raematite or the employment of iron in war might suggest tho association; or, lastly, tho invigorating.and tonieproperties ascribed to medicines containing iron correspond with thé influences attributed to Mars by astrologers. The association of lead with Saturn may be explained on similar principles the protoxide of lead (or Massicot) is of a pale yellow colour, somewhat resembling that of the planet or one may imagine lead assumod as the représentative of thé dull, slow-moving Saturn, from somo such fanciful association of ideas as that expressed by Armado in Love's Labour's Lost, Is not lead a metal heaYy, dull, and slow ?' or, lastly, the association might have been suggested by the chilling and dcieterious effects peculiar to medicines containing lead-still called by doctors Saturnine medicines. Why tin and copper should be assigned respectively to Jupiter and Venus is not very obvious. The connection between the name of thé latter metal and that of the island Cyprus sacred to Venus is noticeable. A singular coincidence may be mentioned -hère :–in the list of metals in Numbers, chapter xxxi, verse 22, we have tho representatives of the sun, the moon, and thé four planets probably known to the Jews atthat time and thèse four, 'thé brass, thé iron, the tin, and thé lead,' are arranged in the order of thé distances from the sun of thé corresponding p!anets. That the word translated brass signifies copper is clear from thé words of Job, ehaptor xxyiii, verse 2, brass is molten out of thé stone.'

1 do vengeaunce, and pleine correction, While I dwell in the signe of thé leon. Min is the ruine of the high halles, The falling of the toures and of the wallea Upon the minour, or the cajpenter I slew Sampson in shaking the piler. Min ben also the maladies colde,

The derke tresons, and thé castes olde My loking is the fader of pestilence."

Sol gold is, and Luna silver we threpe

Mars iren, Mercurie quicksilver we clepe

Saturnus led, and Jupiter is tin,

And Venus coper, by my faderkin.*

D


Let us now turn from the false systems and idle fancies which throve with rankest luxuriance-like fungous growths in darkened nooks–amid the ignorance and superstition of priest-ridden ages, to the awakening of science at the dawn of a new era. The life of Nicolaus Koppernik, or Copernicus–thé restorer if not the discoverer of the true system of the universe-belongs to the latter part of the fifteenth and the beginning of the sixteenth century an age-as bas been well remarked by Humboldt–~ coinciding in a wonderful manner with the age of Columbus, Gama, Magellan the age of great maritime enterprises the awakening of a feeling of religious freedom the development of nobler sentiments of art. During the first years of the sixteenth century Copernicus was engaged at Rome, at Padua, and at Bologna, in discussing with the astronomers of the day the various theories which had been invented to explain the planetary motions. Struck with the complexity of these theories he was led, after trying several hypotheses (probably including the system generally attributed to Tycho Brahe) to the conviction that thé sun is the centre around wbich the planetary scheme revolves. We nnd in this arrangement,' he says, what can be discerned in no other scheme-an admirable symmetry of the universe, an harmonious disposition of the orbits. For who could assign to the lamp of this beautiful temple a better position than the centre, whence alone it can illuminate all parts at once ? Here the sun, as from a kingly throne, sways the family of orbs that circle around him.~ The new system met with fier ce opposition not, at first, from tbe priesthood, but from astronomers. It was not merely that the views put forward were opposed to opinions that bad been held so long this would in any case have been sufficient to rouse a strong feeling of opposition; but the system presented by Copernicus was wanting in simplicity. If he could have done away altogether with the old hypotheses of eccentrics and epicycles, the new system might have been more favourably received. This, however, he was unable to effect. His own observations bad shown him that the apparent planetary motions were too complex to be satisfacCosmos,' vol. ii, part 2, § vii.

t De Reyolutionib~ia Orbium Ccelcstium,' lib. i. cap. 10.


torily explained by any hypothesis of simple cireular orbits. He therefore retained in a modified form parts of the cumbrous systems of his predecessors.

Nearly three-quarters of a century after the publication of tbe celebrated work of Copernicus, Kepler, who had become in early youth an ardent couvert to the new doctrines, was able to remove from the scheme of the universe the last traces of the Ptolemaic hypotheses. Tycho Brahe, strenuously opposed to the views of Copernicus, had erected an observatory at Uraniberg, where he had traced the paths of tbe planets on the celestial sphere with instruments more powerful and accurate than those employed by Copernicus. Kepler availed himself of a series of observations of the planet Mars made by Tycho Brahe with these instruments, and applied them to an investigation of the Copernican system. It was not his object to overthrow the doctrines of circular motions and uniform velocities, but to determine by what combination of eccentrics and epicycles the actual movements of the planets could be explained. Mars was in every respect the best selection he could have made. This planet is the nearest of the superior planets, and therefore its motions on the celestial sphere are swifter than those of Jupiter and Saturn; its orbit is also very eccentric on both accounts the true combination of epicyclic and eccentric motions should be more easily detected in the case of Mars than of any other planet.

Kepler calculated the motions that would result from such combinations with wonderful patience and accuracy, compared them with the actual motions of thé planet, and was compelled to rej ect successively nineteen different hypotheses. Having exbausted the combinations of circular and uniform motion, he began at length to inquire whether the orbit of Mars, obviously oval, might not be an ellipse; and whether his velocity, obviously variable, might not–on thé supposition of an elliptic orbit-be found to vary by some simple law. At this new problem he worked with unnaggmg energy and patience, trying and rejecting Mars in aphelion is more than 162,500,000 miles, in perihelion little more than 126 600,000 miles from thé sun the diffcrence of these distances is greater than onefourth of thé carth's mean distance from thé sun. Sec fig. 3, Plate VI. D 2


numerous hypotbeses. Finally, his labours were rewarded by the discovery of the true laws of planetary motion, constituting the two first of the laws of Kepler.' They are these

1. Every planet moves in an elliptical orbit, in one focus of wbich thé sun is situate.

2. The line drawn from the sun to a planet (or the radius-vector of the planet) sweeps over equal areas in equal times.

From Saturn's motions in bis orbit we can draw an illustration of these two laws. Let s, ng. 3, Plate VI., be the sun, E E'E~' the orbit of the earth, s s~ Saturn's orbit. Thèse orbits are both ellipses, but in the figure they are represented by circles, because (on the scale of the figure) the difference of the axes of Saturn's ellipse would be very nearly, the difference of the axes of the earth's orbit altogether imperceptible even on measurement. The eccentricity of the earth's orbit is also too small to be noted in the figure;. the eccentricity of Saturn's orbit will be at once observed. At e the earth is in perihelion E, E', E~ and E"' are the positions of the earth at the winter solstice, at the vernal equinox, at the summer solstice, and at the autumnal equinox, respectively: at s Saturn is in perihelion, at he is in aphelion, and s s" bears to s s a proportion rather greater than that of ten to nine. More exactly-the radius of the circle E E~E"' being taken as 1, the radius of the circle 8 N is 9'5388ÔO s s" is 10'072a33 and s sis 9-005167. The two orbits, as already stated, lie in different planes, the line of whose intersection passes through thé sun: in ourngureNSN'is this line, N being Saturn's ascending node thus if the earth's orbit be supposed to lie in the plane of the paper, thé part N of Saturn's orbit lies above thé paper, and the part N~N below. The lines k k' and indicate the distances from the plane of the ecliptic of the points s' and s~, at which Saturn attains his greatest departure from that plane, f It is hardly necessary to remark that the eccentricity may be very observable in an ellipse, even when the outline differs inappreciably from a circle tho difference of thé semi-axes of such an ellipse bears a very small ratio to the distance of either focus from the centre-the ratio, namely, of thé versed sine to the sine of a very amall angle. For instance, the distance of the sun from tho centre of Saturn's orbit is no less than 48,917,000 miles, while thé difference of the semi-axes of Saturn's orbit is only 137,000 mites, or less than ~yth part of tho former difference.

t The orbits of the planets Mcrcury, Venus, Mars, and Jupiter, are respectively


By thé first law of Kepler, then, we leam that Saturn's orbit 8 s~~W~ is an ellipse, and that the sun is situated at s, one of the indicated by the circles m m', v v~, M and J j~, the points m, v, M, and J being thf) perihelia of those orbits. The Une 8 S in each orbit is the line of nodes, S being tho rising node. In thé c~se of Jupiter the greatest departures from thé plane of thé ecliptic are indicated by the lines i if and~y; in the other orbits the corresponding departures are too small to be thus represented. The angles of inclination of thA orbits ofMars, Venus, and Mercury, to the ecliptic, are, respectively, 1° 61' 5~6, 3° 23' 33~-2, and 7° 0' 25~-0. The corresponding angle in the case of Jupiter is 1° 18' 36"'7. It will be observed that the orbits of Mars and Mereury are more eccentric than those of thé other members of the system. The dotted ring A AW marks the probable extent of the zone of asteroids, the orbita of four of which-Harmonia, Nemausa, Polyhymnia, and Nysa-are indicated respectively by tho curves a a', p~ and n n', the perihelia of thèse orbits being at h, a, p, and n. The two first are the least eccentric of tho asteroidal orbits, and differ little from the circular form. The orbits of Nysa and Polyhymnia are remarkably eccentric. Professor Nichol remarks that Nysa recedes farther from the sun than any of the others, and, with thé exception of Hsestia, approaches him the nearest.' If, however, thé elements of the asteroidal orbits aro correctly given by him in his Cyclopsedia of the Physical Sciences' (article Asteroids), Hsestia is by no means remarkable for its near approa.ch to the sun either as respects mean or perihelion distance, while the perihelion distance of Nysa is less than the ~M'<!?t distance o/' Mars. As will be seen from the figure, part of thé orbit of Nysa absolutely falls within <Ae orbit of Mars, a circumstance that will seem still more remarkable when it is considered that tbe centre of the ellipse in which Nysa moves lies outside the orbit of the earth-falling, in fact very near the o?'&~ of Mars. The orbit of Polyhymnia is not so eccentric as that of Nysa; yet the centre falls only just within the earth's orbit. To avoid confusion, the nodal lines of the four asteroidal orbits aro not drawn in the figure; the following table indicates their positions, and tho angles at which the planes of the four orbits are inclined to thé ecliptic

Longitude of the Inclination ot

ascending Node. Orbit.

Harmonia 93° 32' 28" 4° 15' 48" Nemausa 175 39 8-2 9 36 37-9 Polyhymma. 9 16 ô'O 1 66 66-0 Nysa 127 6 3 03

It will be seen from thia table that the path of Nysa does not actually intersect that ofMars.

The asteroid Melpomene is also remarkable for thé close proximity of a part of ils orbit to the aphelion of Mars.

It has been noticed by Mr. Cooper, of Markree Castle, tliat in the positions of the asteroidal orbits a speciality is observable which eau hardly be tho result of accident --the perihelia and the ascending nodes are not distributed indifferently, but are found chiefly in the semicircle from 0° to 180°. The observation may be extended to the larger planets all of those introduced in the figure have their perihelia and rising nodes within the semicircle from 330° to 1~0°, which-more nearly than the semicirelo just indieated–corresponds to the région in which thé asteroidal perihelia and rising nodes are most remarkably crowded. The planets Uranus and Nephmo do not


foci of this elllpne. The second law of Kepler indicates the law of Saturn's motion in tbis orbit, wbich may be illustrated as follows Suppose thatpp~ Q Q', and R R' are arcs over which Saturn passes in equal intervals of time then Kepler's second law asserts that if straight lines s p, s p~ s Q, s Q', s R, and s R~ be drawn (to a.void confusion, these lines are omitted in the figure), the areas spp', s Q Q' and s R R', are equal. Since the sector spp' is plainly shorter tban the sector s Q Q', and SQQ' than s R R', it follows from the equality of these areas that the arc pp' is longer tban the arc Q Q', and Q Q' than R R'–increase in the breadth of the sectorial area compensating deficiency in length. In other words Saturn's velocity in bis orbit increases aa he approaches perihelion, and diminishes as he approachea aphelion. Thus, when he is near perihelion, he appears to be describing an orbit smaller than his actual orbit, with a velocity greater than his mean velocity; when he is near aphelion, these relations are reversed. His period, tberefore, would appear too small, if determined when he is near peribelion, and too great if determined when he is near aphelion.

deviate from the same law: the longitudes of their rising nodes are respectively 730 14~ 38~; and 130° 10' 13~3, tho longitudes oftheir penhelia. 168° 27~ 24~~nd 47° 17~8~ Thé speciality as regards the perihelia is certainly remarkable, and its physical interpretation worth seeking. The congregation of the rising nodea in the region indicated is obviously due to the choice of the ecliptic as the plane to which we refer the positions of the other orbital planes. Convenient as tbis selection is in many respects it has its disadvantages in fact, with the single exception of Merc~, no planet could be selected the plane of whose orbit is less suitable as a plane of référence in viewing the grander relations of the planetary scheme.

The orbits of Uranus and Neptune have not been introduced into the figure on account of their dimensions. The mean distance of Uranus from the son is about twice, the mean distance of Neptune more than three times, that of Saturn. Tho eceentricities of the orbits are respectively '0466 and -0087, their inclinations to tho plane of the ecliptic 0° 46' 29~-9 and 1° 46' 59".

The absolute velocity of a planet at any point of its orbit varies inversely as tho length of the perpendicular on the tangent at that point the angular velocity of the planet about thé sun's centre varies inversely as the square of the planet's distance from thé sun. There is a slight error in Nichol's statement that 'by an appropriate choice of an eccentric circular orbit the sun's motion relative to the earth or to any planet,' (or, which is thé same thing, any planet's motion relatively to the sun), 'may be very closely approximated to,' on the supposition of uniform velocities. See article 'Eecentric' in Nichors Cyclopœdia of thé Physical Sciences.' On such a supposition the angular velocity of a planct about the sun's centre would appear to vary inversely as thé distance, instead of as the square of the distance of tho planet.


The absolute dimensions of the ellipse in which Saturn nioves are as follows his mean distance from the sun (or half the greater axis of his orbit) is no less than 874,321,000 miles, his least distance (or sa) is 825,404,000 miles, and his greatest distance (or ss") is 923,238,000 miles. The eccentricity of the orbit is very nearly '056. In this vast orbit he moves with a. mean velocity of 21,160 miles an hour, sweeping out a mean hourly angle of 5"-025 about the sun. He occupies 10759-2197106 days in moving once round his orbit, or in completing a sidereal révolution.*

Kepler next inquired whether there existed any relation between the periods of the planets and the dimensions of thé planetary orbits. He selected the mean distances (or thé semi-major axes of tb e orbits) for the comparison, considering that aome relation might probably be found between the powers of these distances and of the periodic times. It was, however, only after many years' inquiry, that he arrived at the conclusion that it was here, and thus, that some new harmony in the planetary scheme was to be sought. One would have thought the rest of the work was simple; yet even when the very law he was seeking had occurred to him, two months and a half elapsed before he was able to verify it Let us consider how the law might have been determined from the orbits and periods of Saturn and the earth, Calling the mean distance of the earth 1, Saturn's mean distance is 9-53885 again, calling the earth's period 1, Saturn's period is 2 9'45 66 :–now what relation (if any) exists between these numbers, 9-53885 and 29-4566, or their powers ? The first is less than the second, but the square of the first is plainly greater than the square of the second we must therefore try higher powers of the second number. Trying the next power, that is, the square of the second number, we immediately find the relation we are seeking; thus :-The square of the first number is less than the square of the second but the next power, or the cube, of the first number is almost exactly equal to the square of the second.! Ail the elements of Saturn's orbit are iindergoing slow processes of change tho natures and causes of some of these are examined further on; the tables of Appendix II. indicate the amount of the annual \M'ia.tion of each element.

t The cube of 9-53885 is 867-9369 and thé square of 29-4566 is 867-691, difforing from the first by less than 0-246.


Here then is the required law, if, only, it sball appear that the relation is confirmed when we try it upon other pairs of planetary orbits. On trial it appears to be true for every such pair, and thus the third law of Kepler is established viz., tbat,

3. The squares of the periodic times of the planets vary as the cubes of their mean distances.*

Such are the laws of Kepler-laws purely empirical as presented by bim, but destined to prepare the way towards, if they did not directly lead up to, the grandest law of nature yet discovered by man-the law of universal gravitation. Strictly speaking, none of Kepler's laws are correct: the planets being of appreciable mass and exercising attractions upon each other and upon thé sun, their motions deviate from the orbits they would follow if these conditions did not exist-orbits which would be strictly in accordance with the laws propounded by Kepler. The accuracy of the laws, however, corresponded with, if it did not surpass, the accuracy of instrumental observation in Kepler's time, and for many years following the announcement of his important discoveries.

In the latter half of the seventeenth century, Newton commenced the investigation of Kepler's laws. Kepler had sought to learn what are the patbs of the planets, and what the laws tbey obey in pursuing those paths Newton devoted the powers of his piercing intellect to inquire the planets follow such paths and obey such laws. He sougbt, in fact, the physical interpretation of the observed phenomena.

Newton first proved that a body moving in such a manner with respect to any point that its radius vector describes equal areas about the point in equal times, is moving under the influence of forces constantly directed towards or from tbat point. According as the orbit thus described is concave or convex towards the point, the force acts towards or from the point. Since, then, each planet describes equal areas in equal times about the sun, and moves in an orbit whose convexity is towards him, the sun exerts an attractive force on each member of the system.

The law may also be expressed as follows :–F!xed units of time and space being chosen, the square of tho number expressing the periodic time ofa planet bears a constant ratio to thé cube of the number expressing thé nican distance of thé planet.


Secondly, Newton demonstrated that if a body revolves in an elliptical orbit (or in an orbit whose for m is any of the conic sections) under a central attracting force residing in one of the foci, that force varies as the inverse square of the distance of the attracted body. He further showed that Kepler's third law was a necessary consequence of attraction so varying.

In obtaining these results, Newton may be considered to have empirically demonstrated the existence of an attractive force exerted by the sun~s mass, and to have established the law under which that force acts. The reader must be careful, however, to distinguish such a result from the establishment of the great law of gravitation. The mere determination of the law of attraction exerted by the sun on the planets and by these on their satellites, however interesting, would have been neither particularly valuable nor-except in being demonstrated–novel. The idea of attractions so exerted, and the very law of such attractions, had occurred to many astronomers long before Newton's day nor does it appear that Newton himself attached any great value to the result, thus far, of his inquiries into the planetary laws of Kepler. The history of the process by which Newton arrived at the great discovery which bas rendered his name famous bas been repeated so often that it would be idle to give it here at length. The idea that the moon was retained in its orbit about the earth by the same attractive energy that causes unsupported bodies to fall to the earth,* appears to have occurred to Newton about the year The story of thé apple, whose fall suggested thé first idea of his great discovery to Newton, is probably apocryphal. Whether it is true or not, the manner in which it is usually related in works on popular science is calculated to lead to altogether erroneous ideas of the nature of Newton's discovery. Ib would not have been thé question, 'Why does the apple fall ?'-that Newton would have asked himself the attraction of gravity had been known for many ages the laws of its action on falling bodies had been discussed, however erroneously, by Aristotle, and had boen correctly established by Galileo. Thé inquiry might have been suggested, What if this attraction ofgra~-ity, so famitiar to philosophers, of whose operation I have just witnessed an effect, bas a wider range of action ? what if an attraction whose innuence appea.rs to be exerted alike on bodies of the most varying natures, and to be unaffected by differences of elementary conformation, of forrn, or of physical condition, in the bodies acted upon, is itself exerted equnlly by bodies so differing; is a property dopending not upon tbe quality but simply on thequantityofmatter;–is, in fact, a "primitive power of nature," exerted by every atom in immcas~u'able space, with a range altogethcr


1666. He was unable, however, at that time, to establish the identity of the attractive energies displayed by the earth upon the moon and at her own surface, owing to the erroneous measure of the earth's radius then accepted. At length, in 1684, making use of Picard's more correct determination of the earth's magnitude, he was able to remove the discrepancy which had till then bamed him. He had already proved that, so far as terrestrial bodies were concerned, the earth's attraction is not influenced by the nature of the attracted object–tbat all solids, liquids, and gases, elementary and compound, in whatever physical state, are in the same degree under the influence of this omnipresent agency he had now shown that the only celestial object whose motions are guided chiefly by the earth's attraction, shows by its main movements that it is influenced in the same degree as any terrestrial object would be at the moon's distance, supposing the earth's attraction to diminish as the square of the distance and, lastly, he had proved that this law of variation prevails in the attractions of the celestial bodies. The conclusion deduced was announced by Newton-the last to rush from particular phenomena to general theories- in the grand cosmical law :–< Every particle of matter in the universe attracts every other particle with a force varying directly as the product of the masses and inversely as the square of the distance.' Under this law the satellites sweep round their primaries, thèse round the sun, the sun on his course within the star cluster to which he belongs, that cluster amidst its companion nebulae, and the whole system of nebulee amongst other systems in immeasurable spaceall in their movements actin~ on and reacted upon by each other. And through the same great principle of nature, the least movement of the smallest insect on our globe has its influence on the motions of the most important members and systems of the universal Cosmos.

It is interesting to notice how admirably the characters of the three men whose labours had led up to and culminated in this uniimited, however it may be modified, by distance ? 1 It is quite possible that some simple event of the nature described might have started such a train of ideas in a mind like Newton's; it is certain that the l~v he established after eigliteen years of patient waitiDg, bas no narrower significance.


MODERN ASTRONOMY.

magnifient discovery, were adapted to the parts each had to perform. To Copernicus was given the confidence without ostentation necessary to the philosopher who is to refute ideas long held unquestioned 7~7' says Kepler on this point, < m~a~~o ingenio, et quod in /&oc exercitio ~c~ est, animo ~~er.' Kepler's mind was cast in a different mould. He was not one who could originate a system, but rather one who, receiving a system from the hands of another, could appreciate its value, investigate its relations, and trace in it laws and analogies hidden from its discoverer. Inquisitive, ingenious, and imaginative, he pursued his inquiries with singular energy and untiring- patience. In thé Inidst of poverty, and tried grievously by a series of thé most distressing domestic afflictions, he pertinaciously pursued, during twenty-three years, the path he had adventured upon.t Newton was endowed with a more comprebensive genius than either of his predecessors: bold and original like Copernicus-as observant, inquisitive, and patient as Kepler-he added to these qualities a piercing insight into those hidden operations and laws of nature to which celestial and terr estrial phenomena are due, and a wonderful aptitude in inventing and conducting experiments to confirm or correct his views. He was, on the one hand, the true philosopher of the Baconian type, forcing nature to reveal her secrets by sedulous and reiterated inquiries; on the other hand, he afforded an early illustration of Bacon's error in supposing his system of philosophy would raise all its followers to one level, however various might be their talents or capacities :–As in genius, so in thé work he accomplished, ~e~~s /c~m< s~e~

Preface to thé Rudolphine Tables,' published by Kepler in thé yea.r 1628. t 'We find him in the ycar lô9o, at the age of twenty-three, seeking the laws of thé planetary orbite in simple numerical relations, in the residua. of sines and cosines,' and in the radii of circles inscribed in and circumscribed about triangles, squares, and polygons he e-ven adopted, temporarily, n, rough approximation drawn from tlie relations among the l'adii of spheres inscribed in and circumscribing tho regular polyhedra. The singular law called the law of Bode or Titius is due to the ingenuity of Kepler, who also preceded Olbers in the supposition that some invisible planet occupied tho space betweon thé orbits of Mars and Jupiter.

+ It is a rather singular coincidonce that Kepler and Ne-wton, to whose laboura, chiefly, the discovery of tho system of the universe is due, were both prematurely born into the worid:–Kepler four days before Christmas-day in thé year 1671 Newton on


In succeeding chapters of this work, we shall see how the theory of gravitation enables us to determine Saturn's weight and density. It has been applied also to determine the weigbt, and thence thé probable thickness of Saturn's rings. In the sixth chapter, the great inequality of Saturn and Jupiter produced by the mutual attractions of these, the two most important members of the solar system, is examined and explained.

If any doubts could hâve remained of the truth of the Coper nican theory after the revelations of the telescope and the investigations and discoveries of Kepler and Newton, Bradley's discovery of the aberration of light must have finally removed them. By this important discovery he proved that every star in the heavens, in tracing out its yearly aberration-ellipse, reflects the motion of our earth about the sun,* and becomes, in fact, a shining record of the ceaseless movements of that world, which seems to the untutored mind the aptest type of immobiiity.

Christmas-day 1642, the year in whieh Galileo died. We read of Kepler that 'he was a seven-months' child, very sickly during early life, and at the age of fourteen he was forbidden all mental application ;of Newton, that 'he was so small at birtb, that he might have been put into a quart pot,' and'that the attendants successively despatched for medical aid were astonished to find him alive on their return.'

It is plain that the stars are not the only objects whose positions on the celestial sphere are affected by the aberration of light thé planets, asteroids, and satellites arc similarly affected in different degrees according to the directions of their motions and those of the earth; the sun's position is aiso affected by aberration, butwith less varin.tion in the amount of such affection. The moon is thé only celestial body whose motions are not affected by aberration due to the earth's motion tho aberration due to her own motion is very smalL The planetary and solar aberrations have been exactly computed, aud are duly taken into account in determining the daily motions and positions of tho sua and planets.


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CHAPTER III.

TELESCOPIC DISCOVERIES.

IN the beginning of July 1610, at Padua, Galileo first examined Saturn with his largest telescope. Poor as this instrument would now be considered,* utterly insignificant as it would appear beside the gigantic tubes with which the Herschels, Rosse, Lassell, and Bond, bave scanned the celestial depths, he hadjaiready effected with it a series of the most important discoveries. He had completed its construction in thé preceding year-the year in which Kepler announced his first and second laws and on the 7th of January, 1610, he had discovered by its means four new members of the solar system circulating around Jupiter, tbe least of whicb is nearly as large as our moon, while the greatest is equal in magnitude to the planet Mercury. We can imagine with what emotions of interest and expectation he applied his telescope to the examination of the more distant planet.

In July 1610, Saturn was approaching opposition, and very favourably situated for observation. Yet the result of Galileo's inspection was not satisfactory. He could detect a peculiarity in Saturn's appearance, but he was unable to determine the cause of that peculiarity. It appeared to him that on each side of Saturn's dise there was a minor dise. The two lesser dises seemed to be Galileo's largest telescope had a magnifying power of thirty-two diameters two others he employed had powers of four and seven diameters only; the feids of view in all of them were very small. We leam from Brewster, who examined thé largest a few years ago at Florence, that thé object-glass was reduced to one-third of its area by a diaphragm of card, and the field was like a small hole.' A more powerful and far handier instrument may now be obtained in any optician's shop for a fcw shillings yet if we regard the absolute importance of the discoveries effected by different telescopes, few, porhaps, will rank higher than thé little tube now lying in the Tribune of Galileo' at Florence.


perfectly equal and symmetrically placed on opposite aides of Saturn, whose dise they appeared to overlap. Continuing his observations for several months, Galileo found that the two smaUer dises retained the same position and were apparently unaltered in magnitude. These appearances were altogether perplexing to him no phenomenon with whicb his telescope had hitherto made him acquainted, had prepared him to anticipate or understand a conformation so remarkable. The minor dises were evidently different from Jupiter's satellites and, even if they were orbs attending on the central globe, it remained inexplicable that they should be always seen in the same position with respect to it, for this required that they should always be in the same position with respect to the liné of sight from the observer on earth, a line whose motions partly dépende as we hâve seen, on the motions of the earth; so that it would appear as if these singular attendant orbs were partly guided by the earth in their movements about Saturn. Notwithstanding this apparently inexplicable circumstance, Galileo accepted the triplicity of Saturn as the only possible explanation of the phenomena, and in November 1610, he told Kepler tbat Saturn consists of three stars in contact with one another.' He announced the supposed discovery to the world of science, in the form of an anagram produced by transposing the letters of the sentence a~MS~m ~)~%6~~ ~~67yM~~m o&se7'~Œ ~1 have observed that the most distant planet is triform adopting this fanciful plan to prevent other astronomers from claiming the honour of the discovery.

After an interval of a year and a half, Galileo again examined Saturn. To his infinite amazement not a trace was visible of the appearances that had perplexed him before; there in the field of view of his telescope was the golden-tinted dise of the planet as smoothly rounded as the dise of Mars or Jupiter.* We can imagine how in his perplexity, he must have thought bis telescope in fault, and how, adjusting the instrument, and cleaning the From Table X. it will be seen that thé ring disappeared on December 28th, 1612, its plane passing through thé sun; in the spring of 1613 the ring reappeared, its plane passing through the earth. There was no other disappearance at this passage of the ring's plane across the orbit of the carth. See Chapter IV.


glasses, he must again and again hâve brought thé planet into thé field of view,-still to see a single dise, where he had expected to see his triform planet. Finally, confused and amazed by a change so startling, he seems to have been inclined to put faith for the moment in thé assertions of his enemies, that the discoveries he had reported had been mere illusions, justly sent to punish a spirit too prying and inquisitive :–< Is it possible,' he exclaimed, that some mocking demon bas deluded me ? 1

The changes that G alileo afterwards detected in Saturn's appearance were still more perplexing. The minor orbs reappeared, and waxed larger and larger, varying strangely in form finally, they lost their globular appearance altogether, and seemed each to have two mighty arms stretched towards and encompassing the planet. From a drawing in one of his manuscripts it has been supposed that Galileo suspected the true cause of these startling changes. In this drawing Saturn is represented as a globe resting upon a rino-. It seems more probable, however, that this drawing is a modern addition to the manuscript, and that Galileo was never able to explain the phenomena whose succession he had observed and recorded.*

Hevelius, with more powerful instruments, but in a elimate less favourable to the astronomical observer, was not more successfui than Galileo in explaining Saturn's mysterious changes of form. In the year 1656 he published his treatise ~<~ ~~w~ Saturni /c~e,' in which he announced the result of his observations, concealing bis real perplexity under a flight of sesquipedal words. <Saturn/ he informed his contemporaries, with an amusing attempt at accuracy, présents five various figures to the observerto wit first, the mono-spherical secondly, the tri-spherical; thirdly, the spherico-ansated; fourthly, the elliptico-ansated; fifthly, and finally, the spherico-cuspidated.'

A year or two before, Huygens, with a telescope of 12 feet focal length, had detected dark spaces enclosed within the as yet unexplained appendages on each side of Saturn's disc. Thus

It will be seen from Table X. that the ring disappeared again in thc year 1626, the plane of the ring passing through the earth early in September, and through the sun on the 15th of September in that year. Galileo became blind in 1637.


Saturn appeared as a globe, wi'th two handles symmetrically placed on either side or, as Ilevelius expressed it, as an ansated spheroid. Subsequently, with a telescope of 23 feet focal length, and magnifying 100 times, Huygens saw these dark spaces more distinctly but the true figure and structure of Saturn remained still a mystery to him. Some of the changes observed in Saturn's appearance could be explained by supposing the two appendages to be actually ansse, or bandle-formed structures attached to Saturn's body, but others remained inexplicable. It was not credible that the motions of Saturn's globe should be so exactly adjusted to those of the earth in her orbit, that the diameter through the ansae should be always at right angles to the Une of sight from the observer on earth yet, if this were not the case, it remained impossible to explain how it happened that-whatever variations might appear in the forms of the ansse–they always seemed to stand out to the same distance from the dise of tbe planet.

In the spring of 1656 Saturn appeared without his ansae,* though Huygens examined him with a telescope of 123 feet focal length- one of the aërial telescopes he had himself invented. After observing the circumstances attending the disappearance and reappearance of the ansae, and carefully investigating the theories whicb appeared most plausibly to account for tbe phenomena, Huygens at length arrived at the true explanation. He announced to his contemporaries, in the year 1659, that Saturn is girdled about by a thin Sat ring, inclined to the ecliptic, and not touching the body of the planet.f He showed that all the variations in the appearance of this ring are due to the inclination of its plane to the ecliptic, while the tenuity and flatness of the ring explain its disappearance when the edge is turned to the spectator or to the sun. He found that the diameter of the outer circumference of the ring exceeded The plane of the ring passed tbrough the sun early in March 1656 (see Table X); it had passed through the earth in the autumn of 1655, but Saturn was not then favourab]y situated for observation. After ita plane had passed through thé sun thé ring became visible, but disappeared a few weeks after, its plane passing through thé earth. The ring reappeared, finally, in the summer of the same year.

t Huygens propounded this important discovery in the form of the following sentence, anagrammatically transposed, annule cingitur tenui, piano, nusquam cohœrente, ad eclipticam inclinato.'


the diameter of Saturn's globe in thé proportion of about 9 to 4; and be considered the breadtb of the ring about equal to the breadth of the space Letween its inner edge and Saturn's body. Four years before, on March 2ath, l6oo, Huygens had made another important discovery: by aid of the 12-feet telescope already mentioned, he had detected a satellite attending on Saturn. Judging from the brightness of this satellite at so vast a distance, he considered that it must greatly exceed the largest of Jupiter's satellites in magnitude, and be little, if at all, inferior to the planet Mars. It revolves round Saturn in rather less than 16 days, at a distance of nearly 760,000 miles. In ~659, Huygens published a table of its mean motions. As this discovery raised the number of secondary planets to six (including our moon) and as but six primary planets (including the sun) were known to Huygens, he sought for no more satellites-sharing the idea, then commonly entertained, that the numbers of thé primary and secondary members of thé solar system must certainly he equal. Otherwise, with the powerful telescopes be subsequently constructed, he could not hâve failed to detect two (if not all) of the four satellites discovered by Cassini.

Huygens discovered that Saturn's globe, like Jupiter's, is marked by belts parallel to the equator, and on one occasion he observed as many as five but be was unable to detect any other signs of Saturn's rotation.

ln 1665, William Bail discovered a black stripe of considerable breadth, running quite round the northern surface of the ring, and having its outer and inner edges concentric with the edges of the ring. Ten years later, Dominic Cassini observed a corresponding stripe on the southern surface of the ring. He observed also that thé part of the ring's surface outside tbis stripe is not so bright as the part within. He suggested, in explanation of these phenomena, that the ring is divided into two concentric rings, the inner ring being the brighter.

Four years before, in October, 1671, Cassini had discovered a second satellite, revolvin at a mean distance of about 2,209,000 miles from Saturn, in rather more than 79 days. This satellite is not so bright, and is therefore probably smaller than thé satellite


first discovered, but is certainly not inferior in magnitude to the largest of Jupiter's moons. Cassini soon detected a singular phenomenon in this satellite; through nearly one half of its révolution about Satum, it disappears regularly, even when sou~bt with the same telescope in which, through thé rest of its révolution, it is a conspicuous object. He concluded that one half of the surface of the satellite must be less capable of reflecting light than the other, and that, like our moon, it rotates once on its axis in each revolution about its primary.* He subsequently abandoned these views but they were confirm ed by Newton and Herschel, the former showing that no explanation can be given of the regular disappearance of the satellite but that suggested by Cassini the latter. by a series of car eful observations with his powerful reflectors, estabUabing the correctness of Cassini's observations. Thèse and similar observations by M. Bernard at Marseilles in 1787, and by later astronomers, seem to leave no doubt on the suhject.f We have here, then, a secondary planet rotating on its axis in 2~ months, while (as will presently appear) its primary, whose volume is 15,000 times as gréât, rotates on its axis in less than 10~ hours. On December 23rd, 1672, Cassini discovered a third satellite

The only satellites whose motions of rotation have bpen detected exhibit thé same peculiar relation between rotation and revolution. They are six in number:-our moon, the four satellites of Jupiter, and the outer satellite of Saturn. Either the surface of thé largest of Saturn's satellites is little marked with irregularities, or these are distnbuted with tolerable uniformity, since it presents no appreciable changes of brilliancy. Of thé other six satellites of Saturn, thé satellites (variously estimated at four, six and eight) of Uranus, and Neptune's satellite, nothing is likely to be known till teleseopes far more powerfui than any now in use shall have been constructed. t In the year 1705, it was observed that thia satellite was visible through a complète revolution, and it was bence concluded that the irregularities upon its surface are variable. Far more probably, however, the phenomenon was due to thé exceptional clearness and steadiness of thé earth's atmosphere during the interval of two or three wfeks occupied by the satellite in traversing the part of its orbit in which it usually disap.pears. Any one who is in thé habit of using a telescope of even moderate power systematically, must soon become awaro that there are occasionally brief intervals during which the power of the telescope seems increased, though the eye detects no corresponding change in the appearance of celestial objects. Unfortunately, such intervals occur but rarely in our latitudes, and seldom last more than two or threo days. They generally occur in early spring and late autumn; winter and summer are seldom favourable seasons for astronomical observation, notwithstanding the brilliance of some of our winter nights, and the softer splendour of the nocturnal skies in summer.


whose orbit lies within those of the other two. He effected tbis discovery by means of a telescope of Campani's, 35 feet in focal length. Tbis satellite revolves about Saturn in rather more than 4~ days, at a mean distance of about 328,000 miles. Judged by its brightness, it is probablymuch smaller than either of the two satellites first discovered. It exceeds the outer satellite in brightness, however, when thé latter is at or near its easterly elongation. In March 1684, Cassini discovered two more satellites by means of Campani's object-glasses of 100 and 136 feet focal lengtb.* These satellites revolve within the orbits of the first three, their mean distances from Saturn's centre being about 224,700 and 180,000 miles. Thus both are nearer Saturn's surface than our moon to the surface of thé earth. They occupy about 2~ days, and 1~ days, respectively, in completing their revolutions about Saturn. They are about equal in brightness, being each slightly inferior in this respect, and therefore probably in magnitude, to the third satellite discovered.

Cassini found that the orbits of the five satellites hitherto discovered correspond with the laws of Kepler (see Table V.). He found also that the four inner satellites move in planes very nearly coincident with the plane of the rings, while the fifth moves in a Cassini also used object-glasses of 200 and 300 feet focal length, and Auzout constructed glasses having focal lengths of 600 feet. Of course, glasses of such enormous focal length werc not fixod in tubes. They were attached to frames constructed to slide up and down tall uprighta. The pye-glassM of such telescopes were simply connected with thé object-glasses by wires of the proper length. Observation with such telescopes must havo been wearisome work, and we cannot wonder that thé invention of reflecting telescopes was gladly hailed as offering a relief from tlie use of such cumbrous and imperfect instruments. The reflector presented by Hadley to the Royal Society, in 1723, though it hada. focal length of only 10 feet 5~ inches, was fully equal in power to the refractor of 123 feet focal length given by Huygens to the same Society. Yet the difficulty of grinding the spécula accurately, and of preserving them when ground from changes of form and loss of reflecting power, must always prevent reflecting telescopes from rfplacing refractors, now that the construction of achromatic object-glasses has att<uned such perfection. That absolute truth of form has been obtained in reflecting specula by the most ingenious systems of grinding may be doubted,. when we remember that the Harvard refractor, with an object-glafs of flfteen inches diameter, bas clearly resolved nebulae in which but doubtful indications of resolvability are afforded by thé splendid 6-feet speculum of Lord Rosse's reflector. It may bo questioned whether, in certain applications of the telescope, tubeless telescopes might not be occasionally used with advantago, diminution of weight and consequent cheapness of construction compensating a slight loss of illuminating power.

E 2


plane inclined at an angle of about 15° to thé plane of the ring. The younger Cassini investigated these relations more closely, and in 1717, published a table of thé distances, mean motions, and inclinations of the orbits of thèse satellites. He determined also with considerable accuracy, the position of the ascending node of the rings' plane on the ecliptic, and on Saturn's orbit, and the position of the ascending node of the fifth satellite on the same circles. Halley corrected the results obtained by Huygens and the elder Cassini; and later, in 1720, published the elements of the orbits of the five satellites, corrected from a series of observations made by Pound. Halley also detected an eccentricity in the orbit of the largest satellite, and roughly determined its amount, and the position of the line of apsides. Cassini called the four satellites he had discovered Sidéra Lodoicea,' in honour of Louis XIV., under whose patronage his labours bad been conducted.* Tbis name bas, however, long since been disused. The satellite discovered by Huygens bas received the name of Titan and the four discovered by Cassini bave been caUed (in the order oftheir distances from Saturn), Tethys, Dione, Rhea, and Japetus. But the most convenient method of indicating these and the satellites since discovered, is by numbering them in the order of their distances from Saturn thus the satellite discovered by Huygens is now known as the sixth satellite, while the satellites discovered by Cassini are known as the third, fourth, fifth, and eighth satellites. By referring to Plate I. thé reader will be able to form an idea of the relative brightness of these bodies, and of the probable proportions they bear to each other, to the globe of Satura, and to the other bodies represented in that engraving, all of wbich are on the same scale. In fig. 1, Plate VII., they are represented at their proper relative distances from Saturn; while in fig. 2, the dimensions of their orbits are represented on a smaller scale. Thé elements of tbe eight satellites are given in Table V.~ Appendix II.

For nearly a. century after the discovery of Tethys and Dione no new features of importance were revealed by the teleCassini vas natnralized in France in 1673. His son Jean Jacques Cassini, and his grandson César Francois Cassini, were both born in France. The family, however, originally came from ItaJy. Cassini bimself was born at Périnaldo, in Nice.


scope in the Saturnian system. Several phenomena already suspected were verified, however, and others-not wanting in 'interest-detected. Hadley discovered tbat the outer part of the ring is thinner than the inner he observed also the shadow of the ring on Saturn,* and the shadow of Saturn on the ring. He confirmed Huygens' observation of belts on Saturn's dise, and found tbat, like the belts of Jupiter, they vary in form and number. Halley, also, observed Saturn's belts, and concluded from their changes of form as Saturn traverses different parts of his orbit, that Saturn rotates on an axis perpendicular (to the sense) to the plane of the rings in other words, that the plane of Saturn's equator coincides (to the sense) with the plane of the rings. In October, 1714:, a few days before the disappearance of the rings, the earth being nearly in their plane, Maradi observed a singular phenomenon :–thé narrowing ansœ of thé ring appeared to be unequal in size; the eastern being the larger; yet after an interval of two nigbts the eastern ansa had disappeared, while the western was visible, though reduced to a faint line of light. From these observations he concluded that the rings are not of uniform thickness, and that they revolve about Saturn in their own plane.'}' In this conclusion may be traced the germ of the important discovery of thé rotation of the ring afterwards made by Herschel. It may be noticed, however, that in arriving at this conclusion Maradi made two assumptions, neither of which (as will presently appear) is correct. He assumed, first, that the ring is a solid formation and secondly, that it is a r~K~ solid. The first assumption was justified by the appearance of the ring, and was maintained, or rather never disputed, till the discoveries of the last few years led to a Cassini, in 1675, observed a dark belt on S~tum's body, parallel to thegrnater axis of the rings. This was probably either the shadow of the ring on Saturn, or the first indication of the existence of the dark innpr ring lately discovered. In 1675, the rings were well opened, but not to their full extent at such a time the outlines of thé belts are elliptical. The outlines of thé daxk ring and of the shadow are, it is true, also elliptical, but they form parts of larger ellipses, and appear nearly straight and parallel to thé greater axis of the ring.

t It will be seen from Table X. that the plane of thé ring passed through the sun in February 1715, reappearing. After this the plane of the ring passed twice through the earth, disappearing at the first passage and reappearing at the second, These passages occurred in the summer of 1715, and within a few weeks of each othor.


~4

SATURN AND 1TS SYSTEM.

different view. Tbe second assumption, on the other hand, is altogether -tinreasonable. It was not to be expected but tbat so vast a formation, subject to so many disturbing attractions, and whose thickness is obviously disproportionate to its other dimensions, should be subject to vast undulations and these, for anything known to the contrary in Maradi's day, might sweep round the ring, altogetber independently of any absolute motion of rotation in the system, and would thus sufficiently account for the phenomena observed by Maradi.

The motions and distances of the satellites, and the dimensions of the ring, were determined with considerable accuracy, by several astronomers, during thé interval above mentioned. Some of these measurements will be made use of in a future cbapter, but most of them have given place to the more exact determinations of the present century.

One or two observations, rather curious than valuable, were also made in the interval named. Thus, Whiston records that his father had seen a star through one of the openings between the planet and the ring. Such an occurrence, though uncommon with the telescopes in use in his day, is not infrequent with modern telescopes, especially when Saturn is traversing the constellations Taurus and Gemini in one part, Scorpio and Sagittarius in the opposite part of the Zodiac. No star of the first four or five magnitudes baa ever, I believe, been seen through these openings. Again, Cassini bas recorded tbat in 1692 he saw a fixed star occulted by Saturn's largest satellite, an occurrence that must be exceedinglyrare even with the most powerful telescopes, and when Saturn is traversing those parts of the Zodiac in which stars of all magnitudes are most profusely scattered.

During the last fifteen years of the eighteenth century, many important discoveries were made by the elder Herschel in the Saturnian system. When the northern side of the ring was visible before the disappearance of the ring in 1789, he carefully examined the black line discovered by Bail. He appears during this time to have been strongly opposed to the idea that the ring is divided, even where this line is seen still less was he willing to accept the hypothesis of the multiple division of the ring. Four observations


in 1780 bad appeared to indicate thepossibility that other divisions be&ides thé great one exist in thé ring and Laplace–his inferior as a practical astronomer, but bis superior as' a mathematician–had assert.ed that such divisions are absolutely necessary to the stability of thé formation. Herschel niaintained, however, and with some reason, that observation afforded no support to the theories of the French mathematician. Conndent that bis 20-feet reflectors were equal, if not superior, in power to the best telescopes of his day, he refused to put faith in the records of observations wbich his own telescopes failed to verify and the idea of the ~myo~~ existence of such lines either never occurred to him, or was rejected as improbable.* His observations of the ~broad black mark,~ as he at first spoke of the great division, were conducted with his usual accuracy and clearsightedness. He found that the outer and inner boundaries of this mark are both ellipses, concentric with and similar to thé boundaries of the rings. He argued tbat the black stripe could not be the shadow of hills on the surface of the ring, since such a shadow would vary with thé position of Saturn in his orbit, and when Saturn is in opposition no shadow would be visible at the ends of the longer axis of the elliptical. mark, whereas it is precisely at these points that the mark is broadest.. For similar reasons he rejected the idea that tbe line indicates the existence of a vast cavernous groove on tbe northern surface of the ring. On the reappearance of the ring in the winter months of 1789-90,t he examined its southern face with bis 40-feet reflector, and after carefully measuring the stripe on this face, he found that it corresponds exactly in form and dimensions with the stripe on the nortbern face. Accordingly, in the year 1790, he announced his suspicion that the formation is divided into two rings by a vast circular gap of uniform width-at the same time recording bis opinion that this is the only division existiug in the system.

On August 19th, 1787, Herschel tbought he could detect a sixth satellite attending on Saturn. He remained incertain as

He bas, in fact, recorded his opinion that thé rings are undoubtedly solid formations, since they cast a strong shadow on the body of the planet.'

t The disappearances and reappearances of thé rings in the years 1789-1790 are considered in Appendix II. See explanation of Table X.


to the existence of this body until the completion of bis 40-feet reflector.* On August 27tb, 1789, thé first evening after the completion of this powerful instrument, he directed it towards Saturn. No sooner had he brought the planet into the field of view than he plainly saw six stars shining round its dise. Five of these were the satellites already discovered it remained to be seen whether the sixth were a satellite or a fixed star. Saturn was then not far from opposition, and retrograding at the rate of 4' 30" daily thus the motion of his system was carrying him across the celestial sphere, slowly indeed, but with a motion readily detected, even in a short time, by a telescope of such power as Herschel's. Thus, 2~ hours after the first observation, Herschel found all the six stars had accompanied Saturn in his slow motion across the celestial sphere-all, therefore, were satellites.

Herschel fonnd that the orbit of the newly-discovered satellite is within those of the other five. It is less conspicuous, and, therefore, probably smaller tban any of the satellites that had hitherto been discovered. It revolves about Saturn in rather less than one day and nine bours, at a distance of about 148,000 mi)es from Saturn's centre, or about 112,000 miles from the surface of the planet. While continuing his observations of this satellite, and within three weeks of its discovery, Herschel detected a seventh satellite, about as small-or, at least, as little conspicuous-as the other, andfonowinga smaller orbit. This satellite moves at a distance of rather more than 115,000 miles from Saturn's centre, or about 79,000 miles from bis surface. Its mean distance from the outer edge of the ring is les? than 32,000 miles. It accomplishes a revolution around Saturn in about 22~ hours-a period of revolution shorter tban that of any known satellite in our system. Herschel published tables of thé motions of the two satellites he had discovered. He found that the planes in which they move are either absolutely coincident with the plane of the ring, or so nearly so that no difference can be detected. Owing- to tbis coincidence, as well as to their minuteness at so vast a distance from thé eartb, This splendid telescope, only exceeded in size by tbe great Parsonstown reflector, had a spéculum four feet in di~.ter. It will serve to give an idea of the patience and energy ofHersehcl to record that, between the years 1775 and 1781, he cast, ground, and polished 80 specula of 23 feet, 150 of 10 feet, and 200 of 7 feet focal length


they are not favourably seen, even in thé most powerful telescopes, except when the ring is very nearly closed, as was the case at the time of their discovery.

Herschel examined the belts on Saturn's surface with great care. He found that their outlines are straigbt lines when the rings are invisible, and change into ellipses of less and less eccentricity as thé rings open more and more that, in fact, thèse outlines are always similar to the outlines of the rings. From this observation it follows, assuming that the belts are due to thé rotation of the planet on an axis, that the axis of rotation is perpendicular to the plane of the ring or, in other words, that the plane of the planet's equator coincides with the plane of the ring, as had been already suggested by Dr. Halley. Herschel established beyond doubt the connectiun between thé belts and the rotation of the planet, by the discovery of certain spots on Saturn's surface. Carefully observing the motions of these spots for some time, he found that Saturn rotates upon his axis in 10 hours, 29 minutes, 16-8 seconds.* This rotation, like that of the earth, is from west to east; so that to thé Saturnians the sun appears to travel across the sky -from east to west, as with us. Instead of 365 days, however, the Saturnian year contains no less than 24,618 Saturnian days. The investigations of Laplace into the stability of a solid flat ring (such as Saturn's was supposed to be) about a central attracting body, had led that distinguished mathematician to the conclusion that Saturn's rings must rotate about the planet in their own plane. In July, 1789, when the edge of the ring was turned directiy towards the earth,t Herschel observed that it continued visible as a broken line of light when viewed tbrough one of his 20-feet reflectors, and that certain spots of light were carried along this line as if by the rotation of the ring in its own plane. Continuing his observations, he found that the spots of ligbt travelled nearly to thé ends of the ansae, so tbat he concluded they belonged to thé outer ring. He found that they occupied 5 hours, 16 minutes, 7'5 seconds in travelling from end to end of the fine line presented Herschel first gave for this periocl 10 hours, 16 minutes, 0'44 seconds. f Thé ring at this time was reappearing; thé earth which for a few weeks before had been on thé unilluminated side of the ring passing to the illuminated side. Sce explanation of Tubip X, Appendix II.


by the ring, and he therefore announced that the outer ring rotates in ita own plane in 10 hours, 32 minutes, 15 seconds. Herschel's measurements of the diameters of the planet and rings are somewhat in excess of the measurements now generally adopted as the most trustworthy. He considered that the breadth of the system of rings was about one-fourth greater than the breadth of the space between the inner edge of the iuner ring and the planet's equator. It will be remembered that Huygens considered those breadths equal. Pound, with the same telescope as Huygens, and using an excellent micrometer, considered that the breadth of the ring-system was even somewhat less than the breadth of the space between the planet and the rings. So remarkable a discrepancy can hardly be ascribed to errors of observation, and it will presently be seen that the change which would thus appear to bave taken place in the shape of the rings between the years 1659 and 1790, was part of a progressive increase of the breadth of the system, that bas continued to our own time. Herschel at first considered the form of the planet to be spheroidal, and the polar axis shorter than an equatorial diameter in about the proportion of 10 to 11. He subsequently changed his opinion. as to the form of the planet, concluding, from observations taken m April, 1805, that the outline of the planet's dise is not a regular çurve. He compared its form to tliat of a parallelogram with rounded corners, whose longest diagonal i$ inclined at an angle of 4~20'to the equatorial diameter, while its shortest diagonal is the polar axis of the planet. Subsequent observation bas not connrmed this view, which probably arose from an optical illusion. Atthe time of observation the ring was not favourably situated for the measurement of the planet's dise. For this purpose the ring should be altogether, or very nearly closed. In April, 1805, the line of sight from the observer was inclined at an angle of about 13° to the plane of the ring, so that the ring was sufficiently open to Doubt has been thrown on this conclusion, since Schroeter, at the next disapDearance of the ring in 1802-3, and Bond in 1848, observed that spots and irregularities along the thin line of light maintain their positions absolutely unchanged for hours. The positive évidence of the ring's rotation afforded oy Herschel's observation is not affected, however, by the observations of Schroeter and Bond. The spots seen by thèse astronomers have been satisfactorily explained by the latter as belonging to thé general configuration of the rings, not to irregularities of form at particular parts of the rings' surface.


interfere with tbe measurement of thé dise, an operation at all times sufficiently dimcult.

From a series of observations made in tbe years 1789-1790, during which the eartb passed three times through the plane of thé ring, Herschel arrived at the conclusion that the ring must be very thin. When the edge was turned directly towards the earth, the ring continucd visible in his 20-feet reflectors as a fine line of light and in his gréât reflector the ring was visible even when the earth and sun were on opposite side of the ring's plane,-that is, when the unilluminated side of the ring was turned towards the earth. Along the fine line of ligbt visible in the former case, the satellites appeared to move like golden beads upon a wire,' as Herschel bas described the phenomenon. He did not, however, conclude from this circumstance alone that the ring's thickness is necessarily less than the diameter of the least of the satellites for he considered that the dise of thé satellite might be rendered visible on both sides of the ring by refraction through an atmosphere which he supposed might envelope the ring.* He was doubtfu] whether tbe fact that the ring is visible when its dark side is turned towards the earth is due to the partial illumination of that side of thé ring by light reflected from Saturn and from his satellites, or whether he only saw the illuminated edge of the ring. He judged that the edge of the ring if! not perpendicular to the faces of the ring (so as to be part of a cylinder of very short axis), but thatit is rounded (so as to form part of the surface of an oblate spheroid, whose axis is very short compared with its other dimensions) or, as he expressed it, 'that the edge of the ring is not flat but spheridical.' Herschel found that when the satellites are occulted by Saturn, they appear both at ingress and egress to cling to his dise for a longer time than would be due to the dimensions of their own

Thé supposition bas not been conArmed by observation, however. To produce thé effects described, the atmosphere of thé ring must cling round the edges of the ring, since the mere presence of an atmosphere on the flat surfaces of thé rings could have no other effect than to dim the lustre of thé satellites. Now, it is plain that as thé satellites reached (apparently) the ends of the Une presented by the ring, their motion would appear to be, considerably modified by refraction fOM?!~ the ~'M~'se~; they would, in fact, appcar to cling to thé extreme end of the line for an appréciable interval: this is not thé ca~e, however; their apparent motions along and beyond thé line being exactly those due to thcir motions in their orbits.


dises. This phenomenon can only be ascribed to the presence of an atmosphere of considerable extent and densitysurrounding Saturn. The existence of such an atmosphere, supporting vast masses of aqueous or other vapeurs, is indicated by the belts that cover varying zones of Saturn's surface. In November, 1793, Herscbel obtained a favourable view of the Saturnian belts with his 40-feet reflector. He observed a broad and brilliant white belt of nearly uniform width, covering the equatorial regions; next to it he observed a broad dark belt of a. yellowish colour,~ divided into three unequal bands by two narrow and somewhat irregular white strèaks less brilliant than the equatorial belt. At first sight the natural assumption would seem to be that the dark belts are bands of clouds upon the surface of the planet. It must be remembered, however, that the clouds of our own skies appear dark to us only because they intercept part of the solar light. When they are so placed as to reflect the sun's light to the observer they appear briiliantjy white. Now it is precisely such reflected light-the silver lining' of the proverb–tbat an observer on earth receives from cloudbelts encircling a planet. On the. other hand, the surface of the planet's body, diversified probably, like that of the earth, with continents and oceans, would exhibit in different districts varyingshades of ligbt and colour, and thèse–blended by the effects of distance and of the atmospheric envelope through which we see them -would combine to present precisely such dusky regions, faintly tinged with the prevailing colours of the planet's surface, as are visible in the belts of Saturn. The equatorial bright belt, which Herschel found to be permanent, may be ascribed to tbe presence of a permanent zone of clouds covering this part of Saturn's surface. On our earth we have a corresponding equatorial zone of calms, in wbich the sky is never free from clouds and vapours, and in which rain is almost constantly falling.

The series of discoveries effected by the elder Herschel cannot be better closed than by his own account of the features of the Saturnian system There is not, perhaps,' he says, ~another object in the beavens that presents us with such a variety of extraThe best modem telescopes, under favourable circumstances, exhibit thé dark belts as of a faint greenish colour.


ordinary phenomena as the planet Saturn: a magni.ficent globe encompassed by a stupendous double ring; attended by seven satellites ornamented with equatorial belts; compressed at the poles turning on its axis mutually eclipsing its rings and satellites and eclipsed by them the most distant of thé rings also turning on its axis, and the same taking place with thé farthest of the satellites all the parts of the system of Saturn occasionally reflecting light to each other-the rings and moons illuminating the nights of the Saturnian, the globe and moons enlightening the dark parts of the rings, and the planet and rings throwing back the sun's beams upon the moons when they are deprived of them at the time of their conj unctions.'

During the present century many observers of the highest reputation for skill and accuracy have detected divisions in the rings concentric with thé great one. One such division, separating the outer ring into two rings nearly equal in breadth (see figs. 2 and 3, Plate I.) appears to be permanent, though it is only visible through its entire circumference when the ring is open to its full extent. Even then it can only be seen with telescopes of the first class for power and definition, and under the most favourable atmospheric conditions. Thé late General Mit~hel, thé American astronomer, bas asserted that with the full power of the Cincinnati réfracter-~ defining in thé most beautiful manner all the other delicate characteristics of Saturn and his rings/ he bas never been able to perceive this division in thé outer ring, or a trace of any other than the principal division.' In the spring of 1856, however, when the Thé care with which Herschel here confines himself to wha.t is proved and established is in singular contrast with the magnificent audacity of his conceptions when he advancnd, with no guide but his own genius, into unfiunitifi.r and awe-inspiring regions ofspccula.tion. It is this combination o.' bolduess ~nd a.ccura.cy, enttmsinsm and caution, which constitutes Herschel's claim to bc ch~sscd in t)te very first nmk tt.mong astronomers. The patient care with which he examined Sit.ttu'n's ring for ten years before he would accept tho theory of its division, and watched a satellite for two years before he would pronounce an opinion on its rotation, w~s iUi importtmt .t piu't uf his character as thé brilliant imagination that cnabled him (as is well cxpresscd on his monument at Upton) to 1 break through thé enclosures of Heaven,c<x~MM jp~rumpere claustra.'

t This refractor, made by Messrs. Merz and Mahler of Munich, has an aperture of twolve inches, its focal length being 17~ feet. Under favourable atmospheric conditions it will bear a magnifying power of 1200.


~)

ring was open to its full extent, the division in the outer ringwas seen by many observers; and it is therefore probable, tbough not absolutely certain, that it is a permanent division in the rings. The other traces of division tbat have been seen from time to time, have only been traceable through short arcs, and bave not long continued visible. Those seen by dînèrent observers, or by the same observer at different times, have occupied different positions, and have belonged to different circles. If each division thus detected were considered as a satisfactory indication of a permanent division through a complete circumference, it would follow that the system consists, not of two or three, but rather of thirty or forty separate concentric rings. Strange as such a conclusion might appear, and manifold as are the conditions of instability tlie complexity of such a system would introduce, we should bave no resource (on the assumption of the solidity of the rings) but either to accept tbis solution of the question, or else to reject the testimony of most accurate and skilful observers-of such men as Encke, the Struves, Captains Kater and Jacob, Mr. Dawes, and tbe astronomers of the Collegio Romano. The telescopes, also, through which these divisions have been repeatedly seen, have been among the most éelebrated instruments of modern times. These appearances are examined and explained in Chapter V.

On. September 19th, 1848, an eighth satellite was discovered by Bond, at Cambridge, America, with tbe Harvard réfractera and by Lassell at Liverpool, with bis great reflector. The orbit of this satellite lies between the orbits of Titan and of the onter satellite, so that it is the seventh in order of distance from the planet. It completes a revolution in rather more than 21 days-at a distance of about 919,000 miles from Saturn's centre.t Judged by its brilThis celebrated instrument bas an aperture of 14~ inches, and a focal length of 21 feet. It will bear a. magnifying power of 2000. Thé telescopes of PuIkoTa and Grcenwich are of thé same dimensions, and manufactured by the same opticians, Messrs. Merz and Mahler of Munich.

t A law shnilar to that known as 1 Bode's Law of the Planetary Distances,' may be traced in thé distances of Saturn's satellites from their primary. Thus, if to each of the series of numbers, 0, ], 2, 4, 8, 16, 32, 64, we add 4, the resulting series corresponds in a remarkable manner with a series representing in order the distances of thé eight satellites of Saturn from their primary (calling the distance of the first satellite 4). The following table presents those relations synoptieally:


liancy, it is probably the smallest of the system of satellites attending on Saturn, and presents in this respect a striking contrast to the two satellites between whosé orbits it rëvolves. It bas received thé name of Hyperion.

Two years later a most remarkable discovery was made. A third ring, inside the two others, and of a singular appearance, was discovered on November 15th~ 1850, by Bond, and a few days later (but independently) by Dawes and Lassell in England. This ring is not bright like the others, but exhibits a dusky, almost purple tinge and through it, the undistorted outline of the planet's dise can be distinctly traced. The inner edge of this dark ring is concentric with the edges of the other rings, its outer edge appearing in general to coincide with the inner edge of the neighbouring bright ring. Mr. Dawes has remarked, however, that this is not always the case,-that the dark ring at times appears to be separated from the bright ring by a distinctly marked interval. This accurate observer considers, also, that the dark ring is occasionally divided into two or more concentric rings. Perbaps the most remarkable circumstance connected with this mysterious formation is the fact that it was not discovered sooner. Had it existed in its present state in the time of the elder Herschel, it would have presented a marked appearance in his gréât reflector. For although the telescope with which Bond discovered the dark ring probably exceeds Herschel's reflector in power (though inferior in size), yet in this telescope it was so distinctly and easily visible, that its detection obviously taxed but lightly the powers of the instrument.* The reflecting telescope of Lassell is probably

i. il. III. iv. V. VI. VII. vin. 44 444 44 4 0 1 2 4 8 16 32 64

4 5 6 8 12 20 36 68

Sj U 4 513 6-36 8-14 11-37 26-36 31-88 76-60

~.3 4 5-13 G~36 8-14 11-37 26'36 31-88 7G~G0

'q

In tho three outer satellites there is some irregularity, corresponding with tho breacli of Bode's law in the case of Neptune.

It is worthy of notice that Bond discovered tins ring ou a night, iu other respecta


little, if at all inferior in defining power to Herschel's great reflector; and Mr. Dawes' extraordinary vision supplements the powers of bis telescope; but the same remark applies :-the dark ring is easily visible with both instruments. Further, soon after its discovery, thia ring was found to be visible with telescopes far inferior in power to many that had been repeatedly directed towards it without discovering it and, as the rings opened more and more, the dark ring became so conspicuous that it was visible, Professor Nichol asserts, in a good achromatic of/o~y ~c/ aper~~6. That the dark ring existed in Herschel's time is obvious from drawings of bis, in which a belt is marked on the planet so exactly concentric with the edges of the bright rings, that it can be no other than this formation/mistaken by the astronomer for a belt on the body of the planet. That it was far less conspicuous in bis day than at present is obvious from the fact that be so mistook its nature, tbough using so powerful an instrument as his great reflector.

Another remarkable circumstance connected witb this ring is its increase in width since the time of its discovery. Thé measurements of the best observers of the day seem to leave no doubt of such an increase, the causes of which will presently be examined. In the spring of 1856, when thé ring was open to its greatest extent, Mr. Bond observed a singular darkening of those parts of thé inner bright ring which lie nearest to the extremities of the apparent longer axis of the dark ring. These dark spaces, as represented by Mr. Bond, are bounded by well denned outlines, forming parts of an ellipse concentric with the other elliptical outlines of the rings, but of greater eccentricity. While tbe semimajor axis of this ellipse exceeds thé semi-major axis of the outer boundary of the dark ring by about one third of the breadth ofthe inner bright ring, its minor axis is not greater tban that of thé inner boundary of thé dark ring. Thus the outlines of these dark spaces meet the outer boundary of the dark ring in acute angles, at four different points. In pictures of thé planet and rings taken at about the same time by other observers, correspondfavourable for ast=ronomica.l observation, but so hazy that only the brightest stars were visible to thé na~ed eye.


ing dark spaces are exhibited, but the darkening is not bounded by a defined outline.~ A similar darkening of the outer bright ring, near thé extremities of thé major axis of the great division, also appears in several pictures of the planet taken at this time. Thèse dusky regions have been termed thé shadows on thé ring,' a term not very well chosen, as will presently appear. Figs. 2 and 3, Plate I., exhibit the general appearance of these dark spaces :t their nature is discussed in Chapter V.

In the years 1855, 1856, and 1857, Messrs. Bond and Dawes were occasionally able to trace dusky, ash-coloured, and mottled stripes, concentric with the outlines of the rings. These were not always visible, however they reappeared along different circles on the rings' surface and, in fact, were as variable and mysterious as the dark traces of division.

A singular discovery was made by Mr. Wray during the disappearance of the ring in thé winter months of 1861-62. Observing Saturn on December 17th, 1861 (when the dark side of the ring was turned towards the earth), with an achromatic of only seven inches' clear aperture (with which he expected to be able to detect no trace whatever of the ring), Mr. Wray was surprised to nnd the illuminated edge of the ring distinctly visible, not only where it crossed the dark shade on the body~ but also extending on each side of the planet's margin.' Continuing his observations, he was led The same phenomenon is indicated in Plate I. of the first edition (1833) of Sir John Herschel's Outlines of Astronomy.'

t Mitchel, with a less powerfui instrument than Bond used, saw these spaces less satisfactorily. He writM, 'Ibave sometimes been conûdenttha.tthebreadthofthH dusky ring at thé extremities of its. longer axis was much greater than that wlucli would be due to an elliptical figure concentric with the bright rings.' It seems clear, however, that what Mr.'Wray bas described as 'thé edge of thc e ring crossing the dark shade on the body,' was a stnp of the planet's surface. For, at thé time of this observation, the earthwas on the northern or dark side of ttie ring, and thorefore, in an inverting telescope, the bright pdge of the ring must have been thé upper boundary of the dark surface and thé sun being on thé southern side of the, ring, the shadow of the ring was north of the ring, or, in an inverting tolescope,below the ring. Both thé dark stripes being below the bright edge of the ring, of course this edge could not be seen hetween them. But thé sun being much more elcvated the plane of thc ring on one- side of it than the earth on t.he other, it is clear that a. strip of the planet's surface must have been visible between tho two dark st ripes, and it is this strip (I imagine) which Mr. Wray mistook for thc rim of tlie ring. Mr. Wray's sketchps do not, it is truc, accord vory well with this explanation but it is possible that, in drawingthcse-figures (which he exprcssiydescribes F


ik< (

(Dec. 23rdj to suspect that the edge of the ring was thicker and somewhat nebulous about the region on either side, where it joins the planet's Hmb.' Finally, on Dec. 26th, he completed the discovery of certa-inly the most singular phenomenon detected in thé appearance of the rings, since the discovery of the dark ring. The atmosphere being fine, and thé image of Saturn exquisitely steady and well defined,' he observed a prolongation of very faiut light stretched on either side from the dark shade on the bail, overlapping the fine line of light formed by the edge of thé ring, to the extent of about one-third of its length, and so as to give the impression that it was the dusky ring, very much thicker than the bright rings, and seen edgewise, projected on the sky.' He saw this faint overlapping lig'ht on four other occasions, in January, 1862. M. Otto Struve, using the magnificent refractor of Pulkowa, rediscovered these singiua,r appendages when thé plane of the ring was passing through the sun, in May, 1862. M. Struve observed that 5~ hours before the computed time of this passage (which took place, on the 18th 'ôf May, at 8h. 30m. A.M.), one ansa of the ring was plainly visible; and on the 19th of May he was able to trace the luminous appendages along the ansœ. He had seen them less distinctly on May 15th,when they appeared only on the southern (or, in an inverting telescope, the upper) side of the ansae. He describes them as resembling clouds of a less intense light lying on the ansae.' On May 19th, they appeared to him to differ much in colour from the ordinary colour of thé ring to be, not yellow, but more of a livid colour, brown, and blue/ Later, he saw them still more favourably; they appeared unequal in length along the two ansae; extending on one side to a distance equal to about two-fifths of the planet's diameter, on thé other half as far again the breadth of these appendages increased in the neighbourhood of thé planet, giving them the form of sharp wedges.'

as rough), ho was more caroful in giving thé détails of tho appearances wbich tho sketches werc meant to illu.tr:ttp, than thé outlines of thé thin lines of light visible across the dise, and on either side of it.

In Chapter J.V. the reader will find a complote account of the disappearances and reappearanccs of hhc rings in the years 1861-1862.

The observations of Wray and Struvo are recorded in tho 'Reports of the Astro-

1 Socicty,' for Janua.ry, 1863, from which the ab


Mr.Carpenter, usingthe Greenwich equatorial, observed Saturn on the same days as M. Otto Struve, without detecting these appearances. It may therefore be concluded that they are so little conspicuous, that a slight difference in atmospheric conditions affects their visibility. The earth was on the southern side of the rings throughout the observations of M. Struve, and raised more tban five times as high above thé plane of the rings as it had been during the observations of Mr. Wray; it was also nearer to the rings. On the other hand, the sun, which throughout thé observations of M. Struve was nearly in the plane of the rings, was raised from 1° 50' to 2° 16' above that plane during Mr. Wray's observations. The discrepancies between the two accounts are not greater than we might expect from this differ ence in the circumstances under which Saturn was observed. The probable nature of these appendages will be considered in Chapter V. On March 26th, 1863, Mr. Carpenter made an observation of some interest.' When Saturn was passing across the field of view of the transit-circle of the Greenwich Observatory, it appeared to him ~that the dark space between the ring and the hall was much contracted.' Upon looking at Saturn with the equatorial, he ~found that this arose from a great increase in the brightness of the dusky ring, which appeared nearly as bright as the illuminated ring, and might easily have been mistaken for a part of it/* At the time of this observation, however, the earth was raised about 4° 23', the sun less raised above the plane of the ring; thus it is clear from the laws of refraction and reflection of ligbt at the surfaces of transparent média, that the dark ring, whether we consider it to be a semi-transparent solid or m.ud, would not, at thé time of this observation, differ greatly in brightness from the outer rings. The results of Chapter V., however, will be found to afford a more probable explanation, both of the nature of this ring, and of the cause of its brightness when viewed at small angles.

La.stly, two observations by Mr. Dawes, rather singular than particularly valuable, are recorded in the February number of the Astronomical Reports' of the year 1863. Ife observed the transit of the shadow of Titan (the largest and brightest satellite) across 'Reports of the Astronomical Soeicty,' April, 1863.

F 2


the disc of Saturn and an eclipse of Titan itself in Saturn's shadow the former a rare, the latter, in Mr. Dawes' opinion, an unique phenomenon.

Among telescopic discoveries may be classed the measures that have been taken of the planet's polar and equatorial diameters, of thé diameters of the various rings, and of the orbits of the eight satellites. The absolute measures, and even the proportions between the several dimensions obtained by different observers, vary considerably. The following are the dimensions of the rings as given respectively by Hind* and Struve

Hind. Struve.

miles miles

Exteriordiameterûfouterring 170,000 176,418 Intenordmmeterofouterring 150,000 155,272 Exteriordianipterofinnerring 147,000 151,690 Intenordiameterofinnerring 114,000 117,339 Breacibhofouternng 10,000 10,573 Breadth of inner ring 16,000 17,17.5 Breaclth of division between the rings 1,500 1,791 Breadth of thé system of bright rings 27,500 29,539 Sp~eobetwecnpia.netand rings 19,250 19,090 Equa.toria.ldmmeterofpla.nct 75,500 79,159

Str uve's measures were probably taken at a later period than those adopted by Hind (? Bessel's).

Thé most remarkable feature, at first sight, in the comparison of the two tables, is the excess of every measure but one in Struve's table over thé corresponding measure in Hind's. This excess will not appear so remarkable, however, when it is considered that, at the immense distance to wbich Saturn is removed from us, a space of about 4,240 miles corresponds to an angle of one second of arc. t The single measure of Hind's table which exceeds the corresponding measure of Struve's, marks a more significant discrepancy. Thus the breadth of the system, which is given by Hind as only 27~500 miles, Struve estimates at 29,539 miles; yet the space between the planet and the inuer edge of the inner br ight ring is given as 19,2.50 miles by Hind, or 160 miles greater than Supermtendpnt of thé Nautical Almanae.'

t That is, abouty~-th part of the angle subtended by the moon's apparent diametcr (mean). Even in thé most powcrfui telescopes an arc of 1" of a great circle of thé ce~est~l sphcre uppears a very small space so thut a double star whose compoucuts are .{t.h or ~-rd of a second npart, severely tests their dcfining po\vers.


the corresponding measure of Struve. In other words, while Hind gives the ratio between the breadth of thé system of rings and the breadth of the space between the rings and planète as 10 7 exactly, Struve determines the same ratio as somewhat less than 10: 6~. Such a discrepancy is not likely to be accidental and it becomes still more significant when we compare the ratios just given with thé corresponding ratios obtained by Huygens in the 17th, and by Herschel near tbe end of the 18th century. As ah-eady mentioned, thèse were respectively 10:10 and 10:8. Thus it would appear that from the first discovery of the rings to the present time, thé ratio of the breadth of the rings to tbe space between the rings and planet bas been continually increasing. As it does not appear tbat anyperceptible change bas taken place in the exterior diameter of thé outer ring, it would follow that thé rings bave been continually spreading inwards. The absolute increase in the breadth of the rings, and the probable cause of this singular phenomenon, will be discussed in Chapter V.

At the time of the first discovery of the dark ring, its breadth was variously estimated–thé lowest estimate being 6,000 miles, the highest not exceeding 8,000 miles later, this ring appears to have grown broader, and the latest estimates of its- breadth vary from 8,000 to 10,000 miles.

The compression of Saturn's globe bas not been satisfactorily determined. It is usually given as ~tb that is, the polar diameter is considered to be less tban an equatolial diameter by about -j~tb of such diameter. Herschel, on the other hand, considered tbe compression less than Y~r~ Hind gives it as about y~yt.b and in the ~Nautical Almanac' it is assumed to be thé same as the compression of Jupiter's globe, or about -y~th. It is obvions that if the compression of Saturn's globe were accurately known, as well as the proportions of bis equatorial diameter to the internai and external diameters of his rings, then the exact appearance of the system at any moment could be readily determined. We should only have to calculate (from the known orbits of Saturn and the earth about the sun) the élévations of thé sun and the earth above the plane of the ring: these being known, the figure of the rings, thé position of their shadow on the planet, and thé position


of the planet's shadow on the rings, are simply matters of calculation. Now it happons that if either of the tables given above be applied to such a calculation, the moment chosen being that at which thé earth attains its greatest élévation above the plane of the ring (as in Marcb, 1856), the calculated appearance of the system does not correspond with pictures taken at that time with the most powerfui telescopes, unie 's we suppose Saturn's globe to be much more compressed than the best observers have considered it. For in these pictures the dark division on the ring is visible above the edge of the planet's disc (in a picture taken by Bond with thé Harvard refractor nearly the whole breath of the division is thus visible), and it can readily be shown that, for the outer boundary only of this division to appear just touching the dise at its highest point, the compression of Saturn's globe should be nearly ~th if Hind's measures are correct, and nearly -~th if Struve's measures are correct. It is impossible to suppose so many observers deceived in a matter of such simplicity as thé visibility or non-visibility of the great division above the dise of the planet on the other hand, it is equally improbable tbat the compression of Saturn's globe should be so great as ~th or ~th. It seems more likely that some of the measures given above are erroneous. The measures in Tables III. and IV. (Appendix II.) bave been adopted as the best average dimensions of thé rings and planet. Assuming these measures to be correct, and that the compression of Saturn's globe is about the system of rings, when open to their greatest extent, would present the appearance shown in ng. 3, Plate I. and this appearance corresponds very well with pictures taken by the best observers.~

The tbickness of the ring is a quantity too small to be made the subject of measurement, at the immense distance to which Saturn is removed. When the edge of the ring is turned to the observer, thé ring appears, in the most powerful telescopes, The measnres of the planet's equatorial diamcter, of thc exterior diameter of thé outer ring, and of the inner diameter of thé inner ring, adopted in the Nautical Almanac,' are respectively 75,000 miles, 173,430 miles, and 115,330 miles. Thé two first dimensions correspond closely with those I have adopted thc last Mongs, as we havo seen, to a. variable quantity. The compression of Saturn's globe is, howcver, certainly greater than -~th, the amount adopted in thé Nautical Almanae.'


as an inconceivably delicate line of light. Beside it, the filaments of a spider's web across thé field of view of the telescope look like câbles. Sir William Herschel considered that the thickness of the rings certainly does not exceed 250 miles, but of their actual thickness even his great refiector gave no indication. Sir John Herschel considers tbat the rings are certainly not more than 100 miles thick. Bessel, of Konigsberg-, calculated thé mass of the rings, from their effect in disturbing the motion of Titan's line of apsides. He found that their mass must be about y-~s-th part of the mass of the planet. As we have no means of determining the ratio which the mean density of thé ring bears to the density of Saturn's globe, Bessel's calculation does not enable us to determine certainly thé thickness of the system. If we suppose thé mean density of thé rings to be about equal to thé mean density of Saturn's globe, then it follows, from Bessel's determination of the mass of the rings, that their thickness does not greatly exceed 100 miles-about -g-th part of the breadtb of the system. An idea of the proportions of the system may be readily obtained by cutting a ring of stout writing paper, whose exterior diameter shall be 2 inches, and its' breadth balf an inch. If such a ring be sbaded on both surfaces across a breadth of nearly ~th of an inch from its inner edge, and a dark circle about ~th of an inch in breadth be described on both sides of the paper at rather more than kth of an inch from thé outer edge, a tolerably exact conception may be formed of the dimensions of Saturn's ring-system.*

The distances at which the satellites of Saturn revolve have already been mentioned. I shall close the series of telescopic discoveries in the Sa.turnian system by showing how Saturn's mass and density may be determined from thé observed distance of one of his satellites-selecting for this purpose the satellite Titan, the first discovered, and larges! of the system.

We have the following data for the solution of our problem The dimensions of the rings in Plate XII. correspond to a thickness far less than that of the paper on which they are engr~ved, even if wc suppose the thickness of the rings to be 250 miles. On tho seule of Plate I. thé thickness of tho rings would probahly be represented pretty cxactiy by the thickness of thé paper.


The moon revolves round thé earth in 27'32166 days, at a distance of 238,767 miles; Titan revolves round Saturn in lo'94a43 days, at a distance of 759,990 miles. We may, for our present purpose, consider both orbits as circles described witb uniform velocity.

First, let us consider what proportion Saturn's mass should bear to that of the earth, that a satellite at Titan's distance sbould move with the same velocity as the moon. This imaginary Titan would, ')f course, be longer tban thé moon in completing a revolution, in he proportion that thé radius of its orbit bears to thé radius of the moon'sorbit. Hence it follows that the attractive force by which onr pseudo-Titan would be retained in its orbit is less than the earth's fLttractive force on the moon, in the proportion of the moon's distance from the earth to Titan's distance from Saturn. For the direction of the moon's motion is altered through four right angles while she completes one revolution, and so of Titan and the former period is less than the latter, and therefore (since the velocities are equal) the deflecting force in the former case greater than in the latter, in the above-named proportion. Now, if Saturn's mass were eqnal to that of the earth, his attractive force at Titan's distance would be less than the attractive force of thé earth at the moon's distance, in the inverse proportion of tbe s~c~e-s of those distances whereas we have seen that for the false Titan to move as supposed, the former force should be less than thé latter in the inverse proportions of the SM?~6 distances. Thus, if Saturn's mass were equal to that of thé eartb, bis attractive force would be too small; and, it is perfectly clear that for Titan to move in the manner imagined, Satnrn's mass must exceed that of the earth in the clirect proportion of thé distances of Titan and the moon from their respective primaries the diminution of attraction in the proportion of the ~~<~r6S of the distances thus leaves Saturn's attractive force less at Titan's distance, than that of the earth at the moon's distance, in the required proportion.

Now let us take into account the difference in the orbital velocities of the real and false Titans. In the first place, it is clear that since thé actual Titan moves more rapidly than the imaginary Titan, a greater denective power is necessary to alter the direction of Titan's


motion through a given angle in a given time, than would be requisite in the case of the imaginary Titan. And in the case of circular orbits uniformly described, it is easily seen that the former force should exceed the latter in the direct proportion of the velocities of thé real and false Titans respectively. But the direction of thé motion of Titan is moved through a given angle in less time than that in which the direction of motion of the false Titan is so moved for it is deflected through the four right angles while Titan is completing one revolution, and he accomplishes this in less time than the imaginary Titan ~n the inverse proportion of their respective velocities (since their orbits are equal). The attractive force, then, which would have had to be greater on the real than on the imaginary Titan in the proportion of tbeir velocities, if their deflections were equal in equal times, must, in the actual case, be greater in the proportion of the s~CM'es of their velocities. Thus the mass obtained, on our first hypothesis, by increasing the mass of the earth in thé proportion of the distances of Titan and the moon from their respective primaries, must be still further increased in the proportion of the square of Titan's velocity to the square of the moon's velocity. This could be readily effected from the data given above but the calculation will be simplified if we consider tbat the velocity of a body revolving in a circle varies directly as the radius of the circle, and inversely as the period of revolution. Thus, to obtain Saturn's mass, the earth's mass must be increased as the cubes of the distances of Titan and the moon, and the result increased as the squares of thé periods of revolution of the moon and Titan.* Hence,

= the earth's mass x 94'6766. On several accounts this result requires modifying, however. The moon's mass bears an appreciable (though small) proportion to the mass of the earth, and, strictly speaking, it is not about the earth that thé moon revolves, but about Thus,–let d, D be thé respective distances of the moon and Titan from their prirniiries v, y their respective orbital velocities p, p their respective periods then thé

m ass of Saturn = the mass of the earth x y2 but v D D D thus the mass

n):tss of Satum == thé masa of thé earth x -y– but -==-= thus thé mass

? f p jp ft p

D~'

of Satarn==the mass of thé earth x -r.

~p~


the centre of gravity of the earth and moon. Again, Titan's mass bears an appreciable (though very small) proportion to that of Saturn the masses of the rings and of the seven otber satellites disturb Titan's motion and other such considérations bave to be taken into account. But a more important circumstance than any of tbese is, that the attraction of the sun operates, on the whole, to diminish thé earth's attraction on the moon and thus to increase the moon's mean period of revolution about the earth. Taking tbese considerations into account, it appears that Saturn's mass is about 91-433 times as great as tbat of the earth.

Saturn's volume exceeds that of the earth in thé proportion of the squares of their respective equatorial diameters, multiplied by their respective polar diameters. Thus, Saturn's volume = thé earth's

(7225°)2(65680)

volume x ~)Y~~) =the earth's volume x 691-362. Now

7924 7898

we have seen that Saturn's mass is only 91-433 times as great as that of the earth. Hence Saturn's density is less tban that of the earth in the proportion of 91'433 to 691-362. If we call thé eartb's mean density 1, then the mean density of Saturn is '1323 Thé mean density of tbe eartb is about ô~ times as gréât as thé density of water. Or, more exactly, if the density of water be called 1, the mean density of the earth is 5'6 74~. Thus Saturn's mean density (if the density of water be called 1) is only -7505; or about equal to the density of oak ('75)., and very little greater than the density of sulphuric ether (-72).* It will be shown, however, in Cbapter VII., that the materials of wbich Saturn is composed are not necessarily different from those constituting our earth. The relative proportions of Saturn and his rings, and of the smaller members of the solar system, are exhibited in Plate I. Tbe dimensions of the satellites must be considered merely as guesses, founded on their relative brightness; no actual measurements have yet been made of these bodies. On the same scale the distances of the satellites would be respectively 2~in.,4~-in., o~in., 6~in., 9~in., Ift. 9in., 2ft. 1~-in., and 5ft. l~.in. The relations of Sir John Herschel, in his Outlines of Astronomy,' remarks that Saturn 'must be composed of materials not much hcavier than cork.' Thé density of cork, ho'wevcr ( water as 1), is only '24 Saturn's mean density is more than three times as grcat.


these orbits are exhibited on smaller scales in Plate VII. The distance of the moon'from the earth, on the scale of Plate I., is 6-6inches, corresponding very nearly to thé distance of the figure representing Saturne eigbth satellite from the figure of the earth. On the same scale the diameters of Uranus and Neptune would each be rather less than 1 inch, and the diameter of Jupiter rather less than 2~ inches, while the diameter of the sun would fall short of 2ft. by less than hait an inch. Again, on the same scale the mean distance of the earth from the sun would be nearly half a mile, and thé mean distance of Saturn from the sun more than 4~ miles. From these relations the reader will see :-first, how insignificant are the dimensions of our earth compared with those of thé larger members of our System secondly, how small even these globes appear when compared with the sun and lastly, how minute are the proportions even of that gigantic globe when compared with the distances at which bis attendant orbs revolve around him.* Only the most powerful telescopes exhibit (under favourable atmospheric conditions) the complete series of phenomena described in this chapter. The two inner and the seventh satellites of Saturn are especially difficult objects. Mr. Wray records, however, that Mimas and Enceladus were visible in December, 1861, (when the dark side of the ring was turned towards the earth,) with his achromatic of only 7 inches clear aperture. The third, fourtb, and fifth satellites are not very dimcult objects. The nfth is slightly brighter than thé other two but ail three are visible with a good achromatic of 4 inches aperture, the atmosphere being clear and steady. f The sixth and eighth can be readily detected with telescopes of When we compare the dimensions and orbits of the satellites with the diameters of their primaries, we do not nnd thé same uniformity of disproportion. Thus, while the satellites of Jupiter and Satum are mere atoms compared with their primaries, thé volume of the earth does not exceed that of the moon more than nfby-ûvo times on the other hand, while thé three outer satellites of Saturn, tho outer satellite of Jupiter, and our own moon, rovolvo at distances from their respective primaries compared with which the diameters of those primaries appear very small, the same is not true of thé other satellites of Saturn and Jupiter. The three inner satellites of Saturn revolve in orbits of very moderate dimensions, the mean distances of ail falling within five and a half semi-diameters of Saturn.

-t- 'Wargentin relates that hc saw thé nve hrightest satellites with an achromatic of 10 fcet focal length. On December lOth, 1793, Sir Wm. Herschel saw them with a


moderate power, Japetus requiring a power of 100, and Titan being easily visible with a power of 80. In gênerai,'Japetus must be sought for at a considerable distance from the dise of his primary. The lowest power with which the rings become visible (as such) is about 50.* A power of 150 is required to exhibit them with distinctn.ess. The division between the rings can be seen with a power of 200, when the rings are open to nearly their full extent and viewed under favourable conditions. Under the same circumstances, the dark ring may be seen, as already mentioned, with a good achromatic of 4 inches aperture. The division in thé outer ring and the variable divisions are only visible with a few of thé finest reflectors and refractors in the world.

The belts on the surface of thé planet are visible, under favourable atmospheric conditions, with a good achromatic of 4 inches aperture. In general, however, they require telescopes of greater power to reveal their outlines with distinctness.

No object in the heavens presents so beautiful an appearance as Saturn-viewed with an instrument of adequate power. The golden dise, faintly striped with silver-tinted belts the circling rings, with their various shades of brilliancy and colour and the perfect symmetry of thé system as it sweeps across the dark background of the field of view, combine to form a picture as- charming as it is sublime and impressive.

power of 60 applied to a refcctor of 10 feet focal length. They can be detected, however, with smaller instruments. I have repeatedly seen aïï five with perfect distiuctness thi*ough an achromatie of 4 inches aperture, and 5~ feet focal length. Since the diameter of Saturn when in opposition is about 19~-2, a power of 50 presents him to the eye with an apparent diameter of 16~rather greater than thé mean apparent aemi-diameter of the moon and it might at nrst sight appear that when the planet has so great an apparent diameter, thé rings must be consptcuonsly visible. Such is not the case, however and, in fact, this mcthod of estimating the appearance of the magnified dise of a planet is altogether dcceptive. The dise really appears of the dimensions calculated but, in the first place, thé apparent size of thé moon is over-estimated by tlie unaided eye; and, secondly, when we so view thé moon, its dise is not perceptibly distorted by atmospheric undulations, whereas thpse undulations are ail magnified fifty-fold when we use a telescopic power of fifty, and thé dise of a planet so viewed is corrcspondingly distorted. If to tbcse considerations be added the difference in the illumination of Saturn and of the moon, (see Chap. YIL), and the loss of light by reflection at the surfaces of thé lenses and by absorption in passing through them, it will readily be seen that an observer who should found bis expectations on such a calculation as that given above, would be altogether disappointed by the view he would actually obtain of the planet.



CHAPTER IV.

TIIE PERIODIC CHANGES IN THE APPEARANCE 0F SATURN'S SYSTEM.

IN describing his orbit about the sun, Saturn retains the direction of his polar axis (or axis of rotation) unaltered, or very nearly so. As in the case of the earth, there are small motions of this axis, owing to which, in the course of many thousands of years, the poles of the Saturnian beavens travel witb an undulatory movement round two opposite small circles of the celestial sphère but so far as a single revolution about the sun is concerned, we may consider thé polar axis of Saturn as retaining its direction absolutely unchanged. This axis is inclined at an angle of 63° 10' 32" to the plane of Saturn's orbit-in other words,the plane of Saturn's equator is inclined at an angle of 26° 49' 28" to the plane in wbich Saturn moves. I propose, in this chapter, to consider thé effect of this inclination in producing changes of appearance in Saturn's rings and dise, and in modifying the apparent orbits of his satellites leaving to a future chapter the consideration of the variations- due to the same cause-in the Saturnian seasons, and in the appearance of the rings to the Saturnians.

The complete revolution of Saturn's vernal equinox occupies upwards of 412,080 years, the annual precession of his equinoxes being 3~-146. The right ascension of thé north pole of the Saturnian ecliptie is 18h. 23m. 31'7s.; and the declination G7° 22' 20"N. The poles of the Saturnian heavens revolve in two small circles, having this point and the opposite point on the celestial sphere for their respective poles, thé angular radius of each small circle being 26° 49' 28".

At present no conspicuous star lies near either pole of the Saturnian heavens. The right ascension of the northern polo is 2h. 23m. l-7s., the declination 82° 52~ 36", this pole, therefore, lies near thé northorn foot of Cepheus, and nearly 6° from the polar star thé nearest visible star is 2 Ursse minoris of the fifth magnitude-about 3° from Sat,urn's north pole. Saturn's south pole lies in the constellation Octans, and less th:m 1° from the star S Octantis of the fifth magnitude. As with the earth, the conspicuous stars, a Draconis and a Lyrre (the bdlliant Vega) are possible north-polar stars for Saturn, and Argus is a possible south-polar star but many centuries must olapso bofore any of these stars will occupy such positions.


The plane of the rings coincides in general with thé plane of Sat~irn's equator, but is subject to oscillatory movements, whose extent and period have not yet been determined. Such oscillations will not be taken into account in considering the general changes of appearance presented by the ring, as, following the planet, it sweeps on its path round the sun.

In fig. 1, Plate VIII., let N r N'M be Saturn's orbit, E E'E"E"' the orbit of the earth about s, the sun let N s N' be thé line of nodes of Saturn's orbit on the eclïptic, being the ascending, and S the descending node suppose, also, that N Q N'R represents the projection of Saturn's orbit on the plane of the ecliptic. The longitude of the ascending node of Saturn's equator--and therefore the mean longitude of the ascending node of his ring–on the ecliptic, is at présent 167° 43' 29~while the longitude of the point N is 112° 29' 18": so that if we draw the line Q s Il inclined to s N at an angle of 55° 14' 11", Q s R is the <ec~o~ of the line of nodes of the ring's plane on the ecliptic. It is not <xc~c~ the line of nodes, since that moves with the ring but wherever the ring may be on N p N~M, the line in which its plane intersects the ecliptic is parallel to Q s R and twice in each revolution of Saturn this line coincides with Q s n. Now the plane of the ring is inclined at an angle of28°l(/ 22" to the plane of the ecliptic; hence, when the line of nodes of the ring's plane on thé ecliptic coincides with the line Q s R~ the plane of the rings intersects thé plane of Saturn's orbit in the straight line r s M, such that. the plane r s Q is inclined at an angle of 28° 10' 22" to the plane of Saturn's orbit. The heliocentric longitude of the point F is 171° 43' 35"; the latitude of r is 2° 8' 26" N; and the arc N p is 59° 15' 42" The line p s M gives the direction of the line of nodes of the ring's plane on Saturn's orbit; wherever the ring' may be, the line of nodes is parallel to p s M, and when Saturn is at p or M~ the line of nodes coincides with the line p s M.

Let us now trace the motion of the ring through a revolution about the sun, starting from the point p. In the first place, let us neglect ail consideration of the earth's motion in her orbit, and suppose the observer to be placed at thé sun's centre. The arc from r to Q is 32' 15".


When Saturn is at P, P s R is the line of nodes of thé ring's plane on his orbit, and therefore thé line of sight, s P, coincides with the plane of the ring.* Thus, when Saturn is at P, the spectator at s is looking at the edge of thé ring, and it appears to him as a fine line of light inclined at an angle of 26° 49' 28" to the line of Saturn's motion-the eastern extremity of the ring being elevated --as shown at i, ng. 1, Plate IX. As the ring passes on to position II (fig. 1, Plate VIII. ), the line of sight from s becomes more and more inclined to the line of nodes of the ring's plane on the plane of Saturn's orbit. When the ring is at il, thé line of sight from s, inclined at an angle of about 23° to the line il-vm, passes above the nearer, and below the farther half of the ring, and is inclined at an angle of 10° 10' to the plane of the ring :-thus the appearance of Saturn and his rings is as shown at il, ng. 1, Plate IX., the northern side being visible. As Saturn passes on through thé positions 111 and iv to v, the angle between the line of sight from s and the line of nodes of the ring's plane on Saturn's orbit, increases continually. When Saturn is at 111 this angle is about 46°, when he is at iv it bas increased to about 68° and, finally, when Saturn is at v it is a right angle, the corresponding angles at which the line of sight is inclined to the plane of thé ring being respectively 18° 5~, 24° 44', and 26" 49' 28". Thus the planet and rings appear as shown at III, iv, and v, ng. 1, Plate IX., the northern side being still visible. At v the ring is seen opened to its greatest extent, the division in the ring just appearIt must be understood that in 6g. 1, Plate VIII., the curve N QN'R is supposcd to lie in the plane of the paper thus the half N P N' of Saturn's orbit lies above, and thé dottcd half N~t N below the piano of the paper. The lower half of each figure of the ring is supposed to lie above the plane N p the upper half lying below that plane to avoid confusion the figure of thé ring is omitted at the points p and M. The lines t xni t', xiv-xii, xv-xi, T v T~, represent the line of modes of the ring's plane on Saturn's orbit in different positions these lines are paraUel to oné another, and the dotted part of each is supposed to lie below the plane of thé paper. The other lines through tho points 1, 2, 3, 13 (in which thé former set of Unes meet thé line of nodes of Saturn's orbit on the ecliptic), represent the corresponding positions of the lino of nodes of thé ring's plane on the plane of thé eeliptic these lines also are parallel to one another. The proportions of the rings are greatly exaggerated on the scale of the rings thé diameter of thé orbit should bc moro than two miles long on thé present scale of thé orbit thé sun's diameter would be less than ~th part of an inch, the outer diameter of the rings less than 3703~ part of an inch.


ing above the edge of Saturn's dise. Throughout these changes thé apparent major axis of the ring has become less and less inclined to the line of Saturn's motion,. until at v it coincides with that line.

As Saturn passes on to the position ix (ng. 1, Plate VIII.) the line of sight from s becomes less and less inclined to the line of nodes, and the planet and ring pass through the same changes as before, but in a reverse order the northern side of the ring still continues visible, but the apparent major axis of the ring now has its western extremity elevated above thé line of Saturn's motion. Thus the planet and rings appear as shown at yi~ vu, an~ vm, ng. 1, Plate IX. Finally, when Saturn is at ix, ng. 1, Plate VIII., thé line of sight, s M, again coinciaes with the line of nodes, and the ring appears as a fine line of light inclined at an angle of 26° 49' 28~ to thé line ôf motion of Saturn's centre (or as shown afix.ng. 1, Plate IX.).

As Saturn passes from ix to xin, he goes through the same changes, in the same order, as in moving from i to v. But it is plain that the line of sight from s now passes below the nearer and above the farther part of the ring; thus the planet and rings appear as sbown at x, xr, xn and xiu, ng. 1, Plate IX., thé southern side being visible. The western extremity of the apparent major axis of the rings still continues elevated above the line of Saturn's motion until it coincides with that line when Saturn is at xni. Finally, as Saturn moves up to i, the system presents successively the appearances shown at xrv, xv, and xvi, ng. I, Plate IX., thé southern side continuing visible, but the eastern extremity of the apparent major axis of the ring elevated above the line of Satuin's motion.*

The mathematical reader will imd no diiïicuky in ven~ying thé following simple construction for determining the appearance of the ring–supposcd to be viewcd from thc sun. With centre c, ng. 2, plate VIII., describe a. ch-cle Ai: B D, whoso diameter shit.U represent thf apparent major axis of the ring's outer boundary; draw tho diametcrs A n and E D a.t right angles to each other through c draw c F, so that F c B is an angle of 26° 49~ 28"; draw F G perpt.ndicular to c D with centre c describe thé circle o K, K, K, and from c draw lines c K,, c K~, and c Kg. First let K,c B be the angle that, at tho moment considered, Saturn bas swept out around thé sun from the point r (fig. 1) of his orbit; draw K, L, and K, M, perpendieular to C D and c n respectively, and join n L, and D Mi. Then c i.j is the apparent semi-minor axis of thé outer boundary of thé ring. Furthf-r, CD L, approximatelyrppresents the angle at which the line ofsigitt is


Thé variations in the appearance of the system, viewed from the earth, are not different from those just described but they are presented in a less simple succession. Besides the continuous increase and decrease in the minor axis of the ring, corresponding to the motion of Saturn in his orbit, tbere are changes corresponding to the motion of the earth in hers. When the line of nodes of thé ring's plane on the ecliptic is passing across the limits of the earth's orbit, the variations arisingfrom the motion of thé earth are still more marked, as will presently appear. To illustrate the general effects of thé earth's motion in modifying the appearance of Saturn's system, let us trace the motions of Saturn and the earth from the conjunction which took place in thé autumn of 1864, to the conjunction which will take place in thé autumn of thé current year (1865)–neglecting, for the présent, thé departure of the earth from the plane of Saturn's orbit; that is, supposing both orbits to lie in thé same plane. The first-mentioned conjunction took place on October 14th, 1864, at 3h. 9m. A.M., Saturn being at K and the earth at the point in which the line from K, through s, meets the orbit E E~E~ (beyond s). If, then, Saturn Lad not been at this time hidden from view by the superior effulgence of the sun, he would have presented the same appearance (on a slightly diminished scale owingto increased distance) to the observer on earth as to the supposed observer at the sun's centre; inclined to thé plane of the ring, and c D M, approximat~y represents thé angle at ~vhieh the apparent major axis of thé ring's outline is inclined to the apparent path of Sn.turn's centre. [The true va-luRS of these angles are somewhat greater, and are obtaincd by describing circles about c as centre, with radii c i., and CM, rpspectivc'Iy, and dt'awing tangents to these two circles from thé points H and D respectively; thèse will '!)e inclined to the lines C B and c D, respectively, at thé rfquu'cd angles.] Similarly, if thc angle K2C n, or KgCB (greater than two right angles), représenta thé angle swept out by Saturn about the sun (from ?), we can obtain (i.) c J~ or c Lg, thc semi-minor axis of thé apparent outer boundary of thé ring; (ii.) thé angle c B Lg or c 1.3, at whieh (approximately) the line of sight is inclined to thé plane of the ring and (iii.) thé angle c D M.~ or CD M; at wbich (approximately) the apparent major axis of the ring's outline i.s inclined to the line of motion of Saturn's centre. According as thé point corresponding to LI lies above or below A B, the northern or southern face of the ring is visible, and according as the point corresponding to M, lies to the right or to the left of D B, tho castcrn or western extremity of the ring's major axis is elevated aboyé the Hnc of motion of Saturn's centre. If c B represents the semi-major axis of any other outline of tho ring than thé outer boundary, then the line corresponding to c Ll represents thé semi-minor axis of the cor~~oM~ outline.

G


for the line from the earth to Saturn is inclined at thé same angle to P M (or, wbich is the same thing, to the line through K parallel to r M) as the line from thé sun. But as the earth moved on in her orbit, Saturn moving on slowly in his, thé former angle obviously increased more rapidly than thé latter, until Saturn was in quadrature preceding opposition (which happened on January 20th, 186o, at Oh. 5m. A.M.). At this time the earth was between and E' Saturn at i~, and the former angle exceeded the latter by about 6°. Hence, since thé extent to whicb the rings appear opened obviously depends altogether on the angle at which the line from thé spectator is inclined to their planer the rings were opening out more rapidly to thé observer on earth, during the interval from conjunction to quadrature, tban they would bave been to an observer placed at the sun's centre. On thé other hand, as the earth and Saturn move on in their respective orbits to opposition (which takes place on April 17th, at Oh. 32m. A.M.), it is plain that thé line of sight from the earth moves up to coincidence with the line from the sun's centre. During the first part of this interval, thé rings appear to thé observer on earth to be opening out, but more and more slowly, till in the beginning of February they attain their greatest expansion (the line of sight from the earth being then inclined at an angle of about 16° 15' to the plane of the rings). After this the rings appear to close, more and more rapidiy, till finally, when Saturn is in opposition (at in, the earth being in the line from s to 111, near E~), his System presents the same appearancc (on a slightly increased scale owing to diminished distance) to the observer on earth as it would to an observer placed at the sun's centre. As Saturn and the earth move on to conjunction, thé rings continue to close, but more and more slowly, till thé last week of June (the line of sight from the observer on earth being tben inclined at an angle of about 13° 40' to the plane of the rings). After this they open out till Saturn is in quadrature, following opposition (wbich happens on July 16th, a.t If a. ûgure be constructed as shown in the preceding note, to détermine thc appcarance of thé ring as seen from the earth and from the sun at this time, it will bo ibund 1 that the angle at which the lino from thc earth is inclined to thé plane of thé ring, exceeds thé angle at which the line from the sun is inclined to that plane, Ly about 2° 15~.


Ih. 2m. F.M.) Saturn having moved through nearly 2° from ni, and thé earth being between n' and E'~) and thence more rapidly till finally at conjunction (which happens on October 26th, at lh. 16m. P.M., Saturn being at K~ and the earth not far from E), the line from the earth is again coincident with the line from thé sun to Saturn. It appears, then, that although during nearly five months of the synodical revolution considered, the rings will bave been closing up, yet on the whole they-will hâve opened out by the same amount to the observer on earth as to an observer supposed to be placed at the sun's centre.

The departure of the earth from the plane of Saturn's orbit is so small compared with Saturn's distance from the eartb, even when in opposition, that its effect in modifying the appearance of Saturn's rings (as viewed from the earth) is very slight. At opposition, when, in general, this effect is greatest, the opening of the rings may be diminished or increased according to the position of the line on wbich opposition occurs. If this line lies within the angles N s P or N'S M, the opening of tbe rings is slightly increased for when within the first angle, the earth is below thé plane of Saturn's orbit, and also below thé visible face of the rings, so that the departure of the earth is from that face and, within the second angle, the departure of the earth is still from the visible face of thc rings, for the eartb is above tbat face and also above thé plane of Saturn's orbit. On thé other hand, if opposition occurs within the angles PSN~ or MSN, the departure of the earth from thé plane of Saturn's orbit plainly brings the earth ~o~c~v~ the plane of the ring; for within the former angle the earth is below thé plane of Saturn's orbit, and above the visible face of the rings; and within the latter angle the earth is above the plane of Saturn's orbit, and below the visible face of the rings thus the opening of the rings is diminished at or near opposition occurring within these two angles. The increase or diminution is very small, bowever, in either case, and any change in thé opening of the rings when Saturn and thé sun are not in opposition, is in general still less important. There is one case, however, which requires to be noticed. If the earth moved in the plane of Saturn's orbit, it is clear that thé rings could never appear more open to the observer on carth G 2


than they would appear to an observer placed at the sun's centre when Saturn is at v or xiif. The opening of thé rings would, in fact, only actually attain such an extent when opposition happened to take place along one of the lines s y or s xiii~–though thé difference would be inappréciable if Saturn were even in quadrature when at v or xui.~ But since the earth moves in a plane inclined to the plane of Saturn's orbit, the observer on earth is occasionally able to see Saturn's ring slightiy more open than it would ever appear to an observer placed at the sun's centre. For instance~ suppose Saturn at or near xiii~ and the earth at e (as in the winter of 18551856) then we have just seen that the eartb, being sUghfly above the plane of Saturne orbit while moving from e to and below the rings' plane, the rings appear less open than they would if thé earth were in thé plane of Saturn's orbit, or than they would to an observer at the sun's centre; but when the earth bas passed n, and begins to dip below thé plane of Saturn's orbit–that is, away from the plane of the rings-these appear more open to the observer on eartb than they would to an observer at s. In the meantime, Saturn is moving away from that part of his orbit at which his rings would appear most open to an observer at s, and so far as this motion of Saturn's is concerned, the rings would appear to be cbsing to the observer on earth. The departure of thé earth from thé plane of Saturn's orbit bas at first the greater influence but as it gradually becomes slower and slower the effect of Saturn's motion in his orbit begins to show itself,-the rings ceasetoopen~and commence slowly to close. Thus, on January 1 st, 1856, the proportion of the minor to thé major axis of the ellipse presented by thé outer circumference of Saturn's ring to the observer on earth was '4491 on January 15th this proportion was '4ô01 (or very nearly the same as the corresponding proportion-when the ring is most open-to an observer placed at the sun's centre); on March 21st~ this proportion Lad increased to Thé proportion of the minor to the major axis of the ellipse presented by any outline of Saturn's ring (say the outer edge) to an observer at s, when Saturn is at v or xni is '4501.5; the corresponding proportion in thé case of an observc'r on thé en.rth (Suturn bcing supposcd to be then in quadrature to the sun) is '44765. If two ellipses, having cqual major axes, and minor axes in these proportions respectively, were drawn, thé minor axis of the first would exceed that of the second by only ~th part of thc major axis of either.


'4548 ;*on April 15th it had diminished to '4516,though the earth had then attained its greatest distance from the plane of Saturn's orbit and, finally, when the earth again reached thé plane of Saturn's orbit at ?~ this proportion had diminished to '4349. Let us next examine the phenomena presented when the line of nodes of the ring's plane on thé ecliptic is travelling across thé orbit of the earth (E E'E~E~). It is clear that during this passage the plane of the ring must pass once through thé sun once, at least, through the earth; and (unless those two passages happen to be simultaneous) the plane oftbe ring must lie for a time between thé earth and the sun. In any one of these cases the ring will be invisibl e except through telescopes of gréât power: in thé nrst, because the sun is shining on the outer edge, and does not illuminate either face of the ring in the second, because the edge of the ring is turned directly towards the observeron earth; and in thé third, because the dark side of the ring is turned towards him. It may happen, however, that thé plane of the rings will pass more than once through thé earth during the interval we are considering. Let us examine two or three ways in which the passage of the line of nodes across the orbit of the earth may take place. To avoid confusion the words invisible, c~op~e~a~ce and ~c<~e<~?Y~c~ are used without the addition of thé words in ordinary télescopes it is to be understood, however, that in telescopes of gréât power the rings are probably never altogether invisible.

Draw the lines Q'6 R~ and Q~R" parallel to Q s R, and touching the circle E E~E~at the points e and e~, respectively then, when the line of nodes of thé rings' plane on the ecliptic is in any position between Q'n' and Q~R~, it passes across the earth's orbit. Through the points 5 and 9, in which the lines (/ R~ and Q~R" meet the line N s N~, draw p'5 M' and r~9 M~ parallel to r M then, when thé line of nodes is in the position (~ e R', Saturn is either at i~ or M~ and when the line of nodes is in the position Q~e~R~, he is eitberat r~ or M~ thus, whenever Saturn is between the points p~ and pli, or M" and M~ of his orbit, thé plane of the ring intersects At this time thé line of sight from thé earth to Saturn WM inclined at an angle of rather more than 27° 13' to thé plane of the rings. This is very nca.rly thé grentcst angle at which it can bc so inclined. Saturn's appea-rance at this time is rcpresentcd in ng. 3, PJatc I.


the earth's orbit. Now each of thé arcs p'p'~ and M~' is slightiy greater than the diameter of the earth's orbit and therefore each is approximately equal to one third part of the circumference of that orbit. And since Saturn moves along tbe arcs l~p~ and M~i~ with a velocity rather less than one third of the earth's velocity in her orbit, it is clear that Saturn will occupy rather more time in traversing either of the arcs p'p~ or M'M~, than the earth in travelling once round her orbit; in other words, the line of nodes of the ring's plane on the ecliptic occupies rather more than a year in passing across the earth's orbit. The actual interval is about a year and a week for the arc p~, and about a year and three weeks for the arc M~ M~

Now let us suppose that when Saturn is at p~ (and the line of nodes in the position Q~ n~ the earth is at or near n. The eartii moving on frorn n, continues in adva.nce of the line of nodes while tbat line moves up to the position Q R. During this time tbe earth and sun are both on the same side (thé southern side) of the plane of the ring, which therefore is visible during this interval. But when the line of nodes bas arrived at the position Q s R (Saturn being at r) the plane of the ring passes through the sun, and the ring disappears. After Saturn has passed the point p the sun is on the northern side of the ring, and the earth (somewhere between e' and 7!/ on its orbit) is on the southern side of the rino- the ringis therefore still invisible. When the earth, passing on towards E~ meets the advancing line of nodes, the plane of the ring passes through the earth, and at this epoch thé ring is invisible as before. But as the earth now passes to thé northern side of the ring's plane-the sun being also on the northern side of that plane-the ring again becomes visible. The earth proceeds to traverse tbe partof E~E~of her orbit; when the earth bas nearly reached I/ Saturn is at p~ or the line of nodes is in the position Q~c'R~ thus the earth does not pass again through the plane of the ring, whose line of nodes on the ecliptic now passes beyond the range of thé eartb's orbit.

The interval ia different for the two arcs p'p" and M~: In the former Saturn moves with a nn'an daily veloctty of about 2~ 3~-4-; in the latter with a. mcan daily velocity of abont 1~59~-0. Thus the interval for tho arc M~ is greater than the mterval for thé arc p~, in the proportion of about 28 to 27.


It appears, then, that in thé case considered, the plane of thé rings passes only once tbrough the earth there is one disappearance, and one reappearance of thé ring; and for some weeks between these events the ring is invisible.

Again, if we suppose that when Saturn is at ]/ the earth is at E~, it is clear that in this case also thé ring's plane will only pass once through the earth this will take place before Saturn reaches P. Thé plane of the ring will then disappear, and continue invisible until the planet passes thé point p. After this, the sun being on the same side of the plane of the ring as the earth, thé ring will be visible.

Further, if the earth is anywhere between n and E"* when Saturn is at r', the plane of the ring will pass only once through the earth, and there will be one disappearance and one reappearance. But now let us examine another case, and as it happens that in the years 1861-1862 thé rings actually~exhibitedthephenomenacorresponding to this case, let us take the actual dates of 'the disappearancesand reappearancesofthe ring in those years. When Saturn was atthe part p' of his orbit, in the autumn of 1861, the earth was approaching the point E, and the southern side of the ring was visible. On Nov. 23rd, 186 Ij at 3 F.M., the earth was atE, Saturn at and thc line of nodes of the ring's plane on the ecliptic was in the position 6 E so that thé plane of the ring passed through the earth thus the ring disappeared at that instant, and the earth passing to the northern side of the ring's plane, the ring remained for a time invisible. On Feb. Ist, 1862, at 3 A.M., the earth was at E', Saturn at p~, and the line of nodes in the position g~/7 T~ so that the plane of the ring again passed through the earth thus thé ring was invisible at that instant; but the earth passing to the southern side of the ring's plane,t the ring reappeared. The ring continued visible until Saturn arrived at the point r, when thé ring's plane passed through thé sun. This took place on May 18th, 1862, at 8h. 30m. A.M., thé earth being then at E~. Thé ring disappeared at this instant, And H. few degrees beyond thpsc points in fact, over the whole of thé arc eE~, except about 7° from thé points e and <

t Fig. 1, Plate L, represents Satarn a day or two after this reuppf'arance. T])c sun being raised about 1° 38' aboyé the plane of thé ring, thé shadow is visible as a dark Jinn crossing Siltujn's dise.


the sun illuminating only the edge of the ring. After this, the sun being on the northern, the earth on the southern side of thé ring's plane, the ring continued for a time invisible. Finally, on August 13tb, 1862, a.t 4 A.M., the earth was at E~, Saturn at~ and the line of nodes in the position <~8 E~ thus the plane of the ring passed through the eartb, and thé earth passing to the northern side of this plane, the ring again became visible. When the earth had reached E (that is, in November, 1862), the line of nodes had passed to the position 0~6~ thus the northern side of the ring bas since continued visible.

It appears, then, that while the line of nodes of the ring's plane on the ecliptic was crossing the earth's orbit in the years 1861-62, the plane of the ring passed three times through the earth, that thé ring disappeared twice and reappeared twice, and continued invisible during two intervals, the first of nearly ten weeks, the second of twelve weeks.

If thé earth had been at e' when the line of nodes bad reached the position Q'e R~ it is clear that thé plane of the ring would bave passed three times through the earth in this case also. Thé first passage would have taken place before Saturn reached thé point r, until whicb time the rings would have been invisible. Tbey would bave become visible when Saturn had passed the point p, and continued so until Saturn had very nearly reached the point p~ when -the earth being near e~–thé plane of the rings wuuld have passed twice through the earth, disappearing at the first passage and reappearing at the second.

Furthet', if the earth is anywhere on the arc e E e', and for a few degrees beyond the points e and e~ wben Saturn reaches the point p~, thé rings' plane will pass three times through the earth, and there will be two disappearances of the rings, and two reappearances.

Similar remarks apply to the passage of Saturn through the arc M~M M~ of his orbit. Thus, if the earth is anywhere on the arc e E~, or a few degrees beyond the points e and 6~, when Saturn reaches thé point M~, the rings' plane will pass three times through the eartb, and there will be twu disappearances and two reappearances of thé rings. But if the earth is anywhere ou the remaining arc of its


orbit when Satura arrives a.t M~ the rings' plane will pass only once through the earth, and there will be one disappearance and one reappearance.

In general, when the plane of the rings bas passed through either tbe earth or tbe sun, the rings disappear or reappear. For, it is clear, tbat, if before the passage of the rings' plane through thé earth their illuminated side was turned to the observer, then after such passage the earth must be on the darkened side of the rings, and vice ~ers~. And again, if before the passage of the rings' plane through the sun, the earth and the sun are on the same side of the rings' plane-then, after such passage, the earth and thé sun must be on opposite sides of the rings' plane, and vice It may happen, however, that the plane of the ring passes through thé sun and the earth at the same or nearly the same instant of time and it is perfectly clear that, in this case, if thé ring is ininvisible before sucb passage it will be invisible after it, and vice Thus, if the ring's plane passes only once through the earth at this passage of the nodal line across the earth's orbit, there will be no interval during which the ring is invisible (except the brief interval of the passage of thé ring's plane through the earth and thé sun) and only one such interval if the ring's plane passes three times through the earth. It will readily be seen tbat in the former case Saturn and the sun would be in conjunction at the double passage, and Saturn therefore invisible;* in the latter case Saturn would be in opposition to the sun, and therefore favourably situated for observation.

Again, two passages of thé earth through the plane of the ring may coincide. This will occur if, when Saturn is at Pl, P~, M~, or M", the earth happens to be on one of the points separating the two arcs of its orbit mentioned above. Thus, if the earth is a few degrees beyond the point e when Saturn arrives at r~ the line of nodes of the ring will overtake the earth (which is here moving in a path inclined at a very small angle to that line); but before the ring's plane bas passed beyond thé eartb, the rapid motion of the latter To avoid confusion no notice. has been taken of thé invisibility of Suturn !).t and near conjunction, in tbe description of tho pa~ge of the nodal line of thc ring's plane across the clliptic.


carries it (as the angle increases at which the direction of such motion is inclined to the line of nodes) again in front of the line of nodes, and the rings only disappear for the comparatively brief interval during which their plane passes through the earth. A simiiar double passage will 'happen if the earth is a few degrees from wh en Saturn reaches p~; for, in this case, when Saturn is approaching p~ the earth will have moved round in its orbit (having passed once through the plane of the rings), and have reached the line of nodes; but before the earth bas passed through and beyond that line, thé direction of the earth's motion will have become inchned to the line of nodes at so small an angle, that that line will again pass in front of thé earth. The earth will simUarly banc. for a short time in thé plane of thé rings, without passing through and beyond it, if, when Saturn reaches M~ or M~, the earth is a few degrees from e or beyond In these cases it will be seen that the rings are visible both before and after the double passage. It is plain, also, that at such a double passage the earth would be for a longer time in the plane of the rings than when merely passing through that plane, and thus thé phenomena attending the disappearance of the ring would be very favourably seen. The coincidence described is, of course, very uncommon; if, however, the earth is near one of thé points mentioned, she hangs longer in and near the pla.ne of the rings than at an ordinary passage through that plane.* If the earth passes through the plane of the ring when Saturn is at or near opposition, an observer on earth will be between the planes bounding opposite faces of the ring for about 8 seconds- the thickness of the rings being asIt is stated in Sir John Herschel's Opines ofAstronomy' that thc plane of Saturn's ring in crossing thé earth's orbit generally passes twice through tj earth and in Hmd's 1 Introduction to Astronomy' that there arc usually two, if not three, disappearances about thé time of the planet's arriva thé nodes.' Thé above invest.g~on shows that the earth can ncver pass twicc ~c~ through thé plane of the rings during the passage of this pl.no across thé earth'. orbit, but may pass 1) once or three times. And again, it is clear that there may be two disajpe r ~cr~e~ or, if reappearances and disappearances are~hin~ under thé term 'disappearances,' then there may be two or fom. but can t Thé case supposed by Herschel would leave the earth on of the ring's plane before as after the passage of that plane across the c~t ~1 the case supposed by H.nd would Icare tho rings invisible after such passage


sumed to be 100 miles--for lie is carried from one plane to the otherwitha velocity equal to the difference of the velocities of the earth and Saturn, or at thé rate of 44,000 miles an hour. If the earth passes through the plane of the rings when Saturn is in conjunction, and Saturn could be seen at such a time, the observer would be carried from plane to plane of the opposite faces of thé ring in 4 seconds. On the other hand, when two passages of the earth through the ring's plane coïncide, an observer might be nearly nine hours between thé planes bounding opposite faces of the rings (supposing the thickness of the rings to be 100 miles),-not being carried through both planes, but twice through one plane. If two passages were very nearly coincident, an observer might be four or five hours between the two planes at one passage, and an hour or two at the other, passing each time through both planes. When the earth passed through the plane of the ring in November, 1861, the time of passage of each point on the earth from plane to plane of the bounding faces of thé rings, was very short the corresponding passage in Febluary, 1862, occupied a longer interval. Another consequence of the earth's motion in her orbit is that the shadow of the rings on the planet, and the shadow of thé planet on the rings, become visible. It is clear that to an observer placed at the sun's centre these shadows would at ail times be invisible,since those parts only of the rings and planet are in shadow from which the sun is invisible (through the interposition of parts of thé planet and rings respectively), and the sun being invisible from them, they would be invisible to an observer placed in thé sun. And the more nearly the line of sight from the eartb to Saturn approaches to coincidence with the line from the sun to Saturn, the less conspicuous will the shadows be. Thus, when Saturn is in quadrature to the sun, at which time the angle between these lines is greatest (having an average value of about 6° at that time*), both sbadows are, in general, more conspicuous than at any other time but there is a difference between the two shadows in this respect. When thé rings are open to nearly their greatest extent, the shadow of the rings on thé planet is not conspicuous, even When Saturn is in perihelion this angle is 6~ 22~ 2~-6 when he is in ~phclion h. is 5° 41' 50"-2.


when Satum is in quadrature, for thé motion of the earth in her orbit causes very little alteration in the apparent opening of thé rings at this time thus the earth being elevated at very nearly the same angle as the sun above the plane of the rings, those parts of the planet's dise which would be invisible from the sun (that is, in shadow) are also invisible--or only visible along very narrow strips of their surface-to the observer on earth, in whatever part of its orbit the earth may be. On the other hand, the shadow of the planet on the rings is very favourably seen when Saturn is in this part of his orbit, and in or near quadrature; for the portion of the rings concealed from the observer on earth, and the portion hidden from thé sun (tbat is, in shadow), are shifted from coincidence with each other, through an angle of 5~ or 6~ (according as Saturn is near peribelion or aphelion)" about the centre of tbe rings, and a large part of the shadow of the globe thus becomes visible on one side or the other of Saturn's dise. Further, since thé rings are open to their greatest extent, the shadow, wbich extends nearly across the width of the rings, is less foreshortened at this time than when the rings are less open. Thus the shadow appears as in ng. 3, Plate I., in the form of a broad curved black space, bounded by two elliptical outlines. This figure represents Saturn as he appeared when near the point xiu of his orbit (fig. 1, Plate VIII.), and in quadrature following opposition (that is, when the earth was between E' and E". The sbadow lies to thé right of the planet's dise in reality the shadow lay at this time to the left of Saturn's dise, but in an inverting telescope the shadow appeared as represented. If there were no division in thé rings the shadow would have been visible beyond the uppermost point of Saturn's dise, and for a short distance to the left of this point; for, as we have seen, thé line of sight from the eartn to Saturn was inclined at a slightly greater angle to the plane of the rings than the line from the sun. Since, however, the division in the rings becomes visible above the dise of Saturn, there is no visible sbadow at this point or in its neighbourhood.-f- When Saturn The rings are open to their greatest extent when Saturn is near one or other of the apfiM of his orbit.

t In pic.h.rf-s of Satum hy Bond and oLhcr observers, the division is thus shown. Pos-


(near xm) was in quadrature preceding opposition (in October, 18oo), the shadow presented a similar appearance on the otherside of Saturn's dise.

When Saturn is in other parts of his orbit, the shadow of the rings on the planet is more favourably seen. Thus, if Saturn is at L, and the earth near E-that is, Saturn in quadrature preceding opposition- it is clear that the earth is elevated at a smaller angle than the sun above thé plane of the rings. Thus thé ellipses presented by the rings to the observer on earth have smaller minor axes than the corresponding ellipses that would be presented by the rings to an observer at the sun's centre. The shadow of thé rings is therefore seen outside the outer edge of the rings as a black stripe, whose outline forms part of an ellipse of larger minor axis than that of the ring's outline. Fig. 2, Plate I., represents the appearance of Saturn in an inverting telescope at such a time. He appeared thus in the earlier part of November, 1858. At this time the shadow of the planet on thé rings appeared (in an inverting telescope) to the left of the planet's dise–more foreshortened than thé corresponding shadow in Bg. 3, but sufficiently conspicuous. When Saturn had passed on to quadrature following opposition, or in the spring of 18.59 (the earth being between E' and E~), the shadow of the rings appeared within them* (since thé earth .was elevated at a greater angle than the sun above the plane of the rings), and the shadow of thé planet to the right of thé planet's disc-in an inverting telescope.

As Saturn's ring closes up, the portion of the shadow of the rings visible when Saturn is at or near quadrature increases, while thé sbadow of thé planet on the rings becomes more and more foreshortened. When Saturn is near either of the positions i or ix, the whole of the shadow of the rings becomes visible, at and near either quadrature. As the sun is nearly in the plane of thé rings the siMy the shadow of thé globe has been mistaken for the continuation of the division a.t this point.

As the visible pa.rt of the sh~dow of the rings at such fi time is plainly the shadow of thé dark ring, it will appear probable, from the results of Chapter V., that the shadow is not so dM-k as in the former case, whcre thc shadow is that of thé outer bright ring. It would bo very dLfneult to dctect thé difït.'rencc, even with thé most powci:fu! telescopes.


shadow is very narrow. It appears within or without the outline of thé rings, according as thé earth or the sun is elevated at thé greater angle above the rings' plane. Thus, in Hg. I, Plate I., the whole of the shadow is seen crossing the planet's dise below the putline of the rings. This figure represents Saturn as he appeared in an inverting telescope, a day or two after the reappearance of thé rings in February, 1862, the earth being near E', and Satum neary/. Saturn was at this time between quadrature preceding opposition and opposition. Thé shadow of thé planet on the rings was foreshortened almost to disappearance, and only traceable from its effect in taking off half the breadth of the fine and broken line presented by the ring.

In the other four quarters of Saturn's orbit, the shadows of thé ring and planet present corresponding changes of appearance and position.*

Thé manner in which Saturn's rings move round the sun, their plane remaining always parallel to a fixed plane-or, as it is sometimes expressed, remaining always parallel to itself-may be conveniently illustrated by means of a parallel ru!er. To one of the In Brewster's pdit.OD of 'lerguson's Astronomy,' a table is given for thé deternnnmg the proportion of the minor to thé major axes of the ellipses presented by thé outlines of the rings to the observer on earth. As this table has been calculated on the supposition that the plane of the rings is inclined at an angle of 31° 24~ to thé plane of Saturn's orhit, whereas the true inclination is only 26° 49' 28"; and as, further, the correction for Saturn's geoc~ntric latitude is wrongly given, the table is not very valuable. In the Naut.ical Almanac the éléments for determining the appearance of the ring are given, at intervals of tweuty days. Thé calculation of thèse cléments for any intermedmte day will be aided by Tables VII. and VIII. at the end of this work. (Appendix II.; see, also, explanation of the tables.)

I may notice here a slight error in Hind's valuable Introduction to Astronomy.' In describing thé appearance of Saturn's rings when open to their greatest extent, hewrites Thé caith is then elevated 28° above the plane of thé rings, and as that is the amount of inclination between the plane and the ecliptic, we view thc ring as much open as it will ever be.' The earth, however, can never be elevated so much as 28° above the plane of the ring it is clear that the angle of elevation dépends mainly on thé inclination ofthe plane of the rings-not to thé ecliptic, but to thé plane of Saturn's orbit. The inclination of the ecliptic to thé plane of Saturn's orbit bas an effect in slightly altering the angle of inclination, but not to thé extent implied in the sentence quoted. The earth's orbit is so Bmtdl compared with Saturn's, that, even iftheplaue ofthe ecliptie were Inclined at an angle of 90° either to thé plane of Saturn's orbit, or to the plane of the rings, thèse would never appear much more open than they do under the present arrangement.


movable rods of such an instrument let a ring of paper be fixell so that its plane is inclined at an angle of about 27° to thé face of the rod; then (the other rod being held fixed) let the instrument be opened to its full extent, and closed again by carrying o~ tl~e rod which bears thé ring; then the ring will move through nearly a semicircle (a- point near the centre of which will represent thé sun) in the same way that Saturn's ring moves about the sun. The same motion may be more completely illustrated by such an instrument as tbat represented in ng. 4, plate VIII. If the bandie, H, be turned uniformly in thé direction indicated by the arrow, thé two endless screws, s and s~ will communicate equal and uniform motions of rotation to the toothed wheels, w and w~ thus thé extremities of the rigld curved bars, B and B', will move unifor mly and at equal rates round thé circumferences of equal circles, bearing the bent wire, w~~ with a uniform cranklike motion. If this wire bear a ball~ circled about by a ring, r to represent respectivelySaturn's globe and ring, and a spirit lamp, L, be placed as shown in the figure, to represent the sun, then the motion of thé wire will bear this miniature system about the lamp in a manner that will illustrate more clearlythanany verbal description the motion of Saturne system about the sun.* If ail extraneous light be excluded, the instrument will illustrate the motion of thé shadow of thé rings on Saturn's globe, and the motion of the sbadow of thé globe on the rings. These phenomena are described in CbapterVII. Thé changes in the appearance of Saturne belts in the course ofa complete revolution about the sun, correspond with the changes in thé outlines ofthe rings. Since Saturn's equator is approximately concentric with thé rings, and in the same plane, it would always appear (if it were actually a visible line traced on the surface of the planet) as part of an ellipse similar to and concentric with thé outlines of the ring. Thus when the edge of the ring is turned to the observer on earth, the equator is coincident with the line preIt will bc seen that thé lamp is placed somcwh:it eecentrically, so as t-o correspond with the eccentricity of Saturn's orbit about the sun. Thé wiro is bent at b and (at unequal distances from its extremities) that it may pass freely over thé wick and f!amf of thé lamp. Thc wire can be readiJy removed, and the instrument uscd to illustmfo thé motion of the earth or of any other planet about tho sun. Thé ball, & may bc mad'" of pitk tlie ring, r ?' of card or papcr.


sented by the ring. Wben the northern surface of thé ring is visible, thé equator appears as the half of an ellipse having its convexity turned southwards and when the southern surface of the r;ng is visible, the convexity of the corresponding semi-ellipse presented by the equator is turned northwards.. If the Saturnian latitude-parallels were actually lines on the surface of the planet, it is clear that they would appear as parts of ellipses similar to, but not concentric with, the ellipses presented by the outlines of the rings. Haïf of the equator is always visible, but of the parallels of latitude more or less than half will be visible according to their position on Saturn's globe, and the variations (according to Saturn's position in his orbit) in the forms of the ellipses of wbich tbey form part. Thus, when the convexities of thèse ellipses are turned southwards, parallels on the northern half of Saturn's globe are visible tbrough more than half their circumferences, the visible portion of each increasing northwards, until of parallels near the north pole the whole circumferences are visible; but of parallels on the southern half of Saturn's globe less than thé halves will be visible, the visible portion of each diminisbing southwards, until of parallels near the south pole, the whole circumferences are invisible thèse relations are reversed when thé convexities of the ellipses are turned northwards. Thus the Saturnian belts, whose outlines correspond as to their general contour with parallels of latitude on Saturn's globe, are presented with their convexities turned towards the concavities of the rings' outlines and of thé belta ôn the half of the. dise farthest from the rings a greater part is visible than of the belts on the other half of the dise. It is clear that when the edge of the ring is turned to us (and therefore the equator of the ring presented as a straight line), each of the poles of Saturn's globe lies on the edge of bis dise. When the northern side of the ring is turned towards us, thé north pole becomes visible within the edge of the dise, thé south pole disappearing behind the dise; and when the southern side of the ring is turned towards us the south pole becomes visible, and the north pole disappears. To an observer placed at thé centre of the 'Whpre the. ring crosses tho planet's dise, parts of parallels will of course be invisible this effect is considercd in Chapter VII.


sun, thèse changes would take place in a uniform and continuous manner, just as the opening and closing of thé rings have been shown to do.* The north pole would appear to leave the edge of Thèse changes of appearance, and therefore thé changes of the planet's seasons which depend on them, may be illustrated as follows :–Let p EP'E~, 6g. 3, Plate VJII., represent an oblate spheroid of crystal, or any transparent substance, F o p~ being thé axis, o thé centre and suppose the spheroidto move in a circular orbit in the direction o its axis p o p~ retaining its direction unchanged throughout the motion. Then to an oye placed at the centre of motion, and reforring the motions of thé digèrent parts of the spheroid to the dise presented by it, thé points p and ï~ will appear to move backwards and forwards along two equal lines, p cj~ and p~c~ both parallel to s o N~, not uniformly, but aceording to a simple law. Thus :-draw c o (/ through o, at right angles to ~.tomeetppandp~in cand(/; and with centre c draw the circle PDP (thé lower semicircio is omittedin the figure to avoid confusion); then if p o D be taken to equal the angle that (at thé time considered) has been swept out by the spheroid about thé centre of motion, from the position represented in the figure, and D be drawn perpendicular to r~ will be the apparent position of the pole p at that time, and tl.e Une d o through o will meet p'F' in d', the apparent position of the oth~r pôle p~; so that d 0 d' is thé apparent position of thé axis at thut time. Again, the outline presented by the spheroid will throughout the motion appear to touch two lines, TTA/Y~ and~a~, para!lcl to itnd equidistantfromso~. Thus thé eccentricity of the disc'soutliBewilluppear continually to diminish as thé pole moves to c, thence to increase as thc pole moves to p, and to go through similar changes as the pole returns to p. The point o (referred to the disc's outline) remains fixed throughout. [In reality, of course, the motions of the points p and p~ (referred to the spheroid) are not in straight lines but circles, thé motions of thé axis p o p' (referred to the spheroid) carrying that dine over thé surface of a double cone, whose semi-vertical angle is cop. While thé pole P is moving from p top it is seen througlt the spheroid, and p~ is on the nearer hemispheroid; in the following half-revolution these conditions are reversed.] Again, let circles liaving p, and p~ as their poles (that is, latitude-circles), be traced on the surface of tho spheroid. For instance, let circles A A', a a' corresponding to ajctic circles (df'tcrmined by thé points A~, in which YT~ and tangents parallel to s o~, meet thé ellipse PBp'E~) bo so traced; and again, let circles T'r~ and t t' corresponding to thé tropics (determined by the points T, in which z z' and z z', tangents perpendicula~r to s o meet thé ellipse p B p~) be so traced and, lastly, a circle E B' corr~sponding to the equator of the spheroid. Then these cireles, whieh, in the position of the spheroid represented by the figure, appear as straight lines, will in other positions of thé spheroid appear as ellipses, niways tonehing the outlinc of the spheroid's dise, one part. of each such ellipse (up to the points of contact with the dise) being soen ~roM~ thé spheroid, thé otherupon the nearer hemispheroid the centres x, L, ]/ and K.~ will appear to move backwards and forwards along the lines K L i/~ and K~, (just as thé points p and p' mo've along rp and r'p', so that when these two poles n.re respectively at d and d', the four centres above-named will be found respectively at < f, j~' and </) and, lastly, if lines parallel to o be drawn through thé points A, T', J~, t', T, B, t, and a', the ellipse into which the cirele AA~ is projected will throughout ftppcar to touch the line Y x' and the parallel through A, thc eorresponding ellipse of the cirele T T' will appear to touch the parallcis through T and T~, and so thé ellipse corresponding to each of the eirch's will appear continually to touch thé two parallel lines corrcsponding to it. From tho H


the dise as the northern face of the rings began to appear, to travel farther and farther from the edge as the rings became more and more open, and afterwards, as the rings closed, to approach the edge in the same continuous manner-the southern pole being throughout invisible. Then, as the southern side of the rings becarne visible the southern pole would appear, first on, and then within, tbe edge of the dise (the northern .pole disappearing), and would make a similar advance and retreat. The ellipses that would be presented by the parallels of latitude on Saturn's dise, if these were visibly traced on his surface, would open and close in the same continuous manner. But to thé observer on earth the poles would not appear to advance and retire continuousiy. Just as we have seen that, although, viewed from the earth, the rings, in any complete synodical revolution have been opening orolosiog, yet for an interval in each synodical revolution appear to reverse those movements so the poles, while on thé whole they present themselves within the dise of the planet with alternations correlast property it is clearly seen that the ellipses corresponding to thé circles A. A' and <ï a', always meet the outline of the spheroid's dise at the same points, respect! vely, as the lines Y Y' and

The Sgures of Plate XIII. illustrate some of thèse propfrttcs they Indicate (among other matters) the changes of Saturn's appearance during one quarter of a révolution about thu sun, and as seen by a spectator supposcd to be placed at the sun's centre. Only tite visible parts of the ellipses are introduced in thèse figures. F!g. 2, Plate IX., represcnts thé autumn (i.), winter (n.), spring (in.), and summer (iv.) phases for the northern (supposed the upper) hémisphère of a. planet; or thé spring, summer, autumr, and winter phases, respectively, for the southern hémisphère. They a.re placed in order, from right to left, that being thé direction in which a planet wuuld appear to move to an observer plaefd at the sun's centre.

AU the propositions eontained in thé first paragraph of this note may be very easily proved. For insta-nce, to show that the ellipse presented by a latitude-parallel would always appear to touch two lines parallel to s o and drawn at fixed distances from o:-Since thc spheroid's axis moves parallel to itself, the plane of each latitude-circle is carried paraUel to itself, the centre moving parallel to the plane in which the centre of the spheroid moves thus each latitude-circle may be conceived as sliding between two nxed planes, parallel to eacli other and to thé plane of motion of the spheroid's centre these planes meet the apparent dise of thé spheroid (wherever it may bc) in two parallel lines at fixed distances from the centre of thé dise, and the circle touching those planes must therefore be projected into un ellipse touching those lines. And with similar simplicity the other propositions may be proved. They will appear identical propositions to the mathematician. It must bo remarked that thc distance of thé spheroid from thé observer is supposed to be very great compared witli <l)e dimensions of thf spheroid.


sponding to the Saturnian year, yet have another set of movements corresponding to our -own year. Thus at limes they appear to advance from or retire towards the edge of thé dise more rapidly than they would if the earth were the centre of Saturn's motion at others they reverse their movements for intervais of several months, so that the advance or retreat (on the whole) of either pole takes place in an oscillatory manner. The belts on Saturn's surface appear to thé observer on earth to open and close precisely as the rings have been shown to do.

Owing to the immensity of Saturn's orbit compared with the orbii of the earth, he never presents a gibbous appearance. Itwill be obvious from an inspection of fig. 3, Plate Vf., that in the case of Mars (the only superior planet that ever presents a gibbous appearance), the orbits of the earth and planet are ~o related that the line of sight from the earth to Mars may be inclined at a large angle to the Une from the sun to Mars~ and thus Mars may present to the observer on earth a considerable portion of bis darkened hemisphere when this is the case he appears gibbous. The corresponding angle, however, in the case of Saturn, is always small it obviously attains its greatest value for each synodical révolution when Saturn is in quadrature, and for different synodical revolutions such maximum value will vary-witb Saturn's distance from perihelion; but even when Saturn is in perihelion at thé moment of quadrature tins angle is less than 6° 23~. At such a time a portion of Saturn's darkened hemisphere is actually turned to thé observer on earth, and a portion very considerable so far as absolute extent of surface is concerned t yet the alteration in the figure of Saturn's dise is altogether inappréciable, even on applying the most exact micrometrical measurement. That diameter which is most affected (that is, the diameter through the widest part of the darkened lune,) is not This angle m~y be as gréât as 46° 45' if M~rs is near perihelion at the time of either quadrature. In~this case the breadth of thé dark part of his dise (that is, tho greatest width of the lune-sha.ped invisible portion of the dise) is about ~ths of thc diameter of the dise. In NoYember, 1860, Mars presented this a.ppearnnce, hf).ving p~ssed his perihelion on September 16th, 1860, and being in quadrature following opposition on November 23rd.

t The extent of tho-darkcncd part thus turned towards ~s is co~~8Idcra.b~y grcutfr than thé wliole surface of our earth.

n 2


diminished by -g~-otb part of its length. Now this diameter subtencls an angle of about 17" when Saturn is in. quadrature thus the amount by whieh it is diminished corresponds to an angle of little more than g~th of a second.

Since the seven interior satellites of Saturn move in orbits very nearly concentric with the rings, and in the rings' plane, it is clear tbat if those orbits were visi.ble throughout their extent, they would appear as rings of light very nearly concentric with the rings, and similar to tbem in shape. These orbits would tberefore appear to an observer at the sun's centre to open and close uniformly, while to the observer on earth they would appear to open and close in an oscillatory manner. And though the plane of the outer satellite is inclined to the plane of Saturn's orbit at a different angle than the ring's plane, and bas its line of nodes in a different direction, yet the changes in the appearance of this orbit (supposed visible throughout its extent), would he similar to those of the other orbits. The investigation of thé changes in the appearance of the rings, whicb is directly applicable to tbe orbits of the seven inner satellites, is applicable, mutatis '?7M~a/~M, to the orbit of the outer. Like tbe ring tbis orbit opens out to the observer on earth in an oscillatory manner; but thé extent to which it opens is different, and it does not attain its maximum opening in each successive synodical revolution, or its absolute maximum opening in each semi-sidereal revolution, at the same time as the ring. Owing to the inclination of the planes of the eight orbits to thé plane of Saturn's motion, eclipses, occultations, and transits are less frequent among the Saturnian satellites than among those of Jupiter. The latter revolve very nearly in tbe plane of Jupiter's orbit, and therefore always appear to lie very nearly in a straight line through tbe centre of Jupiter's dise: thus they are occulted, eclipsed, and transit bis dise at nearly every revolution. On the other hand, Saturn's satellites move in orbits which, if visible tbrougbout their extent, would in general appear as ellipses, wbether viewed from the centre of the sun or from the earth it is only when such ellipses, viewed from the sun's centre would be partly hidden by Saturn's dise, that éclipses of the corresponding satellites can take place and only when snch ellipses, viewed from the


earth would be partly hidden, that occultations or transits of the corresponding satellites can take place. Now the mean distance from Saturn's centre at which thé outer satellite revolves is no less than 2,208,720 miles, and on the scale of the figures in Plate I. this distance would be represented by a line more than five feet long thus, if the orbit of this satellite were visible throughout its extent, it would appear as an ellipse whose major axis would be ten feet long and it is clear that a very small elevation of the point of view above the plane of the orbit would make the minor axis of such an ellipse greater than the apparent diameter of Saturn's dise.* Hence it is only when the plane of the orbit passes through, or very near the sun, that this satellite can be eclipsed and only when that plane passes through, or very near thé earth, that an occultation or transit can occur. Further, as the period of this satellite is no less than 79 days, and as it is only for a brief interval in each revolution tbat the satellite is near Saturn's dise, the chance of an eclipse, occultation, or transit occurring is still further diminished. Saturn may pass thé points of his orbit at whicb these phenomena are possible while the satellite is near its easterly or westerly elongàtion, and fourteen years must then elapse before Saturn is again so situated tbat an eclipse, occultation, or transit is possible. Thus thèse phenomena occur very seldom, and as they may take place by daylight or in weather unfavourable for observation, centuries may elapse before anyone of them is actually visible from the earth.

Similar remarks apply with nearly equal force to Titan and Hyperion. The latter satellite is hardly ever visible owing to its minuteness. Eclipses, occultations, and transits of Titan, though uncommon, happen occasionally.~ As already mentioned, an eclipse of Titan, and also the transit of his shadow across Saturn's dise, were observed by Mr. Dawes 'in the years 1861-1862, when the If the line of sight were inclined 58' to the plane of the orbit, thé minor axis of the ellipse would exceed Saturn's apparent diameter.

t The mean distance of Titan from Saturn's centre is 759,990 miles. On thé seale of Plate I., Titan's orbit (if it were visible throughout its extent) would appear as an e~ipse having a major axis 3~ feet long; and if the line of sight were inclined to the plane of Titan's orbit in an angle of about 3° 1I/, this ellipse would be altogether clear of Saturn's dise.


plane of the ring (which is, to the sense, the plane'of Titan's orbit) passed very near both to the sun and the earth. Eclipses, transits, or occultations of Titan are only possible when the plane of his orbit about Saturn is so situated.

Eclipses of the remaining satellites are net uncommon occurrences. They increase in frequency as the distances, and consequently the periods, diminish. The two inner satellites very frequently transit Saturn's dise, and are as frequently eclipsed or occulted. These phenomena are not very often observed, however, the satellites themselves being so difficult to detect. The eclipses of Saturn's satellit-es may be considered in another manner. Since the sun's diameter is 854,928 miles, Saturn's mean distance from the sun 874,321,000 miles, and his mean diameter 68,965 miles, it may easily be calculated that thé cône of total shadow cast by Saturn extends to a mean distance of about 76,718,000 miles. The axis of this cone is not in general coincident with thé orbit-planes of Saturn's satellites, but passes on one side or the other of tbose planes. The intersection of each orbit-plane with the conical surface of the shadow is therefore an ellipse,-that part of each such ellipse which lies beyond Saturn being in darkness. If the orbit corresponding to any such ellipse (that is, the orbit whose plane meets thé surface in such ellipse) lies without the darkened part of the ellipse, the satellite cannot be eclipsed; but so long as the orbit falls within the ellipse, the satellite is eclipsed at each revolution. The planes of thé seven inner satellites are (to the sense) coincident with the plane of the ring,, and parts of the darkened portions of the ellipses in wbich the plane of thé ring intersects the conical shadow of the planet are represented in the eight figures of Plate XII. These figures correspond to Saturn's positions at eight different periods :-thus, ng. 1 corresponds to Saturn's position when the plane of the ring passes through the sun fig. 8 corresponds to his position one quarter of a Saturnian year later, or when the sun is at its greatest possible elevation Since neither Saturn nor the sun is perfectly spherical, the space hcyond S~turn winch (neglecting the refraction of Saturn's atmosphère) reçoives no light from thé sun, is not a eonf, but is bounded by a surface of a less simple form.


above the plane of the ring; the six intermediate figures correspond to his position at six intermediate epochs separated by equal intervals of time.* If thèse ellipses were completed, and the orbits of the seven inner satellites traced at their proper distances from Saturn's centre on the scale of the figure, it would be found that thé orbits of ail the seven satellites intersect thé shadow in fig. 1 (which extends indeed more than eighty times as far as thé orbit of Hyperion) the orbits of thé four inner satellites intersect the ellipse of ng. 2, the orbit of the fifth just passing clear of it; the orbits of the first two satellites (Mimas and Enceladus), intersect the ellipse of fig. 3, the orbit of Dione being not very far beyond it the orbit of Mimas alone intersects the ellipse of ng. 4 and ail the orbits Ue.beyond the ellipses of the remaining figures. As about 384 days elapse before the ellipse changes frorn the form shown in any of the figures to that shown in the following figure, it appears that for about a year after thé passage of the plane of the ring through the sun's centre, the fifth satellite is eclipsed at each revolution the same must have happened for a similar time before the plane of the ring reached the sun's centre :thus, twice in every Saturnian year the fifth satellite is eclipsed at each revolution (that is, every 4~ days), during an interval of about two of our years. The corresponding intervals increase as we proceed successively to the fourth, third, second, and first satellites. In thé case of Mimas each such interval contains about seven years. Amongst the numerous eclipses of the different satellites in thé course of a Saturnian year, several must be partial, thé satellite merely grazing the shadow of thé planet. Such phenomena, bowever, would hardly be detected by the observer on eartb, even in the case of Titan, still less in thé case of the smaller satellites. The eclipses of the outer satellite might be treated in a similar manner, replacing thé plane of the ring by the orbit-plane of that satellite. It would be found that the satellite -would pass through the shadow only for a few days before and after the passage of the orbit-plane through the sun's centre.

Occultations of the satellites by the ring, and transits of the Each mterv~l is thercfore about a sev~th part of thé quurtcr of a Saturnian ycar, or about 384 days.


satellites across the rings can happen, in the case of the seven interior satellites, only whén the plane of the ring passes very nearly through the earth. At this time, as already mentioned, the satellites may be detected travelling, Hke golden beads on a wire,'along the line of the ring tbey are therefore either partially occulted by the ring or transiting it. When the plane of thé ring passes through the sun the satellites would present the same appearance to an observer in the sun, and therefore must, at certain parts of their orbits, be partially eclipsed by the ring, or partially eclipse the ring's edge. Such partial eclipses would not be easily detected, however, by the observer on earth. The outer satellite, whose orbit is inclined to the plane of the ring, may be eclipsed or occulted by, or transit, the ring these phenomena, however, must be more rare even than the eclipses and occultations of this satellite by the planer



IF we consider the vast size and singular conformation of the Saturnian rmgs–appendages altogether unique in the solar system, and; so far as is known, in the universe itself–it will not appear surprising that they should have been the subject of m~ny speculations and hypotheses or that the most wild and. fanciful ideas should from time to time have been broached concerning them. Thus; Maupertuis considered that thé tail of a cornet passing near Satum had been attracted from its course by the planet's mass, a,nd has~ince continued to circle as a ring around him. It is singular that Buffon, who had himself conceived thé fancifui theory that planets are portions of the sun's mass whieh have been struck off by passing comète refused to accept Maupertuis' hypothesisof the cometary nature of Saturn's ring-system. One would have thought that in such a view he would have found a confirmation ofhis favourite tbeory. He mighthave argued, that, as it wiU happen that a strongwrestler, pverbearing his foe, may yet be forced to follow him in his fall, so thé cornet, that had dashed from the sun's globe thé mighty mass of Saturn, and carried it on through space to so vast a distance from the parent orb, was, unable to free itself from ita massive burden, and gradually cooling, formed the vast ring tbat still circles about Sa.turn. Such an explanation is altogether unphilosophical, it is true, but not more so than the theory on which it is founded. The. explanation actually offered by Buffon was different, however. He considered that Saturn's equator originally extended asfaras the outer edge-of the ring, and that the equatorial regions have been thrown o~ by centri-

NATURE OF THE RINGS.

CHAPTER V.


fugal force, thé l'est of the planet gradually contracting to its present dimensions. Mairan supposed that the rings are the remains of outer shells about Saturn, broken up by some vast convulsion.~ Until very lately, whatever explanations might be offered as to the first formation and original state of the rings, thé opinion that the system is at present solid and continuous was universally accepted. Such an opinion seems, at first sight, to be countenanced by the continuons appearance of the rings, and their general permanence of form. On closer examination, however, it will be found that thé most serions difficulties attend the supposition of the solidity of the system.

In the first place, it bas been shown in Chapter III. that the rings frequently exhibit traces of division, but that such traces are not permanent, sometimes varying in position, at otbers disappearing altogether. It is not easy to explain these changes on thé supposition that the rings are solid. The approach of two rings, originally concentric, might, it is true, remove aiï trace of division at the point of approach, or in its immédiate neighbourhood but a wider gap would thus be left at the opposite part of the division's circnmference, and the trace of division thus disclosed would be at once recognized as forming part of the division first seen,-that is, as belonging to a particular cirele concentric with the great division :–on the contrary, the traces of division seen at different times belong to distinct circles. It is still more diScult to explain the appearance of non-permanent mottled or dusky stripes concentric with the rings, on the supposition of the solidity of the system. A division between the rings, whether permanent or not, allowing the dark sky beyond to be seen, should appear perfectly black iLketbe great division so that mottled or dusky stripes would seem to indicate only semi-transparency in those parts of the rings along which they are traceable. If we accepted such an exp]anation, we sbould have to account for the following mysterious conditions in Saturn's ring system:-In solid flat rings non-permanent concentric divisions open at different times along different circles The theory that thé earth itself is composed of several crusts liable to sf~arate destruction w~ maintained by several distingtushed astronomers of the eightccnth ccntury; and, carUer, by Kepler.


while variable concentric bands become at different times semitransparent again,-the divisions close, and the transparent bands résume their opaqueness, after variable intervals.

It may be urged, however, that these lines are not necessarily traces of division that ranges of hills upon the rings would tbrow black shadows, wbile rough districts would appear mottled or dusky, like the stripes seen by Mr. Dawes. Yet how inexplicable in elther case that such irregularities sbould lie always in circular arcs concentric with the rings 1 And to what cause should the nonpermanence of thèse irregularities be ascribed ? Why should they disappear along one circle to be thrown up presently along another ? The presence of an atmosphere bearing clouds over the surface of the rings, and thus concealing the traces of division, may appear, at first sightj a plausible explanation of the phenomena we are considering. JBut the disposition of such an atmosphere necessary to produce the observed effects would be so artificial that, on this account alone, we might well be permitted to reject the supposition and further, the cloudy regions imagined should at least, one would suppose, be as distinct1y visible as the zones on Saturn's dise; indeed, lying over a flat surface, their outlines would probably be more distinct than those of Saturn's be!ts.' But, except the permanent difference of tint observed in the two rings, thé telescope bas revealed no appearances that could be attributed to the existence of an atmosphere surrounding the rings and even if tbat difference of tint be assigned to atmospheric causes, yet, being permanent, it does not avail to explain the variations we are examining. It might, indeed, be urged that the mottled lines on the rings indicate the presence of an atmosphere that they are either clouds or breaks in thé cloudy envelope of the rings or, perhaps, the sbadows of clouds themselves invisible. Their appearance is not favourable, however, to these suppositions nor are such long narrow circular arcs the forms into which we should expect cloudbands to arrange themselves, or the openings in clouds to appear, under the conditions to which the surface of the system is subject. A uniform distribution of light and heat must prevail over the whole of that surface except where thé vast shadow of the planet actually falls, or has lately past, and the disturbing effects of tliis sbadow


(see Plate XII.) must operate across the breadth, or a gréât part of the breadth, of the rings, not along narrow arcs concentric with their edges. The argument against thé solidity of the rings drawn from the varying traces of divisions in the system appears, then, to be little if at ail impaired by the assumption that the rings are surrounded by a varying atmospheric envelope. Snch an explanation is altogether inapplicable to the objections we bave nexttoconsider. We hâve seen that one of our most accurate observers has seen traces of division in the dark ring, which also appears at times to be separated from the inner circumference of the neigbbourinobright ring by gaps of considérable length. These appearances may be passed over, or simply viewed as confirmations of the argument drawn from similar non-permanent traces in the bright rings but there are phenomena connected witb the dark ring which appear altogether inexplicable on the supposition that this formation is solid. In the first place, there is the singular circumstance already recorded that this ring was not visible seventy years ago through one of the most powerful telescopes ever constructed whereas since its discovery it bas become gradually more and more conspicuous, until in 1856 it was visible in telescopes of very moderate power. Secondly, as already stated, this ring is transparent, and the edge of the planet's dise seen through it is not distorted. If the substance of the ring were a transparent solid (or even fluid) possessing properties similar to those of all transparent substances, solid or fluid, with which we are acquainted on earth, the edge of Saturn's dise seen through it would be distorted by the refraction of light passing through such a médium. Too much stress, however, must not be placed on this argument; for if the plane faces of the dark ring are parallel the distortion would be very small (its amount depending on the thickness of the ring) and probably not traceable even with the most powerful telescopes yet constructed. The great, and I think unanswerable, arguments against the solidity of Saturn's dark rings, are drawn from thefacts, that so vast a formation should be transparent, that its transparency should once have been such that it was mistaken for a belt on the body of the planet, and :finally that it should be continually growing more and more opaque, so that it becomes more clearly visible every year.


Let us next consider the dimensions of the rings. We bave seen that the thickness of the system is very small compared with ils other dimensions. A small ring of iron constructed on the scale of one of the rings, or even a ring of iron whose width should be proportioned to that of the complete system of rings, would be a flimsy body, easily bent or broken. But in considering the strengt.h of bodies constructed of any substance, it is not sufficient that we should know their ~'opor~OT~ we must know also the scale on which they are constructed. Th us, if an engineer, who proposed to erect a bridge of iron of given length and to support a given weight, should construct a model a few inches long of thé same kind of iron, and should determine thé proportions of t.he bridge itself from the proportions he found necessary to support a proportionate weight in the model, he would probably erect a bridge bardiy strong enough to support its own weigbt. The larger the scale on which a model in iron of the rings of Saturn should be constructed, the flimsier (in proportion to its size) it would become. If, then, it were possible to imagine a ring of iron constructed of the same dimensions as the Saturnian system of rings, it would be utterly unfit to bear the immense strains to which, as we shall see, these rings are subjected. If, further, we ima-gine such a ring divided into numerous concentric rings, thé system thus forme.d would be still less fit to bear strain or pressure. But this is not ail. We have arrived at the conclusion that thé rings are about 100 miles thick, from the supposition that the mean density of the substance of wbich they are composed is equal to the mean density of Saturn's mass, or '75.* Now the density of forged iron is about 7'7, or more than ten times as great as Saturn's mean density; and it is not probable that any substance (unknown on eart.h) could have the same strength and tenacity as iron with a much smaller density-say with a density less than 3'7ô, or five times that of Sa.turn. If we assume the mean density of Saturn's rings to be 3'75, then, instead of arriving at the conclusion tbat the tbickne~s of the system is 100 miles, we deduce a thickness of only 20 mile.c. With such a thickness a model of the rings on the scale of Plate I.

Thc dt'nsity of watpr hemg as 1.


would be tbinner than tissue-paper. Undoubtedly a solid iron Hystem of such proportions, and of such vast absolute dimensions, 'wQuld be not only plastic~ but semi-ihiid, under the forces it would expérience.'

The change that bas taken place in thé dimensions of the rings during the last two bundred years affords a still stronger argument against the solidity of the system. We hâve seen that the measurement of the width of the ring given by Huygens or Pound differs considerably from that given by Herschel, and that again from the results of thé most trustworthy modern measurements. We cannot, perhaps, place much reliance on the absolute dimensions of the ring or planet determined by the earlier observers. Owing to thé immense distance of Saturn from thé earth, the determination of these dimensions is a task of great dimculty even to observers using the wonderfully delicate instruments of thé present day. Far more reliance, however, can be placed on proportional measurementa, and only such measurements are involved in the question unless we suppose–which will hardiy be considered probable-that the dimensions of Saturn's globe hâve undergone alteration during the interval we are considering. Ail thé measurements that bave been taken of the rings, from the time of their first discovery to the present day, hâve been earefuUy revised and examined by M. Otto Struve. He not only considered the result obtained in each case, but the method of measurement applied, the nature and quality of the instrument used, a.nd the skill and general trustworthiness of thé observer. He arrived at the following conclusions:–Thé width of thé system of &TK/ rings is iucreasing, gradually but continuously, by thé approach of its inner edge towards Saturn's equator; both the rings have partaken in this change, but the inner ring bas increased in width more rapidly than the outer. The dark ring, as already stated, bas increased considerably in width during thé compa.ratively short period that. bas elapsed since its discovery.

The increase in the width of the system of rings must, of course, have been accompanied by a corresponding decrease in Ess~y on the Stability of the Motion of Saturn's Bingf/ by J. CIcrk Maxwell, M. A.


thickness. Let us examine thé extent of both thèse changes in Herschel's time and in our own. For simplicity, we may treat the system of bright rings as a single ring, and neglect ail consideration of the dark ring. The outer diameter of the rings is 166,920 miles, the equatorial diameter of Saturn 72,250 miles. Now, the measurement of Huygens made the width of the ring equal to the breadth of the space between the ring and planet, and the measurement of Pound made the width of the ring somewhat less. Taking the first measurement (as thé least favourable to our case), it appears that thé width of the ring was 23,667 miles in Huygens' time; and it is easily calculated that the extent of either flat surface of the ring was upwards of 10,652,100,000 square miles the outer dotted line in fig. 3, Plate IX., represents the inner edge of the bright ring at this epoch. Again, Herschel found that thé width o.f the ring, in his day, bore to the breadth of the space between the ring and the planet's equator the proportion of 5 4 this gives to the ring a width of 26,297 miles, and a surface of 1 l,617,ô00~000 square miles the inner dotted line in ng. 3, Plate IX., represents the inner edge of the bright ring at this time. Lastly, the best modern measurements give to the ring a width of 28,300 miles, and therefore a surface of 12,324,300,000 square miles. Thus it appearsthat in the first interval of about 120 years, the absolute increase in the width of the rings was 2,630 miles and in the second interval of about 70 years, the rings increased in width 2,003 miles. The average annual rate of increase in tbe first interval is nearly 22 miles, in the second nearly 29 miles, so that the of increase in the width of the ring would appear to be itself increasing. Further, it appears that the surface of tbe ring was greater, and therefore the thickness of the ring less, in Herschel's time than in Huygens% in tbe proportion of 116,l7ô 106,521 (or about 12:11); and in our own time the surface of thé ring had increased, and tbe thickness of the ring therefore diminisbed, in the proportion of 123,243:116,175 (or about'35 33) as compared with tbose dimensions in Herschel's time, and in thé proportion of 123,243 106,521 (or about 8 7) as compared with the corresponding dimensions in Huygens' time. Thus, if we assume the present mean thickness of the rings to be 100 miles, it appears that in Huygens'


time the rings must bave had a mean thickness of 114 miles, and have been narrower than at présent by no less than 4,633 miles. It is'hardly necessary to point out the difficulty of reconci.ling these changes of. form with thé supposition that the formation is solid.

Let us next discuss the results of more exact and systematic inquiries,

The question whether a solid flat ring could remain in equilibrium, under any circumstances, about a vast central orb like Saturn, attracting according to the law of gravity, was first discussed by. Laplace, towards the end of the last century. This celebrated mathematician established three important points, but contented himself with offering an hypothesis respecting thé stability of the system.

Laplace first proved that such a ring must rotate about thé central globe. The enormous attractive force of an orb so vast as Saturn must in some way be counterbalanced. When a satellite revolves about a planet, the attraction between thé planet and satellite is continually used up-so to speak–in cbanging the direction of thé satpllite's motion. If that motion were suddenly checked, the satellite would approach thé planet if the motion were stopped, the satellite would fall on the planet. Now, every portion of the ring is subjected to the immense attractive force of Saturn's mass, and also to the attractive force (by no means insignificant) of the rest of the ring. The first force drags the ring towfu-ds the common centre of the ring and planet. Thé second force bas a different effect it operates to drag the outer parts of the ring inwards, the inner parts outwards the influence of tbis force would chiefly lie in its effect in weakening the ring, and thus rendering it more than ever unfit to resist the tremendous influence of the first force. Thus, if the ring were not rotating it would inevitably give way under these forces, and crumbling up–like an arch beneath a load too great for its strength–would fall in ruins about the planet's equator.

We are led immediately to Laplace's second conclusion. At what rate should thé ring revolve ? Tbat aïï strain should be rernoved, each particle of the rir'g should move as if it were a free


satellite revolving about Saturn the greater part of the strain would be removed if eacb particle of the ring revolved at the rate with which a satellite at the same distance from Saturn would revolve in a circle about him. It is clearly impossible that either kind of motion should be found in each particle of a solid flat ring: if the outer parts of such a ring bad the rate of motion corresponding to the second case, the inner parts would be revolving too slowly, and be dragged inwards if, on the other hand, the inner parts had such a rate of motion, the outer parts would be revolving too fast, and be whirled outwards. It is clear that the supposition most favourable to the existence of the ring is, that it should revolve at the rate due to a satellite at the mean distance of the particles of the ring from Satum's centre. But, even in this case, the outer parts of the ring bave too great, the inner parts too small, a velocity. Thus, the outer parts, if not constrained by the cohesion of the ring, would travel in a larger orbit than that in which they actually move; while the inner parts would seek a smaller orbit. Now the cohesion of a nat ring, of the dimensions of Saturn's ring, would be altogether insufficient to resist these tendencies. The inner and outer rims of such a ring would be stripped off, probably in irregular fragments, and proceed to describe eccentric orbits. Such effects are due to thé width of the system the cohesion of a narrow ring would be sufficient to resist the comparatively small strains to which the parts of such a ring would be subjected. Hence Laplace concluded that Saturn's ring must be divided into several concentric rings. He calculated the rate of motion due to each part of such a system, and bis conclusions were soon confirmed, so far as the outer rim was concerned, by the observations of the elder Herschel.

Laplace next proved that a perfectly uniform solid ring, of moderate widtb, might rotate for ever around a perfectly uniform planet, if subjected to no disturbing influences; but that if such a ring were once disturbed, however slightly, equilibrium would never afterwards be restored. The approach of one part of the ring towards the planet would cause a prépondérance of attraction on that part of the ring thus il* would continue to approach the planet with constantly increasing velocity, and would finally fall

r


upon the planet's equator. Now, in the first place, Saturn's ring is subject to numerous disturbing influences even if we suppose Saturn's globe and the ring itself free from irregularities (which, however, is utterly incredible), yet the attractions of the satellites constantly varying in position, the attractions of the different members of the solar system, of the sun itself, of stars, of cornets,–ail these are disturbing influences, and any one of them would be sufficient to destroy the balance of the ring and effect its destruction. But, secondly, an eccentricity in Saturn's position with respect to the ring (due no doubt to the above-named causes) is not unfrequently palpable to observation. Since the destruction of thé ring has not resulted, as must have happened if the ring were solid and uniform, it follows that the ring, if solid, is not uniform. 1 say the deistrztction of the ring, because it is clear that when once the ring had assumed an eccentric position, the proper rate of motion to prevent destruction would be different for different parts of the ring, and the actual motions of the ring (rotating, and falling towards thé planet) could no longer give to each part its just rate of motion-some parts would be moving too fast, others not fast enough and, finally, when the eccentricity of the ring's position became sufficiently great, the ring would be broken into fragments -like an arch pressed beyond its strength, inwards at some points and outwards at others.

Laplace lastly considered the case of a solid non-uniform rotating ring. He did not, bowever, subject tbis part of the question to the same searching mathematical inquiry that he had applied to the others. He contented himself by suggesting tbat the irregularity of such a ring, properly disposed, and combined with an eccentricity of position, might prevent the destruction of the ring. He considered that the breadth of any ring composing thé system might vary in different parts of its circumference, so that the centre of gravity might be at a considerable distance from the centre of figure; and that thé centre of gravity of such a ring might revolve about Saturn somewhat in the manner of a satellite, and with a period equal to that of the ring. There was one obvious difficulty in the way of this supposition. Under the different disturbing influences to which the rings are aubjected, they would


be liable to leave the plane of Saturn's equator, thé plane of each ring moving with a slow precessional movement about Sa-.turn. Now this movement would be different for each ring, and thus the rings would no longer be found in one plane, and the system no longer present the appearance actually observed. Laplace considered, however, that if equilibrium could be secured to each ring of the system, the attraction of Saturn's bulging equatorial regions might be sufficient to overcome ail such disturbing influences, and to compel ail the rings to move in a single plane very nearly coincident with the plane of Saturn's equator. Thus it appeared to Laplace that the system of rings was probably composed in some such manner as tbat indicated in ag. 4, Plate IX.the bounding outlines of each ring being necessarily circular, since otherwise the motion of the ring would be impeded by collisions with its neighbours. But he saw that it was not sufficient for thé stability of the system that the bounding outlines of each ring should be non-concentric circles. Such an arrangement would leave the centre of gravity too near thé centre of fig ure of the rin~ He conceived that the centre of gravity might be thrown to a sufficient distance from the centre of figure, either by variations in the densfty and thickness of the ring, or by irregularities on the surface. This view was confirmed by Herschel's determination of the rotation of the outer ring. We have seen that he effected this determination by watching the motions of certain bright points whicb might be supposed to be irregularities upon the surface of the ring.

The conclusion arrived at by Laplace was for more than half a century accepted by astronomers as the only possible interpretation of the stability of the Saturnian rings. Of the value of Laplace's investigations of this, as of so many other problems of difficulty, there can be no question; yet the result be arrived at is unsatisfactory. In the following observation, Professor Nichol estimates Laplace's views at their just value:Worthy With such an arrangement (the thickness and density of the ring being uniform throughout) the centre of gravity could never be so far from the centre of figure as half the radius of the outer boundary, whatever the proportion of the radii of the two boundaries, and whate-ver the distance between their centres.

1 2


of every admiration amidst a display of mechanical toys, such hypotheses rarely constitute essential parts of the vast and simple arrangements of nature.'

The discovery of the dark ring roused new inquiries. In 1851, Professor Pierce, of America, examined the second point established by Laplace-the narrowness of the rings composing the system. He found that, if the rings are solid, the breadth of each must be much smaller than even Laplace had imagined, so that the number of rings must be considerable. The éléments of confusion and insecurity that must exist under such an arrangement are self-evident.

On March 23rd, 1855, thé University of Cambridge announced that the stability of the motions of Saturn's rings had been cbosen as the subject of the Adams PrizeEssay; and in 1857 the prize was adjudged to Mr.'J. Clerk Maxwell. Taking up the question of a solid ring where it had been left by Laplace, Mr. Maxwell finally disposed of it. He showed that the irregularity of each ring should be such as to bring the centre of gravity more than nine times as far from the lightest as from the heaviest side of the ring and that the eccentricity of position of each ring must be such that a system composed of such rings would present an appeararice altogether different from tbat of the actual system. He showed, further, that even with such an arrangement the slightest cause would be sufficient to destroy thé nice adjustment of the load, and with it the stability of the ring.' We have also seen that a solid ring very eccentrically placed would be broken into fragments.

We are compelled, then, finally to reject the idea that the system is solid.

The appearance of continuity presented by the rings leads next to the supposition that they may be Buid. The hypothesis seems at first sight an inviting one. The variations in the form of the system, the temporary divisions in the bright rings, and the transparency of the dark ring, no longer appear to offer insuperable difficulties. Yet the notion of an isolated océan of such vast dimensions, and poised in so artificial and apparently precarious a manner, is not one that would be readily accepted save as a resource against the still more serious objections to the solidity of


the formation. And further, if we accept somo such view of the development of the solar system as that embodied in Laplace's Nebular Theory (and the arguments in favour of such an hypothesis appear irrésistible),* we must place the formation of these rings in point of time between that of the satellite nearest to Saturn and that of the planet itself. As there is no reason for supposing either of these bodies to be otherwise tban solid, we hâve at least a negative argument against the fluidity of the rings. But the strict examination, by Professor Pierce and Mr. Maxwell, of the stability of a system of continuous a uid rings, forces us to reject altogether the idea that the Saturnian rings form such a system. The various disturbing attractions to which the rings are exposed would inevitably lead to the formation of waves, under whose influence the fluid rings would be broken up into fluid satellites.

We are compelled, then, finally to assume that the continuous appearance of the rings is not due to real continuity of substance. The sole hypothesis remains that the rings are composed of flights of disconnected satellites, so small and so closely packed that, at the immense distance to which Saturn is removed, they appear to form a continuous mass.

An à priori argument in favour of such a supposition may be drawn from analogous instances in the solar system. In the zone of asteroids we hâve an undoubted instance of a flight of disconnected bodies travelling in a ring about a central attracting mass. The existence of zones of meteorites travelling around tbe sun has long been accepted as the only probable explanation of the periodicity of meteoric showers. Again, thé singular phenomenon called the zodiacal light is, in ail probability, caused by a ring of minute cosmical bodies surrounding the sun.t In the Milky Way and in the ring-nebulse we hâve otber illustrations of similar arrangements in nature, belonging, however, to orders immeasurably vaster than any within the solar system.

See Appendix I., note B, Laplace's Nebular Theory.

t It has been suggested that the appearance of tho zodiacal light in equatorial regions may be explained by supposing it to be a. ring of minute satellites, surrounding the earth. Thé investigations in ChapterVII., which mayb&applied, W!M~6' ?MM<cM~/s, to a ring and globe of any dimensions, prore, however, that thé zodiacal Hght cannot be due to such a cause, the appearance of the meteor in high latitudes bcing altogetIierdiHorcnt from that which would be presonted by a ring surrounding thé em'tb.


Let us consider in what light the difficulties met with when we supposed thé rings to be solid and continuous, appear on tbe hypothesis that the system is composed of disconnected satellites.

The temporary divisions and mottled stripes are easily explained. It is conceivable, for instance, that the streams of satellites forming the rings might be temporarily separated along arcs of greater or less length by narrow strips altogether clear of satellites, or m wbich satellites might be but sparsely distributed. Divisions of the former kind would appear as dark lines, while those of the latter kind would present precisely that mottled appearance seen in the dusky or ash-coloured stripes. The transparency of the dark inner ring is easily understood if we consider the satellites to be sparsely scattered thr ougbout that formation. The fact that this ring bas only become visible of late years no longer presents an insuperable dimculty, for it is readily conceivable that the satellites forming the dark ring hâve originally belonged to the inner bright ring, whence collisions or disturbing attractions have but lately propelled or drawn them. The graduai spreading out of the rings is explicable when the system is supposed to consist of satellites only connected by their mutual attractions while the thinness of the system is obviousiy a necessary consequence of such a formation, for the attraction of Saturn's bulging equatorial regions would compel each satellite to travel near the plane of Saturn's equator.

Another remarkable phenomenon-the elliptical shading at thé ends of the apparent longer axis of the dark ring-must next be considered. These appearances have been called the ~shadows projected on the ring.' It is perfectly clear, however, that they are not shadows for, in the first place, there are no luminous or light-renecting bodies from wbich these parts of the rings are at any time concealed, while the brighter parts are illuminated; and, secondiy, the fact that they are always seen in the same c~jp~e~ parts of the ring, though the direction of the line of sight from the earth to Saturn is continually varying, shows conclusively that their appearance depends on the position of the observer on eartb, whereas the motions of Saturn and of the ring are altogetber


independent of the earth's position in her orbit. There is no dimculty, however, in explaining these appearances, even on the supposition of the solidity of the system. Such explanation will serve to introduce and render intelligible the corresponding explanation on the hypothesis we are actually examining. Consider the great division in the rings it is perfectly clear that if the rings were indefinitely thin, this division would appear to be bounded by two exactly similar and concentric ellipses, and it would therefore appear broadest at the ends of its longer axis and narrowest at the ends of its shorter axis. But now suppose the rings to be of appreciable and uniform thickness-then it is clear that this circumstance will operate to make the division appear narrower at the ends of the shorter axis, while it will not anect the apparent breadth of the division at thé ends of the longer axis. For at thé ends of the shorter axis the apparent breadth will be the angle between two lines of sight, one passing over the upper edge of the nearer boundary of the division, the other passing under thé lower edge of thé farther boundary and it is clear that as the angle diminishes at wbich the ring is viewed, the apparent breadth of this part of the division would rapidly diminish, until at length the Hue passing over the ,upper edge of the nearer boundary would fall upon the opposite face of the division, so that the division would no longer be visible at this point. After this, as the angle at which thé ring is viewed continued to diminish, the arc along which the division is invisible would gradually extend more and more towards the extremities of the longer axis of the apparent outline of the division but until the angle became very small it is clear that thé apparent breadth of the division would be very little affected at the ends of the longer axis, for hère the lines of sight to the edges of the division would fall (approximately) along, and not across, the bounding faces of the division. Similar remarks apply to thé division in the outer ring but this division being so much narrower than the great division, would disappear much sooner at the ends of the shorter axis, as the ring clpsed, and the arc along which it is invisible would extend much more rapidly towards the extremities of the longer axis. Now, imagine the


formation of the rings to be that exhibited in fig. 5, Plate IX. that is, that each ring is formed of a number of concentric hoops of uniform thickness, but the breadths of which diminish, while the intervals between them grow gradually wider towards the inner boundary of each ring. Then it is clear, either from the considerations detailed above or from an examination of the figure, which represents the appearance of such a system of rings, that dark spaces must be visible at the ends of the longer axis of the inner boundary of each bright ring.* These sbaded spaces would vary in form according to the manner in which the rings and the divisions between them varied in width, and might either be bounded by definite outlines or toned off by insensible gradations. It is clear, however, that if the width of the rings diminished, and the width of thé spaces between them increased, by any uniform law, thé sbadings would present oval forms similar to those presented by the Saturnian systein.

The explanation of these appearances on the supposition that the rings consist of flights of disconnected satellites, is similar to the above–thougb not so convenient for illustration-whether we suppose the satellites to travel in narrow rings, or, whicb is more probable, to be in general less regularly disposed. We hâve only to imagine that the satellites are strewn more densely near the outer edges of the bright rings, and especially of the inner bright ring, and that this density of distribution gradually diminishes inwards. For instance, we may conclude that along the inner edge of the inner bright ring tbe satellites are so sparsely strewn that, at thé extremitiea of the apparent longer axis of that edge, the dark background of the sky becomes visible through the gaps between the satellites. If these gaps were separately visible we sbou]d find, as thé eye travelled across the ~Tec~A of the bright ring at this part, that they became smaller and less numerous as the satellites became more and more densely crowded but as the eye travelled round the ring weshould find thé gaps becoming smaller and less numerous from another cause. For a satellite would We must suppose these narrow rings to be so numerous, and, therefore, the divisions between them so narrow, that neither rings nor divisions would be separately visible even in the most powerful télescopes.


appear of thé same size at wbatever part of the ring it appeared, and thus, if separately visible, would occupya much smaller part of the breadth of the rings when seen near thé longer axis, where this breadth is greatest, than when seen near the shorter axis, where this breadth is least. Hence a flight of satellites whicb, in a telescope of sufficient power, migbt be resolvable into its component satellites when in tbe former position, migbt, from such foreshortening, become irresolvable in the latter, though the separate satellites maiutained their relative positions unchanged. If such a flight of satellites could be traced in its motion from the longer to the sborter axis of the system, the dises of the component satellites would be seen gradually to approach, then to overlap each other, until, finally, all the dark spaces between them would disappear. If the satellites were not separately visible, such a flight would appear dusky in the former position, and would become gradually smaller and brighter, until in the latter position it would be as bright as thé outer parts of the bright ring. Now the ring may be considered as made up of flights of satellites; and though the members of such flights in no case maintain their relative positions unchanged, even for a few seconds, yet the general average of density along any band of the ring remains tolerably uniform. Hence we can,readily understand that there should be a graduai increase in the brightness of the rings, whether the eye travels across their width from within outwards, or along any circle concentric with the outlines of the rings from the longer to thé shorter (apparent) axis of the system. Further, as it appears impossible to offer any other explanation of these shaded spaces, we may conclude that in the inner bright ring, and probably in each member of the outer double bright ring, the distribution indicated actually prevails-that is, that the component satellites are crowded along the outer boundaries of the bright rings, and more sparsely distributed along the inner boundaries and that, although there may be local irregularities-such as strips, along which for an interval satellites are more or less crowded than in the neighbouring spaces-yet, on the wbole, thé density with which the satellites are strewn increases gradually outwards in each bright ring.

The appearances observed by Mr. Wray and M. Otto Struve,


which seem altogether inexplicable on either of the hypotheses before considered, may be readily explained on the supposition we are examining at present. For it is conceivable that the disturbing attractions of Saturn's outer satellite may draw the satellites composing the ring from the plane pf Saturn's equator (or the mean plane of the ring), so that when the edge of the ring is turned to the observer thé satellites thus disturbed present the nebulous appearance described. Furtner, tne more densely thé satellites composing any part of the ring are crowded, the more efficient will be their common action to check such disturbances so that the graduai increase in the width of these nebulous appendages, as they (apparently) approach the dise of the planet, is, perhaps, a further indication of thé diminution of density inwards mentioned above. But this phenomenon may be satisfactorily explained in another manner :-The number of satellites at a given distance from the central plane of the ring must rapidly diminish as that distance increases; thus, when this distance is very small, the disturbed satellites may be strewn with sufficient density to become visible near the extremities of the ansse, where the line of sight passes through a small range of satellites but that the sparsely strewn satellites at a greater distance from the central plane of the rings should become visible, it may be necessary tbat the line of sight should pass through a much greater range,-that is, sbould fall much nearer the dise of the planet. Thus, clearly, the apparent breadth of these appendages would be greater near the planet's dise, even though there were not an increase inwards in the numbers of satellites. disturbed from the mean plane of the ring. It is very probable, however, that there is such an increase, and that thé effects resulting from both causes combine to render thé peculiar apparent shape of these appendages more distinct than it would be if either cause operated alone.

The investigation of the motions of a crowd of satellites traveling in rings about a central attracting globe, is a problem of too great complexity to be exactiy resolved. If the motion of our moon is of so complex a nature that even yet all its inequalities bave not been exactiy determined, it will readily be conceived that a problem which deals with the motions of hundreds of moons,


disturbed by and disturbing each other, must lie far beyond the range of our most powerful modes of mathematical analysis. Even if we knew the exact size, shape, and position of each satellite, and the rate and direction of its motion at any instant, the exact investigation of the subséquent motions of the system would still lie utterly beyond the grasp of the acutest human intellect. But of all those elements we are ignorant. AU that we know certainly is tbat the bodies constituting the system are very numerous we may also conclude from the analogy of other. parts of thé solar system that they are not uniform either in size or density. Notwithstanding the difficulty of the problem, and the uncertainty of all its conditions, highiy interesting general results may be deduced from its consideration.

And first, while we cannot assert that such a system is actually permanent, it is undoubtedly safe from sudden destruction. We speak of the orbits of our earth and of the planets as permanent, because, though they undergo various changes, these are oscillatory, and produce no lasting effect. But rings of satellites, subject like all the members of the solar system to numerous disturbing attractions, and mutually disturbing each other, undergo changes of form that proceed continuousiy. Whether such development results in the destruction of the rings (as rings) is not certain. It appears probable, however, that under certain conditions the destruction of the rings might be indefinitely postponed.

We may consider separately two forma of disturbance, chiefly due to the varying attractions of Saturn's eight satellites, but partly to the attractions of the other members of the solar system each form of disturbance also generates the other, or modifies disturbances already existing.

In the first place, the members of these rings will be subject to perturbations out of the general plane of the system. If it were possible to trace thé motion of a single satellite, it would be found that its orbit bas its ascending and descending nodes on the ring's plane, and (at each instant) a definite inclination to that plane. These elements of thé satellite's orbit would be found to be continually changing the nodes at one time advancing, at another regreding–thé inclination now diminisbing, now increasing.


Considering the whole system, the resuit of these extra-planar motions and their variations would be a series of waves, wrinkling (so to speak) both surfaces of the ring. These waves would vary in. extent, and would move with various velocities-travelling neither directly across nor in circles concentric with the rings. They would not of themselves produce any marked or permanent effects upon the extent of the rings,-that is, on their diameters interna.1 and external. Their effects on tbe development of the system would arise chieSy from their influence in generating the form of disturbance next to be considered. But their effects on the appearance of the rings when the edge is turned towards thé earth are, as we bave seen, very observable for it is undoubtedly to such waves as these that the changes observed by M. Maradi and others at the disappearance of the ring, and the nebulous appearances already considered, are to be attributed.

Secondly, the members of these rings will be subject to varia.tions in their distances from the centre of their gigantic primary. If a single satellite were tracked as before, it would be found that t its orbit bas its peri-saturnium, and its apo-saturnium, and (a.t each instant) a definite eccentricity. These elements, like those just considered, would be found to vary continually; the line oi apsides advancing at one time and regreding at another, the eccentricity now diminishing and now increasing. Considering the whole system the result of these variations would be a series of waves of concentration and dispersion.t These would travel It must be remembered that it is not the motions of thé satellites themseh'ea that are here spoken of, but thé motions of the wa.Yes of disturbanco resulting from irregutaritifis in the motions of those bodies. Thé two kinds of motion are as distinct as the motion of a wave on the ocean from the motion of the particles of the océan the wave itself ma.y travel hundreds of miles, while thé particles whose successive mo..tions form thé wave may not be displaced more than a few yards.

f It is not to be understood that waves of this kind, and waves of thé kind before considered, exist separately, and separately travol across or round the ring thcy are only considered separately to avoid confusion, but are in reality commingled, and their motions are varied and interchanged in inextricable combinations. If it were possible to view the rings from their common centre, waves of the kind first considered 'would be visible, apparently travelling round the ring; to nn eye placed anywhere in thé plane of the rings thé same kind of waves would be seen, and their motions round and across thé ring would both be visible. If thé rings were viewed from a point in the axis of Satum produced (so that they appeared as in the figures of Plate XII. )


neitber directlyacross nor in circles concentric with the rings; but it appears probable, from the formation of the system of rings, that there would be a continuai tendency in waves of the kind we are considering to assume thé form of circles concentric with the rings and travelling across their breadth inwards and outwards. Tbeir effects on thé appearance of thé riugs, viewed from the earth, would depend partly on the intensity attained by the wave, and partly on the density with which the satellites are strewn in the particular zone of the ring across which the wave is travelling. If the intensity of the wave is great and the satellites not very densely crowded, the transparent phase of the wave may be traceable in a temporary division or dusky stripe.* Analysis shows that waves of this kind would produce a graduai but continuous increase in the breadth of the system of rings-the inner edge travelling inwards, the outer edge travelling, but much more slowly, outwa,rds. These changes do not, of course, operate only n,t the edges, but throughout the breadth of the rings t probably their effects are smaller at the edges than eisewhere however, itis clear that tbe only marked change visible to us must be the increase in the breadth of the system.

waves of the second kind would be visible as waves of transparency and opaqueness, travelling, in gênerai, concentrically across thé ring, inwards and outwards. A tolerably exact notion of the disturbances to which the rings are subject may be obtained as follows –Let a semi-transparent nuid be poured into a. large circular plate of uniform colour until the bottom of the plate is just hidden if now this fluid be disturbed in any manner waves will be seen travelling across the surface, crossing and interlacing as they are reflected from the edges of the plate if thé Huid be yicwed, however, from above, these disturbances will appear as waves of colour (thé colour of the plate and the colour of the fluid) if a motion of steady rotation be communicated to the plate by suspending it from a twisted string, the rotation of the rings, eonsidered as a system, will be illustrated and it will be found tliat disturbances can be as readily communicated to the rotating fluid as to thé fluid at l'est.

It might be interesting to examine whether the temporary marks that appear on tho rings have any motion across the breadth of thé system in thé intervals during which they remain visible.

t It may be suggested as possible tha.t in the great division of the rings we hâve thé indication of a zone along which, at an early stage in thé development of thé system, the parts of thé ring spreading outwards were scparated from those spreading inwards. This division may possibly be still inereasing in width. The division in thé outer ring seems certainly to be inereasing in width, since it becomes more distinctly visible as thé rings successively attain their greatest opening.


Let us examine the effects of such increase at the inner and outer edges of the system, respectively. It is clear that both changes operate to increase the extent of the rings, and consequently, as the changes proceed, the satellites have more and more space for their movements but it also appears obvious that among satellites near thé inner edge seeking smaller orbits collisions must be much more frequent than among satellites near the outer edge seeking larger orbits. Further disturbance would thus be continually generated among satellites near the inner edge. The satellites no doubt move in the same general direction about Saturn, so that it is only the difference of the velocities of two impinging satellites that cornes into play at a collision but the eccentricities of the orbits of the satellites may be very importantly affected in this manner, and it is clear that a satellite which once begins to move in an orbit of considérable eccentricity must continually cause fresh disturbances, until either its orbit is altered to a form of less eccentricity or it falls upon the planet. The general effect of such collisions would be tbat (after the lapse possibly of many ages) numbers of satellites originally travelling in orbits nearly circular would pursue eccentric orbits. There would still remain a tolerably well defined inner edge but these orbits would lie partly within and partly without its circle. It appears probable that after a time this process would be checked by the formation of a new ring within the original inner boundary of the system, and that the orbits of the satellites composing this new ring would gradually become less and less eccentric. After a further lapse of time, however, the inner edge of this ring would begin to undergo a series of like changes, ending in the formation of a new ring within it,-and so on continually, or until the process were checked or assnmed new forms through the approach of the rings to Saturn's equator. The inner edges of outer rings would probably be liable to sirnilar changes, proceeding, however, much more slowly.

The sa-tellites composing the system tejng bodies of imperfect elasticity, there ia at every collision a loss of n. part, however small, of thé vis -viva. of the system, and <t corresponding génération of heat. The 1 angular moment' of the system about Saturn is not, however, affected by collisions.


We have seen that the appearance of thé rings, and their changes of form, correspond with thé results detailed above. The interior diameter of the system is continually diminishing two distinct rings are visible, and there are indications of the approaching formation of a third ring within them the outer ring, also, is divided into two rings eeparated by a comparatively narrow interval. The exterior diameter of the system bas not perceptibly increased. This, however, may be accounted for in two ways first, the change of this element would not be easily detected, since analysis shows that such change would be very small compared with the variation of the inner diameter of the system and, secondly, it is not impossible that the existence of a resisting medium checks the outward and encourages the inward growth of the rings. It is probable tbat when the rings are again open to their full extent (or in the year 1870), the development of the dark ring will be found to bave made great progress, and that the inner parts of the inner bright ring will appear much darker tban at present. It is not impossible that the disintegration of the inner bright ring (the progress of which is shown by thé graduai iacrease of the dusky elliptical spaces at the ends of the longer axis of the dark ring), may be found to have resulted in the formation of a new dark ring. The dark ring will probably be wider or brighter, possibly both perhaps even traces may be discernible of the approaching transformation of the dark ring into a new inner bright ring separated from the neighbouring bright ring by a well-marked division.


THE GREAT INEQUALITY' OF SATURN AND JUPITER.

ApTER the discovery of the three laws of Kepler, the motions of the planets were diligently watched by astronomers, and compared with the motions due to those laws. The comparison was conducted still more carefully when it became apparent that the law of gravitation could be established or confuted by sucb observations alone. Before long a singular discrepancy was detected in the motions of Saturn and Jupiter :-Saturn's period, instead of being constant appeared to be continually diminishing; Jupiter's period, on the other hand, seemed to be continually increasing. It appeared, further, that Saturn's period was in excess of his mean period (calculated according to Kepler's laws, or, more strictly, according to the laws of gravity), while Jupiter's period was less than his mean period. Accordingly, the observed changes were operating to restore the two periods to tbeir respective mean values. Until this restoration should be effected, it is clear that Saturn was gradually falling further and further behind, Jupiter getting further and further in advance of his calculated place. Near the end of the eighteenth century, the periods of the two planets were restored to their mean values;* and since thattime See Table IX., Appendix II., and explanation. A slight en'or may be rioticed in Sir J. Herschel's account of the great inequaHty. Ho desclibes Saturn's period as inereasing during the seventeenth centnry, Jupiter's period as diminishing and he adds–' In the eighteenth century a. process precisely thé reverse seemed to be going on.' It will readily be seen from Table IX. that the changes in the periods ha.vproceeded in thé same direction from the midclle of the sixteenth century to the present time; they will continue to proceed in that direction for more than a century. Thé correction applies to the first edition of the work in question. Probably this error, a.nd one or two othcrs mentioned in these pages, have been corrected in later editio-ns.

CHAPTER Vf.


Jupiter's period has continued to increase and Saturn'a to diminish. Jupiter's period having thus become greater than his mean period, he bas been continually losing more and more of his surplus progress in longitude; while Saturn, whose period bas become less than bis mean period, bas been continually working off (so to speak) his arrears of longitude. Tbus both planets are approaching, but many years will elapse before they actually reach, their mean places.

For a long time these changes threw doubt on the law of gravitation. Astronomers were aware that mutual attractions caused the planets to deviate from the simple elliptic orbits traeed out by Kepler. But these disturbances-it appeared to them-must be oscillatory, and the period of any such. oscillation not very gréât. Thus, when it appeared that the changes in the motions o.f Jupiter and Saturn were proceeding for centuries in the same direction, grave doubts began to arise as to the truth of a theory with wbich those changes seemed so discordant. To Laplace is due thé bonour of removing these doubts, or rather, of rnaking the discrepancies from which they arose thé means of confirming the Newtonian doctrine. He showed that the observed changes are due to a certain relation between the periods of Sa-tm'n. %nd Jupiter, which will presentlybe pointed out. Before giving an: outline of Laplace's explanation~ however, it will be necessary to, examine,-the various elements of a planet's orbit which admit of change, thé effect (if any) of thé change of each element in altering the period of tbe planet, and the natures of the disturbing forces that produce such changes.

The elements to be considered in examining thé orbit of a planet are,-the mc~o?' ûM?~, the ecce~r~ the pos~~o~ of the ~M q/' apsides, the 'mc~o~<m of ~Ae plane of the 07' a fixecl plane, and the position of the line of nocles on that plane. That is, these elements being known, we know the orbit in which tbe planet would continue to move, if undisturbed. But, owing to the mutual attractions of the various parts of the solar system, every one of these elements is in a state of continuai variation. Thé major axis, eccentricity, and inclination of each orbit, vary within narrow limits, by several variations, which.have periods of different K


length. Again, the changes of each of these elements react on the- others, the varying influences producing such changes commingle their effects, and the different cycles are blended and intercbanged in apparently inextricable combinations. The positions of the apsidal and nodal lines are similarly subject to various changes, but the resulting variations in these elements are not confined within limits. On the whole, these lines travel continually round the orbit, and (except in the case of Venus) in opposite directions, but for short periods these motions are reversed. These changes also act on, and are reacted on by, thé changes in the other éléments.*

Now, it appears from the third law. of Kepler that the period of a planet depends solely on the length of the major axis of its orbit. So long as this element remains unaltered, no variations in the eccentricity or inclination of the orbit, or in the positions of the nodal and apsidal lines, can have any effect in altering the period of the planet and although, as has been stated, no variation can take place in any one of the elements without some influence on every one of the others, yet perturbing attractions, whose direct effect is to alter any of thé other four elements, and which affect the major axis of the orbit only by the transmitted influence of such altération, have little effect in modifying the period of thé planet, compared with forces whose influence di7'ec~ operates to alter the length of the major axis. Let us consider what are the elements of a planet's.orbit on which perturbations of different kinds have thé greatest influence. Let the ellipse <~p AB in each of the figures 1, 2, 3 of Plate X. represent thé orbit of a body revolving according to the law of gravity about an attracting mass at s, a focus of the ellipse,–<~A being the major axis, c the centre, and H the other focus of the ellipse.

The secular inequality of the moon affords an excellent illustration of the interchange of effects alluded to in the above paragraph. Though thé planets exercise but little direct control over the moon's motion, it is to their attractions this inequality is really due-the influence of those attractions on the eccentricity of the earth'a orbit being propagated to the orbit of the moon. Singularly enough, the direct effect of this influence is scarcely perceptible, while the transmitted effect is so marked that it was deteeted long before its cauae WM reeognised.



First, lét us supposé that wben thé body reacbes the point p it receives an impulse in the direction? G (fig. 1) perpendicular to the tangent'<p~ at p, and in the plane of the orbit. This impulse, being applied in a direction perpendicular to the direction of the body's motion, cannot influence the body's velocity estimated in that direction, so that if at the end of a small interval of time thé body midisturbed would bave been at it will at the end of tbat interval, under the actual circumstances, be at some point so situated that is parallel to p G. Now, the impulse must be considered as sufficient only to produce a very small velocity in the direction in which it is applied compared with the original velocity of the body thus, q (the displacement due to that impulse) is small compared with p and since j9 may be considered as a right-angled triangle, it follows that j9 is very little greater than p q and therefore the velocity of the body in moving along p q', is very little greater than thé velocity with which, if undisturbed, it would have moved along jp in the same time. The full effect of the impulse, however, clearly operates in altering the direction of tne bôdy's motion. Now, one of the properties of elliptic motion under the influence of gravity is~ that, if the velocity is known with which a body is moving wben at a given distance from the centre of motion, thé major axis of the ellipse in which the body moves is determined–altogether irrespectively of thé direction in which the body may be moving at the time. It plainly follows that any disturbing force which only influences the direction of a body's motion will not at all affect the length of the major axis of thé body's orbit; and a disturbing force whioh chiefly influences thé direction of motion will very little affect the length of the major axis. Tbus the period of the body whose motion we are considering is very little modified by an impulse in the direction p G. It follows in the same manner that an impulse in the direction p G', which would make thé body move in thé direction p q", would have very little effect on the period of the body. The influence of such disturbances chiefly affects the eccentricity of the orbit and the position of the apsidal lines. In the first case Since the perhirba.tions which the effects ofsueh impulse are intended to illustrate are small compared with the actual motions of the planets.

& 2


considered the body would proceed to describe an orbit p A~B~ of less eccentricity than ~AB< and baving its Une of apsides ~A~ in advance of <~ A in the second case the orbit p A~B~ subsequently described by the body would be more eccentric than pABc~and the line of apsides <~A~ would he behind <x A.* Into such changes, however, it is not necessary for us now to inquire, since tbe period of the body, with which alone we are at present concerned, is not affected by them.

Secondly, let us suppose that when the body reaches the point p it receives an impulse in the direction p G (fig. 2) perpendicular to the plane of the orbit <~A. In this case, as in the former, the impulse does not influence the velocity of the body estimated in the direction in which it was originally moving so that if at the end of a small interval of time the body undisturbed would have been at it will, under the effect of the impulse, reach some point q' (at the end of that interval of time), such that is parallel to p G. And, as in the former case, since q q' must be small compared with p q, and since is a right-angled triangle, p q' must be very nearly equal to p q, and therefore the velocity of the body is very little affected by the impulse received. Hence such an impulse very little affects the length of the major axis of the orbit, or (therefore) thé period of revolution. And, similarly, an impulse applied in the direction p Gr~ would hâve very little effect on the period of revolution of the body. The influence of such disturbances will chiefly affect the plane of motion of the orbit. In the first case considered the body would proceed to revolve in some orbit pA~D~, of which the part p A'r ( p r being a straight line through s) would lie above the plane of the original orbit; and in the second case the body would move in an orbit p A~B~, of which the part ~) A'~ would lie below the original orbit. In both cases the line p s r would be the line of nodes of the new plane of motion on thé Such are the changes if the body is at p when the respective imposes are applied. The effects of such impulses on the eccentricity of the orbit would vary with the position of the body at the moment they were applied. It may easily be shown that the points c, d, thé centres of the three orbits, lie on the circumferenee of a circle about L, the bisection of sp, as centre; and the points H, K' H~ ibei of the orbits, on the circumference of a circle about p as centre.


original plane and clearly such changes could not take place without affecting the inclination of the plane of the orbit to any fixed plane adopted as a plane of référence, and the position on such a plane of the line of nodes of the orbit. With such changes, as they would not affect the period of the body, we are not at present concerned.

Lastly, suppose that when the body is at p it receives an impulse in thé direction p G (fig. 3) along the tangent line ~p In this case, since the impulse is applied in the direction of the body's motion, its whole effect operates to increase the velocity estimated in that direction. Thus, if at the end of a small interval of time the body undisturbed would have reached the point <~ it will, under the effect of the impulse, reach some point q' (in that interval of time), sucb tbat g is parallel' to jp therefore thé velocity of the body must bave been increased, since thé arc ~) q' is clearly greater than the arc p Thus the effect of such an impulse is to increase the major axis of the orbit, and thereforethe period of revolution. The body will proceed to describe some orbit A~B~, to which the line will still be a tangent; and c~A/, thé new major axis, will be greater than and in advance of a A. Similarly it may be shown that.if the impulse were applied in the direction ~& thé body would proceed tb describe some orbit ~A~B"<~ baving a major axis a"A" less than and behind a A, and to which would still be a tangent.* So far as the position of the line of apsides is concernpd, these effects would vary with the position of the body at the moment the impulse is applied but as regards tbe length of the major axis, it'is clear that, whereever the body may be in its orbit, an impulse applied to it in the direction of its motion increases the major axis of the orbit, and therefore thé pericd of revolution of the body, while an impulse applied in the opposite direction diminishes the major axis and thé period of revolution. Thus we have thé apparently paradoxical result tbat an impulse whose immediate effect is to accelerate the In the case illustrated by fig. 2, tbe points c',c, c", and E',H, H~ lie in lines very nearly straight and perpendicular to the pIa.nR of the orbit. In thé case of fig. 3, thé points c',c, c", lie in a straight line with L, the bisection of sp; and the points H~,H, H", in a straight line with p.


motion of the body diminishes its mean angular velocity about s (since thé period is increased), while an impulse retarding the body's motion increases its mean angular velocity about s.~ Let us apply these results to thé actual forces operating to disturb the planetary orbits. Letj~p~Np' (ûg< 4, Plate X.) represent parts of the orbits of two planets (which we may call, respectively, r and p~) revolving about s, the sun and let the plane of the orbit p ~P intersect the plane of the orbit p~N r' in the line s 7!/N~ so that the part ~p of the first named orbit lies above, the part n'p below, the orbit p'N p~ suppose further that both the planets are moving in the saine direction (indicated by the arrows atp, ~). Let p, pl, be simultaneous positions of thé two planets and join p p' then the attraction of the planet p' operates in direction B P~, and is inversely proportional to the square of tbe distance r p~. Now we are seeking to leam the effect of the attraction of the planet p~ in disturbing, not the <~c~c~ motion of r, but thé orbital motion of p about s. Plainly, therefore, we must take into account thé attraction of r~ on s, for it is only thé difference of l~s attractions on p and s respectively, that can affect the orbital motions of p about s. In the actual configuration represented p~ is farther from s than from p, and therefore the attractive force of p~ is less on s than on p, in thé inverse proportion of the squares of tbe distances s P~ and p P'. If, then, we represent the attractive force of p~ on p by the line p P, the attractive force ofp~ on s will be correctly represented by the line p~, along p's~ if P~ bears to p p' the same proportion that the square of p p~ bears to the square of s p~. Let p t be the tangent at p to the orbit p ~'p, and draw p G perpendicular to F t in the plane of that orbit from p draw p le perpendicular to the, same plane; from p~ draw p'm parallel to p& to meet. thé plane t'p k in m, and from m draw m parallel to t' p t. Then the attractive force of P~ on r, represented by the line p p', may be resolved into three forces, represented respectively by the lines P 7~ and m P~; the nrst of these forces is of the kind illustrated in Encke's cornet affords a.n illustra.tioa of the effect of a force acting n.t evcTy instant in the direction of the tangent to the orbit of a body. The motion of this cornet 19 continually retarded (prob~bly owing to the resistanceof the aether occupying space), yet its mean angular velocity about the sun is continually increasing as its period of revolution dccreases.


fig. 2, that is, Is perpendicular to thé plane of the orbit; the second is of the. kind illustrated in fig. 3~ that is, is tangential to the orbit and the third is of the kind illustrated in ng. 1, that is, is normal to the orbit. Similarly the force represented by the line p~ may be resolved into three ~o, o n, and ~T~ respectively parallel to p~, m, and m p~. Thus, in the configuration represented by fig. 4, the actual <~M~M.7'&M~ force perpendicular to thé plane of p's orbit is represented by the difference of the lines p and o, and acts downwards the tangentialdisturbing force is represented by the difference of the Unes and o n, and retards r's motion; and the normal force* is represented by thé difference of the lines r~ and F' and tends to draw F outwards, or from s. In a similar manner we can determine thé disturbing forces in anyother configuration: they are found to vary both in magnitude and direction, according to the configuration, and there are certain points at which one or other disappears altogether. It is not necessary, however, to examine all tbese variations, for we have seen that it is chiefly with the tangential disturbing force that we have to deal in examining the changes of a planet's period. Further, since tbe inclinations of the planes of the planetary orbits to each other are small, we can simplify the preliminary inquiry, with out introducing sensible error, by supposing our illustrative orbits to lie in one plane.

Suppose, first, that both the orbits are circular (fig. 5, Plate X.), and consider the effect of the tangential disturbing force of a planet (which let us call o), supposed to be stationary at o~ while a planet (which we may call r) performs a revolution about s in the orbit Pl pg Pg P~. Let Q~ P~ s ?“ be a straight line and let a circle about QI as centre, and at distance Q~ s meet the circle i~ P2 pg p~ in thé points Pl, Fg. Then, in the first place, it is clear that the tangential force vanishes wlien the planet p is at p~ or p~ since the tangents at these points are at right angles to the line Qi s P~ and in the second place, the tangential force vanishes when the planet p is at Pi or Pg, since at these points Q exerts an equal attractive force on the sun at s and on the planet p, f and furtber, the lines Since p G alwa'va passes very near s in thé planetary orbits, 'which are very nearly circular, the third force may be called tbe radial force.

t It must be remembered that in this case, and in all similar cases, thé masses of


s Qj and p~Q~, or pgQ~ are plainly inclined at equal angles to the. tangent at F;, or pg, respectively, and thus the tangential parts of those equal attractive forces are equal, and tbeir effects (so far as p's orbit relatively to s is concerned) neutralise each other. Again, in the arc P~Pg, the tangential disturbing force plainly accelerates p's motion, for p is nearer than s to Qp and the angle at which s Qt is inclined to the tangent at any point of this arc, is greater than the angle at wbicb thé line from Q~ to p is inclined to such tangent thus the tangential disturbing force on p is greater tban that on s, and .as it plainly acts towards pgj F's motion about s is accelerated in thé arc p~pj~. In exactly the same manner it may be shown that the tangential force is greater on p than on s while p moves from Pg to pg~and as it acts towards pg, p's motion is retarded in thé arc j~Pg. In the arc pgp~, p's motion is accelerated for F is farther than s from Qj, and the line from Qg to any point of this arc is inclined at a greater angle than.the line Q~s to the tangent at that point; t thus the tangential disturbing force is.greater on s than on P~ and as this force on F plainly tends from P3, or acts as a retarding force, while the force on s acts in the opposite direction, as far as p's motion about s is concerned, or acts as an accelerating force, the latter effect prédominâtes and p's motion is accelerated in the arc pgp~. Lastly~ it may be .sho-wn in exactiy the same manner that p's motion is retarded -in the .arc p~.

Now it is perfecbly clear that in describing any number of complete revolutions about s, the accélérations and -retardations of p would neutralise .each other, and that tbus on the whole p's period would not be affected by the attraction of Q.. For in moving

the attracted bodies hâve not .to be considered, any more than tbe mass of a falling body bas to bo cousidered in determining the time of falling. The amount of the attractive force actually exerted by Q on s (in thé case aupposed) would of course greatly exceed the amount exerted by Q on r; Lut the mass of s exceeding the mass of p in the same proportion, the effects of those unequal attractive forces are exaetly equal. This will plainly appear if a tangent be drawn at any point r of thé arc P, p2; the angle that s QI makes with this line is the exterior angle of a triangle, of whieh the angle that p Q, makes with thé same line is an interior and opposite angle.

t This will appear by drawing lines as described in last note. To avoid confusion these lines are not introduced into ngure 5. In the cuse of a point in the arc r~ p~ the line from r to o~ forms with the tangent at p the exterior angle of a triangle, of which thé Unes Q,s and the same tangent form an interior and opposite angle.


from p, to r~ p would be accelerated and his orbit disturbed in moving from pg to Pa he would be retarded, and the original form of his orbit restored; and similar counterbalancing effects would be experienced in the arcs Fgp~ and p~i~ so that on the whole p would arrive at P in the same time as if his orbit had not been disturbed, and if Q were then suddenly removed; p would proceed to describe a circular orbit. This exact counterpoise of enects will not be disturbed if we suppose Q, instead of remaining fixed, to move at a uniform rate in the orbit OjQ~Qg~' The only effect of such motion is an equal increase of each of the arcs P~pj~ and r~Pg, and a greater but still equal increase of each of the arcs pgp~ and p~pj. Thus, supposing P to start from pp and Q from Qj, at the same instant; that they are in conjunction along the line sp~; and that Q at ~g is equidistant from s and p, p being then at pg ;-then, from the uniform motions and circular orbits of P and Q, it follows tbat the arcs p~g and ~9~3 are equal, and that the accelerating effects of Q's action on P in the first arc is exactiy counterbalanced by Q's retarding action on P in the second arc. And similarly if (continuing their motions) Q and r are in the same line with s when at and respectively and if Q at qs is equidistant from s and r (at p5) the arcs jp~ and ~)~pj; are equal, and the accelerating and retarding effects of Q on p in these arcs, respectively, exactly counterbalance each other.

But now let us suppose one, or other, or both of the orbits to be elliptic. If, first, we suppose Q at rest, thé orbit of F elliptic, and the perihelion or aphelion at P~, we plainly get thé same counterbalancing series of effects as in the former cases. But if the line of apsides have any other position than P2P4 the disturbing effects of Q on P will not be equally balanced in the course of a complete revolution of p about s. Thus, suppose thatpg is the perihelion of r's orbit: then, in the first place, the tangential disturbing force no longer vanishes at the points Pl, p~ Pg, and p~ r would not actually move from p, to pj,, but in a disturbed orbit tbat would cnrry him to a point between p~ and Q, and so of the other arcs, the orbit of p relatively to s passing through thé points p, and P3' butoutside the points pg and p~. Thus the more exact mode of expression would be, in moving from Pi to the line p~ a, and similarly for the other arcs. Such a mode of expression would, however, be ineonTement, and that adopted in the text is, as explained, suiHciently intelligible.


for the tangents to thé orbit of F at the points p~ and p~ are not at right angles to the line Qt?~s p~, and the lines Q)?t and Q~pg are not inclined equally with <~s to the tangents at p~ and pg 3 respectively. But neglecting this consideration (as we may safely do if the orbit of P is snpposed to be very nearly circular, so that the actual points at which the tangential force vanisbes lie very near tbe points p~ r~, pg, and p~) we have in the circumstance of p's elliptic motion a more serious disturbing cause. For p passes his peribelion point in the arc p~, and thus moves more rapidly over this arc-in which, as we bave seen, his motion is acceleratedthan over the arc p~pg in wbich his motion is retarded. Thus these dis.turbing effects no longer compensate each other, the retardation exceeding acceleration. On the other band, since the aphelion of p's orbit lies in thé arc PgP~ P passes over this arc in which his motion is accelerated, more slowly than over the arc p~ in which his motion is retarded. The acceleration in the arc pgp~ therefore, exceeds tbe retardation in thé arc p~. Thus, whereas in moving over tbe arc Pi?~ P's motion on the whole was retarded, in moving over the arc PgP~Pj? bis motion on tbe whole is accelerated.* These effects acting in opposite directions, produce a partial, but (unless r's orbit be exactly adjusted in a certain mean position) not a complete compensation and wherever we suppose the perihelion ofp's'orbit to lie, an outstanding retardation or accélération would remain after each revolution; and these disturbances always operating in one way, P's period would continually increase or diminish, and his orbit would be continually more and more disturbed from its original figure.

But now let us suppose tbat Q, instead of remaining stationary, travels uniformly round the circle Q,QgQgQ~, p describing several revolutions in tbemeantime in his elliptic orbit. Then it is clear tbat for a single revolution of p the above considérations hold good, and that P~s period is retarded or accelerated by Q's attracThese effets are partially modifi~d by changes of F's distance from s. It may be mentioned that any difference in p's distance from Q due to this cause produces its full effect in modifying Q's disturbing innuencc whereas; in thé next case considered, only a part of theeffect of Q's change of distance from p's orbit oporates for in approaching p's orhit û is also approaching s, and vice ~e~f! and it is to the difference of Q's attractions on p and s that Q's disturbing effects are due.


tion, and his orbit modified. But in the course of several revolutions different parts of r's orbit are successively presented to Q as Q travels onward in bis orbit; hence Q'8 disturbing effects are altered, accelerations replacing retardations, or vice ~e~o. and on the whole, when Q has completed a revolution, p's period and orbit are but little disturbed. A small outstanding disturbance, bowever, necessarily remains, since Q's conjunctions with p have happened opposite pct-c~ points of p's orbit, and though compensating effects have taken place in different synodical revolutions, tbe compensation (save under an exceptional adjustment of P's orbit) is not exact. Now, if at thé beginning and end of such a single revolution of Q, Q and r are in conjunction, then in the next revolution of Q a similar series of disturbing effects will be produced by Q on p's orbit and period, and so on continually (or at least until tbe modification of r's period prevents the uniform recurrence of conjunctions along or near the same line) thus p's orbit and period would in this case, also, be permanently modified, though not so rapidly as when Q is supposed stationary. Similar permanent effects would be experienced if p and Q returned to conj unction after two, tbree, four, or any exact number of revolutions of Q. The greater tlie number of Q's revolutions in such a cycle the smaller would be the outstanding disturbance of p's orbit at thé end of the cycle. But in the course of many cycles such disturbances, acting always in the same way, must produce permanent and observable changes in p's period and orbit. In the case only in which the periods of p and Q are incommensurable, so that these bodies never return to conj unction along the same line, no permanent disturbance will accrue.

Next, let us consider the effect of an ellipticity in Q's orbit, and suppose P's orbit circular. Let thé perihelion of Q's orbit be at Q,, and Q's motion near perihelion such that as p moves from p~ to p2, Q moves from Q, to Then, since Q's motion gradually becomes slower as Q moves from perihelion, it is clear tliat the arc j~pg passed over by p before p and s are equidistant from Q at Q3' does not so greatly exceed the arc p~a (similarly passed over by p when Q was considered stationary), as it would if Q moved over the arc


M3 with the greater mean velocity belonging to Q in the arc QI <y~ thus the arc ~~g is less than the arc p,~ and further, Q~s distance from p's orbit is continually increasing as Q leaves (~. On both acconnts, the retarding effect of Q's action in the former arc is less than the accelerating effect in the latter arc. Since Q's motion continues to diminish, and his distance from p to increase, it is clear t.hat Q's retarding effect as P moves over the arc p~y~ will be less than Q's accelerating effect as p moved over the preceding arc ~3~; or again there remains a balance of retardation. And so long as Q's motion continues to diminish, and his distance to increase-that is, until Q lias reached aphelion at Qg–p's motion will be accelerated in each synodical revolution of the two bodies. By parity of reasoning, it follows that so long as Q's motion continues to increase, and bis distance from p's orbit to diminish, after aphelion passage–that is, until Q is again at Qt–P's motion will be retarded in each synodical revolution. The final result would not, however, be a complete compensation in a single revolution of Qt, in this, any more tban in the former case. Some outstanding acceleration or retardation would remain at the end of each revolution of Q, and permanent disturbing effects on p's orbit and period would accrue in tbis case as in the last, unless the periods of p and Q were incommensurable.

Similar reasoning holds when the orbits of both p and Q are elliptical; 'but the tangential disturbances which operate according to the varying positions of p and Q, are somewbat more varied and complex. The effects due to tbe ellipticity of F's orbit may either cooperate with or partly neutralise tbose due to the ellipticity of Q's orbit; but there will not be a complete compensation of effects, either in any single revolution of P, or in several revolutions of p taking place dunng a single revolution of Q. And, further, if the periods of p and Q be commensurable, so that after a certain number of revolutions they return to the positions they had respectively occupied at first, there will remain an outstanding disturbance of p's period at thé end of such cycle of revolutions, whose amount will depend partly on the eccentricities of the orbits of p and Q, and partly on thé number of revolutions of P and Q, respectively, which may occur in each cycle. Tbus, if PiP~PgP~ and Q~Q~Q~Q~


(6g. 6, Plate X.) are the orbits of r andQ about s, and Cp and c~ the respective centres of those orbits, it is clear that the ~e~~)~~ea of the tangential disturbance will depend on the distances s Cp and s c~ or rather on the proportions borne by these distances to CpP2 and CqQ~ the respective major semi-axes of the orbits ofr and Q and consequently the o~~<:M~M~<y e~e~s resulting from those irregularities after a given number (supposed very great) of révolutions of Q, during which such irregularities have been sometimes acting one way, sometimes another, more or less effectively-must also depend in some degree on the eccentricities of the orbits of p and Q. But the circumstance on which that effect main].y depends is thé relation between thé periods of r and Q. If thèse are commensurable, then after one, two, or more revolutions of Q, the series of disturbances that had been operating during such revolutions, and which had left a certain outstancling effect, will be repeated, and so on continually, so that the resulting outstanding effects are accumulated, and r's orbit and period permanently affected. The greater the number of révolutions of P and Q that occur before such exact reproduction of a series of disturbances, thé smaller will be thé outstanding effect of such a series, for there must occur a greater variety in the modes in which Q is presented to the orbit of r. Thus, if at the end of only one revolution of Q, p and Q return to conjunction along the line from which they had started, thé effect outstanding will be greater than if two revolutions of Q occur before such exact coincidence the effect in the latter case will be greater than if three such revolutions occur and so on continually. And again, in any of these cases the effect will diminish as thé number of revolutions made by P in each cycle increases.~

It may be remarked hère that even if two planets were moving at any instant so that their periods would be exactly eommensurable if they were not disturbed by their mutual, or by extra.neous, attractions yet, being so disturbed, tlieir penods would no longer remain commensurable. Thus, even if some simple rela.tion of eommcnsurability existed between the periods of two planets at any instant, it is quite possible that disturbances which \vonld at first be accumulative, each cycle adding to the amount, would at length effect their own removal, by destroying thé simple relation of commensurability to whieh they were due. The pcriod necessary to effect such a change would, however, be far greater than the grcatest cycles (so far as our system is concerned) with whieh astronomers have to deal and it is questionable whether the


We have been considering hitherto the disturbing effects of a planet external to the disturbed planet. This case is more convenient for illustration than the case of a planet disturbing an external planet, but the reasoning in the latter case is exactly similar. There is no occasion, however, to consider this case separately for, since action and reaction are equal and opposite, thé internai planet exerts precisely the same force to retard or accelerate the external planet as the latter exerts to accelerate or retard thé former. The 6~6C~ of such equal and opposite forces, so far as changes of orbits and periods are concerned, may be very different, since such effects will plainly depend on the relative masses and orbits of the two planets but whatever outstanding effects of disturbance may appear after a given time in the orbit and period of one, corresponding opposite effects will appear in the orbit and period of the other. Thus we are able to apply the results just obtained to disturbances of the period either of Saturn or Jupiter, produced by the mutual attractions of these planets.

No simple relation of commensurability exists between the periods of any two planets t but in one or two instances we meet amount of disturbance accumulated before sneh change began to operate would not so far modify the orbits thus related that thé inhabitants of the two planets would bo affected injuriousiy, if not destroyed.

We were able in considering the disturbing effect of one body on each of two others to neglect the masses of these latter; but in considering the effect on each of two bodies of the mutual attraction between them tho masses must be taken into account. In thé former case the attraction of the disturbing body on the disturbed bodies varied as their masses. In the latter case, the same force is exerted on cachnamely, their mutual attraction the effect of such attraction will plainly be greater on the body of smaller mass. As an instance of thé kinds of action considcred:–One man can pull a given mass at thé same rate as ten men, of the same strength as thé first, can pull a mass ten times as great but if one man were to pull at one end of a rope while ton men of equal weight pulled at the other end, on a smooth and horizontal surface, the ten would prevail against him by superior weight, even though his strength exceeded their umted strength, for thé united strength of the eleven produces a tension along the rope which acts equally on thé unequal masses at the two ends of tho rope, and therefore prevails on the smaller. Obvious as such considérations may appear, they are frequently lost sight of by the student of astronomy, and a difficulty is feit in conceiving why, in one case, the mass of a' body is not considered at al], while in another case it is one of thé chief points of inquiry.

t It is not correct to say that the periods of thé planets are absolutely incommensurable a set of quantities -whieh, like the planetary periods, undergo continuous (however small) changes of increase or diminution, must at times have commensurable


with an approacb to such a relation, and consequently find an approach to those progressive perturbations which, as we have seen, would result from simple relations of commensurability. In the periods of Jupiter and Saturn there exists an approach to the following very simple relation :–That two periods of the exterior planet should be equal to five periods of the interior planet. The statement of the actual relations of the periods of Jupiter and Saturn is generally presented somewbat as foiïows :–Five periods of Jupiter amount to 21,662-9240 days, and two periods of Saturn amount to 21,018'4394 days; the former interval exceeds the latter by 144-4846 days. Hence, supposing the two planets to start from conjunction, Saturn would reach this line the second time (that is, after passing it once) 144'4846 days before Jupiter reached it the fifth time (that is, after passing it four times). In 144-4846 days Jupiter describes 12° 0'-7 about the sun, so that when Saturn reacbed the original line of conjunction Jupiter is about 12° behind. On the other hand, Saturn in 144-4846 days describes 4° o0'-4 about the sun, so that when Jupiter bas reached that line Saturn is not quite 5° in advance. Thus the two planets are very near, but have not qnite reached, conjunction. Jupiter's daily mean motion of 4~ 59~-3 exceeds Saturn's daily mean motion of 2~ 0~-6 by 2~ 58~'7,–tbis is Jupiter's daily (mean) angular gain Saturn has a start of 4° 50'-4, and this angle contains 2~ 58"'7 rather more than 97~ times thus, Jupiter will overtalœ Saturn, or they will be in conjunction, 97~ days after the passage by Jupiter of the original line of conjunction, or 21,760-4 days from the time of that conjunction.~ In this interval of 97~ days, Jupiter, with a mean daily motion of 4' 59~-3, describes 8° 6''4 about the sun, by which angle, therefore, the line of this conjunction is in advance of the original line of conjunction. This mean value will be of use presently in detervalues. The ~MC mean periods of the planets ~.y be absolutely incommensurable, but they are not known to be so, since they are not exactly determined. It is s~mcient, however, to prevent permanent or injurious changes in the planetary periods that no such simple relation as that approxima.ted to in the cases of Jupiter and Saturn, Venus and the earth, should subsist exactly.

Since there have been two cunjuuctions in the interval, or three synodical révolutions of Saturn and Jupiter, we obtain at once thoir mean synodical period by dividing 21760'4 by 3, giving 72o3~ days, nearly.


mining the period of the cycle of disturbances. In the meantime let us proceed to a more exact inquiry into the motions of Saturn and. Jupiter. The investigation given above presents a suniciently accurate view of thé general features of those rnotions, and is further use fui in determining the mean angle of progression of successive third conjunctions but it will be seen that it does not accurately present the true relations of Saturn and Jupiter. In fact, if it clid, tbe inequality we are inquiring into would not exist, for the uniform progress ofeach set of successive third conjunctions could only result from. the uniform motions of Saturn and Jupiter in circular orbits.

Fig. 7, Plate X., represents the orbits of Jupiter and Saturn about the sun at s. If we suppose that Jupiter's orbit J~Jgj~ lies in the plane of the paper, then the plane of Saturn's orbit Sj~~ must be supposed to intersect this plane in the line N N~* the part N~~ of Saturn's orbit lying above, the part N~s N lying below, the plane of Jupiter's orbit the points at which Saturn's orbit attains its greatest departure from thé plane of Jupiter's orbit lie at and and tbeir respective distances above and below that plaue are represented on the scale of the figure by the Unes and J~ J3 is the major axis of Jupiter's orbit, JI being the perihelion Cj is the centre, and J~ the minor axis: Cj~ is 494,256,000 miles; CjS 23,854,000 miles. SimilarlySiag.is the major axis of Saturn's orbit, being thé perihelion c, is the centre, and s~ thé minor axis the dimensions of Saturn's orbit have been given in Chapter II.

The last conjunetion of the two planets took place on the 28th of December, 1861, at about a quarter past seven in the evening, the heliocentric longitude of each planet being 166° 51' 17~ at the moment of conjunction. Tbus, Saturn and Jupiter were situated as at Fi and Qi respectively, tbe points p~ Qj, and s, being in a The longitude of the rising node of Saturn's orbit on the plane of Jupiter's orbit is 126° 32~ 41~ thèse planes are inclined to each other at an angle of 1° lo~ 41~. It must be remarked that the point marked T in fig. 7, represents the first point of Aries at the commencement onlyof the motions considered. During the interval (more than 99 years) in which the six conjunctions occar, thé first point of Aries regredes (that is, approaches N~) by nearly 1° 23~. Changes, less marked but still not unimportant, occur also in the forma of thé orbits of Jupiter and Saturn, and in the position of thé line N N'.


straight line inclined at an angle of 166° 51' 17" to s T. Starting from this line of conjunction, Jupiter bas been continually gaining on Saturn-so that, for instance, at the present instant (January 1 st, 1865, Ob. 30m. P.M. ) Jupiter is 47° 20' 52" in advance of' Saturn. Thus, when Jupiter again arrives at Q~ Saturn will not have advanced much beyond thepoint N~, and continuing their motions, they will be in conjunction along the line p~Qg,the arc p~N'p~being about two-thirds of the complete orbit of Saturn. Now, by what bas been aiready shown, if Saturn and Jupiter moved uniformly with their respective mean motions, the arc P~pg (or, which is the same thing, the arc <~Q~) sbould exceed an arc of 240° by one-third of 8° 6'-4,–or Pl P2 should be an arc of 242°42''l. This is not the case, however, under the actual circumstances. Saturn's mean daily angular motion is 2' 0"'6 bis maximum daily motion (when lie is in perihelion) is 2' 1.5~'3 his minimum daily motion (when he is in aphelion) is 1'41"'2: again~Jupiters mean daily angular motion is 4' 59~3, while his greatest and least daily motions are respectively 5'30"'5 and 4~32"'3. It is clear that these variations are sufficient to introduce very important modifications into all the circumstances of the motions of the two bodies. In moving from p~ to P2 Saturn passes bis aphelion point, and thus his mean motion during the interval is less than bis mean motion in a complete révolution. Jupiter's motion in the interval may be divided into two parts first, the complete revolution beginning from the point (~–in this, of course, he may be considered to move with his mean motion, or 4~59~3; secondly, the motion through the arc QiQ~, comprising the semi-orbit Jy~J~ in which Jupiter passes from aphelion to perihelion (and therefore may be considered to move with thé same mean motion as in a complete revolution), and the two nearly equal arcs Qjjg and JIQ2' one next to aphelion, the other next to perihelion, Jupiter's small velocity in the former being compensated by his greater velocity In Herschd's 'Introduction to Astronomy' the second conjunction is made to t:~e place 123°, the third 2-~6° and the fourth 368° 6~ from the first. It is clear that if this wern the case, Saturn would perform one revolution while Jupiter performed four, which, as vch~'eseen.isnotthe true relation between their motions. A similar mistake occurs in the description of the motions of Venus and thé earth, in Mitchell's ropidar Astronomy.'

L


in the latter. Thus, on the whole, during the interval between the two conjunctions, Jupiter may be considered to move with a mean velocity almost exactiy identical with his mean velocity in a complete revolution. Saturn, as we have seen, moves with a mean velocity less than his mean velocity in a complete révolution. Thus Jupiter gains on Saturn more rapidly than in the case first supposed, -that is, of uniform mean motions. Accordingly, the arc PtPgis less than thé arc of 242° 42'-1, obtained on that supposition,–and not by a small or scarcely appreciable difference, but by some eight or nine .degrees. `

In precisely the same manner it may be shown, that thé next conjunction falls on the line Qgpg that in the interval Saturn moves with a mean velocity slightly greater than his mean velocity in a complete revolution (passing over a complete balf-orbit from perihelion to aphelion) and that Jupiter moves with a mean velocity less than his mean velocity in a complete revolution (passing his aphelion in moving from Qg to Qg after his first complete revolution). Thus the arc P2P3 is greater tban the mean arc 242°42~'l. In moving to the fourth conjunction along the line p~Q~ near to, but in advance of p~Q~, Saturn passes the peribelion of his orbit, and moves with a mean velocity greater than his mean velocity in a complete revolution. Jupiter also, after a complete revolution, passes his perihelion in moving from Qg to (~, and moves with a mean velocity greater tban his true orbital mean velocity. Her e, then, the variations from mean uniform motion partly compensate each other. But in this case we need not examine the circumstances of motion in the interval between the two conjunctions, to determine the position of the line P~. For, since the first conjunction in this neighbourhood, Saturn will have completed two révolutions and the small arc p~p~ while Jupiter will have completed five revolutions and the small arc Q,Q~ thns the arc P~p~ will only differ from the arc of 8° 6~ 4 (determined from thé consideration of uniform mean motions) by the effects of the variations from mean motion in the passage of Saturn over the small arc p.?., and of Jupiter over thé small arc (~Q~. It might appear that such effects, though possibly appreciable, must be very minute in reality they are important, as will appear from the following calculation


Saturn (as already sbown) will arrive at thé point Pl 144*4846 days before Jupiter reaches the point Q~ Now Jupiter at <~ bas a daily motion of 4~ 34"-9, but his mean motion during 145 days preceding bis arrivai at the point Qg of his orbit is somewhat greater (since he is throughout approaching aphelion) and is approximately 4' 37"'7. With this mean velocity, it is easily calculated that in 144'4846 days he passes over an arc of 11° 4' 52". Thus when Saturn is at p~ Jupiter will be at q, q QI being an arc of 11° 4' 52~ Again Saturn at p~ has a daily motion of 2~ 4~'5, but his mean motion during 145 days following his arrival at the point ?t is somewhat less (as he is approaching aphelion) and is approximately 2~ 4"0. With this mean velocity he moves in 144'4846 days over an arc of4° 58~36~, so that when Jupiter isat Q. Saturn is at j9, pj~) being an arc of 4° 58~ 36~. Now Jupiter moves from Q~ with a daily angular velocity of 4~ 34~-9 about the sun, to overtake Saturn, which moves from p with a daily angular velocity of about 2~ 3~'5 hence immediately after passing Q~ Jupiter gains 2~ 3l'4 daily. But before the two planets are in conjunction, the velocity of each is diminished (since both are approaching aphelion), Jupiter's velocity more than Saturn's; thus the mean daily gain of Jupiter in thé interval is approximately 2~ 30". Since the angle 4° 58~ 36" contains the angle 2' 30" 119-4 times, Jupiter will overtake Saturn-that is, the two planets will be in conjunction–119'4 days after Jupiter bas passed the point QI and Saturn the point p. Jupiter's mean daily motion in the interval being about 4' 33"'o, QIQ4 is an arc of 9° 4' 16~. Thus the line of conjunctionr~Q~ instead of falling8° 6~'4beyond p~Q~ the original line of coDJunction, falls nearly one degree farther forward. In exactly the same way the conjunctions falling nea-r r~Q~ and pgQg can be determined. It will appear that Q2ql, corresponding to QIq, is an arc of nearly 12° 5Ô'-5 that p~p', corresponding to Pt~ is an arc of nearly 5° 8~'ô and that the line of conjunction p~ falls about 8° 24' beyond p~. Lasdy, Qg q", corresponding to thé arcs Qiq and Q~, is an arc of about 12° 4' Pap~ corresponding to The détermination of the arc <yQ, is not nfenssary tothe inquiry the cnicuhmon is introduced to illustra.te thé effects of thé non-nniformity of tho motions of the two planets. It will be remembered tba.t- on the supposition of uniform motions the eopresponding arc was showli to be 12° 0~'7.

i. 2


the arcs p,p and p~, is an arc of 4" 22''5 and the line of conjunction P6Q6 falls 6° 5 F beyond P~Qg.~

Thus the irregularities in the motions of Saturn and Jupiter arise from several sources.

In thé first place, there are irregularities due to the forms and positions of the two orbits. For instance, consider the conjunction which takes place along the line p~This line falls above Cj the centre of Jupiter's orbit, and thus divides that orbit into two unequa,! parts, thé upper (in the figure) being the smaller hence, considering Saturn as the disturbing body, it is clear that the radial part of Saturn's disturbing effect has a smaller purchase (so to speak) on Jupiter as he moves through the arc J., Q~ to conjunction, than as he moves on through the corresponding arc, beyond Q~ from conjunction: on the other hand, the tangential disturbing effect is greater in the former arc than in the latter. Jupiter's motion would (on this account), be accelerated in the former arc more energetically than it would be retarded in the latter; or which is the same thing, Saturn's motion would be more powerfully retarded as Jupiter moved through the former arc, than it would be accelerated as Jupiter moved through the latter arc. But hère another circumstance must be considered. As Jupiter moves from jg to Qi bis motion is contimially diminishing, and it continues to diminish till Jupiter reaches his aphelion at Jg. Further, Saturn's motion as be approaches, and after he passes F~ is continually diminishing. Since Saturn's motion is so much smaller The relations bctween these angles and those resulting from uniform mean motions may be thus exhibited

Arc correspondtng Arc corresponding Arc corresponding toQ, tot'.p. tor.p~urQ.f~

nearp,Q, 11° 4'~ 4~08~36"4~16~ nea.rp~Q:; 126o'5 S'a 8 24 nearPaQ~ 12 4 4 22-0 6 51 mca.n 12 0-7 1 4 50-4 8 6-4

These rcsults, it must be remembered, are not strictly correct. They hâve been obtained on the supposition that Saturn and Jupiter perform their revolutions in their respective mean periods, which, as already mentioned, is not the case. They are, however, sufficiently accurate for the purposes of our inquiry. The errors in fig. 7, plate X., arising from this cause would not be appreciable on the seule of tliat figure.


than Jupiter's, so also the variation of his motion in a given tirne i& smaller in amount; thus throughout the approach and separation we are considering, the relative motion of thé two bodies-that is, the excess of Jupiter's angular velocity over Saturn's-is continually diminishing. Hence the period of separation after conjunction is longer than the period of approach before conjunetion and therefore, of course, the accelerating effects on Jupiter in thé latter period would, on this account, be less than the retarding effects on Jupiter in the former period and similarly of the opposite effects operating on Saturn. Here, th en, the effect of the forms and positions of the orbits, and the effect due to the varying motions of the planets in those orbits, are conflicting. If we analysed the corresponding effects at the conjunction along p~Q~, it would appear that thé two effects are of the same kind as in the case just considered, and are therefore conflicting, but the effect due to rate of motion is much more marked than in the former case (since Jupiter is Jeaving, Saturn approaching, perihelion). If we considered the conjunction along pgQg, it would appear that both thé effects are of opposite kinds to those operating in the other cases, and therefore are still conflicting, but the effect due to the form of Jupiter's orbit* is more marked than in either of those cases, since the line pgQgS is nearly perpendicnlar to scj.

Corresponding variations in the effects of the mutual action of the planets in moving over arcs preceding and following opposition may be considered in the same manner. To avoid confusion, the lines along which the planets are in opposition, during thé interval of 100 years illustrated by the figure, are not indicated. They occupy positions intermediate to those occupied by the lines of the preceding and following conjunctions.t

Secondly, we hâve seen that the angle between successive lines of conjunction is variable, sometimes considerably exceeding, at others falling considerably short of the mean angle 242° 42~'L In Since Saturn only passes over a small part of his orbit while the planets are near conjunction, the effects duc to thé form of Saturn's orbit need not be considered hère they will fall under the consideration of the varying distances of the planets at different conjunctions.

t Thus, at thé opposition occurring between thé conjunctions along p,Q, and p~ Jupiter is near j~, and Saturn near pg.


this, and in the corresponding variation of the interval of time between successive conjunctions, we have new sources of irregularity, ser ving considerably to diminish the approach to compensation which would result frorn a more symmetrical adj ustment of these arcs and periods. Similar irregularities occur, of course, in the angles between successive lines of opposition, and in the intervals of time in which such angles are swept out by the two planets.

Tbirdiy, the distance between thé planets at successive conjunctions (and oppositions) is variable. It is clear from the figure that P~Q~ is less than p~Q~, r~Q~ less than pgQg and similarly p~Q~ is less than P~Qg, pgQg than p~Qg. Since the mutual action of the two planets varies inversely as the square of the distance, this is a very effective source of irregularity.

Fourthly, it appears that at, and in the neighbourhood of Q~, Jupiter gains more slowly on Saturn than near Q~pg, and here again more slowly than near Qgpg. In other words, the two bodies bang longer in the neighbourhood of each otber near p~Q~ than near P2Q2, and near p~Q~ than near pgQg. The disturbing effects due to their mutual attractions necessarily vary in amount according to the time during which such attractions are in opération. Fifthly, it bas been shown that the more nearly the line of any conjunction appr oaches to exact coincidence with the line of some former conjunction, the more nearly will the disturbing effects operating near the two conjunctions resemble each other. Now the arc p~p~ is greater than the arc pgp~ and the arc P2P5 is considerably greater than thé arc pgpg. Thus the effects operating to disturb the period (or any other element) of Saturn or Jupiter, near the conjunction along pgQg, and those operating near the conjunction along pgQg, resemble each other more closely, than do those operating near the conjunctions along p~ and p~ and these again resemble each other more closely than do those near the conjunctions along r~ and p~. Thus that <:MC'~?~'M.o~ of perturbations operating in the s~me on which, as bas been shown, the permanent, or long continued modification of the elements of either orbit depends, is more marked in the series of third conjunctions falling near P3Q3 than in thé series


falling near and in tbis tb.an in the series falling near PtQ).*

Sixthly, the gradual change in the periods of the two bodies affects the approach to commensurability on which it is itself dépendent. For instance, during the series of conjunctions considered, Saturn's period is continually diminishing and Jupiter's increasing; in other words, the two periods are continually approaching more nearly to the simple relation of commensurability already indicated. Thus the répétition of disturbances operating continually in one direction becomes more and more rnarked during the series of conjunctions considered, and for several following sets of triple conjunctions.

Seventhly, thé inclination of the planes of the two orbits has an influence, though a small one, on thé effects we are considering. Thé greater the inclination of the line joirnng thé centres of the two planets to the plane of either orbit, the larger is that resolved part of the mutual action which acts perpendicularly to such plane, and thus the resolved part that plane is correspondingly diminished,–in other words, the perpendicular force gains at the expense of thé radial and tangential forces. This diminution can never be very grea.t, since thé angle in question is always very small. It is plainly greatest in thé series of conjunctions near the line rsQ~ dnd nearly vanishes in the series near rgQg.

Other causes of disturbance and of variation in disturbance might be added these, however, are sufficient to indicate the complexity of the problem. It is necessary, however, to notice that all thé causes considered operate to produce variations in the efficiency of the radial and perpendicular disturbing forces.t Hence there anse changes in the eccentricities and inclinations, and in thé positions of the perihelia and nodal lines of the orbits of the two planets. These effects cannot take place without influencing, in some degree, It does Kot follow th~t the absolute effects of those series are to be placed in the order indicated for a series of c~sdy-resembling small disturbances may be less emcienttliau a series of more marked disturbances less closely rcsembling caeh other.

t Not necessarily in thé same way or to thé sanie extent for instance, a cause operating to diminish thé tangential may increase the radial force, and vice verset. Diminution of distance increases all thé forces.


the action and effects of the tangential force, the variations of which dépend, as we have seen, on those elements of thé two orbits. A more marked effect of suoh changes in lengthening the cycle during which the periods of Saturn and Jupiter undergo tbeir respective variations, will be considered presently.

To ascertain the exact amount of disturbance due to each of thé causes here mentioned, and thence to determine whether, in any set of three conjunctions, acceleration prevails over retardation, or vice ~e?'s~, can only be eûected by rigid mathematical analysis, in which the absolute qu~ntities concerned-as the masses of the sun, Saturn and Jupiter, and thé eccentricities, inclinations, and other elements of the orbits of the two planets--are fully taken into account. The results of such analysis correspond with the results of observation. Foraseries of conj unctions, there will remain-after each set of three conjunctions–an uncompensated acceleration of one planet and retardation of the other tben during a similar series of conjunctions, these effects are reversed, and the accumulated results of the former series gradually worked off, until an almost exact compensation is effected at the close of the complete cycle corresponding to the inequality we are considering. The angle 8° 6~'4 is contained 44-408 times in 360°. Hence, if we were to mark the places of successive third conjunctions from that along p~Q~, we should eventually (after marking down 44 such conjunction-lines) arrive at one falling between F~Q~ and r~. Thus the conjunction-line would not return exactiy to thé position p~Q~. But we may consider tbe cycle during which this conjunctionline travels completely round the circumference~ to be 44-408 times the mean period of three conjunctions,–that is, 44-408 times 21,760-4 days, or about 2,645'74 years. But it is clear that in travellin~ round the circumference this conjunction-line must pass the lines PgQg and P~ and when it is at or near either of these positions thé two other conjunction-lines must bave aiso travelled round, so tbat the three conjunctions in each triple set take place at or near the three original conjunction-lines, p~Q~, r~, and P3Q3. In other words, a complete cycle of disturbances will have taken place in one-third of the period just obtained, or in 881-91 years, if the elements of the two orbits have undergone,


meanwhile, no alteration. This, however, is not the case:–The perihelion of Saturn will bave been advancing at the rate of more than 19" yearly, the perihelion of Jupiter at the rate of nearly 7" the eccentricity of Jupiter's orbit will have been increasing, that of Saturn diminishing, yearly; and the inclinations and nodal lines (on the ecliptic) of the two planets will also have varied. The relations between the orbits at the commencement of a cycle are never exactly reproduced; but it bas been calculated that the series of disturbances is completed, and thé periods of thé two planets are restored to their original values and states (increasing or decreasing) in about 918 years in each such cycle there are rather more than 46 conjunctions. Thus thé disturbance in thé periods of the two planets, or thé ~6~ as it is termed, attains its maximum amount either way at intervals of about 459 years, in each of which are included seven or eigbt sets of three conjunctions. The inequality, at such times, amounts to about 48~' of retardation or acceleration in the longitude of Saturn, and about 20' of acceleration, or retardation, respectively, in the longitude of Jupiter.~ At present Saturn is about 41~ behind his mean place, Jupiter about 17' in advance of bis mean place. But in each set of tbree conjunctions Satum's actual motion is on the whole retarded, so that bis period is diminishing and his mean motion in longitude increasing, while Jupiter's actual motion is accelerated, so that his period is increasing and bis mean motion in longitude diminishing. In other words, the two planets are (at present) being gradually restored to their mean places.

Saturn's period also undergoes alterations, due to the disturbing influence of Uranus, Neptune, and even of our earth and tbe other comparatively minute planets tbat revolve within the zone of asteroids. The alterations due to the attractions of Uranus and Neptune are small, however, the others altogether insignificant, compared with those due to the attraction of Jupiter. For, in the first place, the mass of Jupiter greatly exceeds that of all thé other The proportion bctwcpn the variations in the longitudes of two plancts, due to their mutual disturbances, is thé InTerse ratio of their masses multiplied by the square roots of their mean distances from the sun.


members of the solar system; and in the second place, no approach to any simple relation of commensurability exists between the period of Saturn and that of any of those bodies so that alterations in one direction are compensated by corresponding alterations in the contrary direction.

The eccentricity of Saturn's orbit and its inclination to the ecliptic undergo oscillatory variations in cycles of gréât length, tlie perihelia and nodal lines shifting, meanwhile, round the ecliptic. The latter series of changes is not important: the former would be injurions, if not destructive, if the limits within wbich the variations took place were considerable. This, however, is not the case. Lao-rano-e has shown that, amidst all variations, thé following relations hold between the masses of the various members of the solar system, and the mean distances, inclinations, and eccentricities of their orbits:-

(i) If the mass of each planet be multiplied by the square root of its mean distance from the sun, and the product by the square of thé eccentricity of the orbit, the sum of all such products taken throughout the system is invariable.

(ii) If the same product (of the mass by the square root of the mean distance) is multiplied by the square of thé tangent of the angle at which the plane of the orbit is inclined to a fixed plane, the sum of all such products taken throughout the system is invariable.

The products corresponding to Saturn and Jupiter are by far the most important in either séries.* As these products correspond to but moderate eccentricities in the orbits of these two planets, it is clear that the eccentricity of eitber orbit could never become very great, even if it were possible for the eccentricity of the other absolutely to vanish. This, however, can never happen. If Jupiter and Saturn were the only members of the system the effects of their mutual attraction would be that in a cycle of 70,414 years the eccentricity of Saturn's orbit would vary between The sum of tlie masses of Saturn and Jupiter is fully 11~ times aa great as the sum of the masses of a.n thé remaining members of the solar system (yet known) and the sum of the masses of Neptune, Uranus, Saturn, and Jupiter, exceeds the sum of the masses of Mercury, Venus, the Earth, Mars, and thé asteroids, more than 200 times.


thé limita 0-08409 and 0-01345, that of Jupiter's between the limits 0'02606 and 0-06036,* 'the greatest eccentricity of one orbit corresponding to the least of thé other, and ~~e ~e?~ And what is of far more importance, so far as the inhabitants of the earth or of thé other minor planets are concerned, no large part of thé product corresponding to either of thé two giant members of thé system, or to Uranus and Neptune, can ever be imparted to the smaller bodies.t An intercbange of eccentricities and inclinations is always taking place between every pair of members of the system, whether near or distant, or whether either or both is small or great; but analysis shows that this intercbange is so distributed that the eccentricities and inclinations of the minor orbits can never become very gréât.

Sir J. Herschel's 'Introduction to Astronomy,' let Edition, p. 368. 't' A very simple ca.lculation will sa~Hce to show that if thé orbits of the four exterior planets could become circuler simultaneously, so that the whole of thé eccentricity-products corresponding to them were distributed among the minor planets, ail thèse bodies would be destroyed by falling into the sun, their orbits becoming too elongated to allow them to clear his globe.


CHAPTER VII.

HABITABILITY 0F SATURN.

WïiEN we consider the analogy of our own planet, it seems impossible to donbt that Saturn is inhabited by living creatures of some sort. JEf67'e we find, not only the earth, but the fathomless deptbs of ocean, not only the temperate zones, but the scorched regions of the tropics, and even the solid ice within the arctic and antarctic circles, crowded most abundantly with living creatures. Hère also we find that, not merely while the conditions now holding have subsisted, but tbroughout millions of ages, during which the earth has undergone variations of tbe most marked and startling nature, the same abundance of life has been found upon its surface. That a globe so stupendous as Saturn, and surrounded by a system so magnificent and elaborate, should be devoid of inhabitants, can hardly, then, be reasonably imagined but what manner of creatures subsist on Saturn-whether it is inhabited, as yet, by comparatively rudimentary races, or whether it is already peopled by reasoning and responsible beings, capable of appreciating the wonders that surround them, and adoring their Almighty Creator-it is not given to us to know.

On our own planet we find creatures of every race admirably adapted to the conditions that surround them. Whether we suppose such adaptation to be the result of express creative acts of the Almighty, or-which appears more probable–that, in His infinite wisdom, He bas appointed laws under whose action species are modified with the varying conditions that surround them, analogy points to the conclusion that on the other members of the solar system the same perfect adaptation prevails. It


is, therefore, merely by way of comparison, that I propose to examine, in this chapter, the adaptation of the physical conditions of the planet Saturn to the wants of beings constituted like the inhabitants of our earth it is not necessary to establish the subsistence of conditions so adapted, in order to prove that the planet is the abode of living creatures.

If an inhabitant of our earth could be placed on the surface of another planet, it is probable that the first circumstance in his new condition that would attract his attention would be tbe change in his own weight. If he were removed to Jupiter, he would find bis weight more than doubled, and would be unable to move without pain and dimculty. If, on the other hand, he were removed to Mars or Mercury, he would find his weight diminished by more than one baïf, and his activity and apparent muscular power correspondin~ly increased. If he were removed to Saturn, thé change in his weight would vary with thé latitude of the spot to whicb we suppose him to be conveyed. Owing to the compression of Saturn's globe, bis vast size, and his rapid rotation on bis axis, gravity varies with latitude in a much more marked manner tban on our eartb. If Saturn were not rotating, the weight of a terrestrial pound would be about 1-19 Ibs. at Saturn's pole, and l'171bs. at his equator. But the centrifugal force at Saturn's equator is about 0-164/ by which amount gravity is still further diminished. Thus, a man weighing 12 st. on earth, would weigb only a few ounces over 12 st. at Saturn's equator, but would weigh more than 14 st. at Saturn's pole. The difference of weight in the former case would hardly he appreciable in the latter it would prove a beavy burden but its effect would be somewhat diminished by perfect adjustment, since it would be distributed over the whole body. A Saturnian would find his weight increased in nearly the same degree, if he travelled from Saturn's equator to either pole we shall presently see that this is not the only circumstance in which tbe physical conditions of Saturn's arctic and temperate zones present a marked contrast to those prevailing at and near bis equator.

By this is meant that a mass -wcighing 1 Ib. on the pf).Tth and revolving about a. centre with the sume velocity and at the same distance as points on Saturn's equator about Saturn's centre, would require, to retain it in its orbit, a force sufficient to counterpoise a weight of 0'164lbs.


It bas been considered probable that the appearance of Saturn's surface differs greatly frorn that of our earth. And tbis for two reasons:–In the nrst place, it is urged that bis density being so small, he must be composed of materials very mucb lighter than, and therefore very different from, those composing our earth and, in thé second place, that fluids upon bis surface must either be of less density than the planet, and therefore very different from our oceans, or if of greater density, must all be collected in one hemisphere. Saturn's globe may, however, be hollow, and the mean density of the materials of this hollow globe not very different from the mean density of the materials composing our earth. t And, again, it bas not been established hy rigid matbematical inquiry, that oceans upon a planet of Saturn's figure, would necessarily be collected wholly, or almost wholly, in one hemisphere, if their density exceeded tbat of the planet. On thé contrary, it appears probable that fluid masses on the surface of such a planet would tend to form two vast polar oceans, since gravity is so much grea-ter 'Whewell's 'Astronomy and Général Physics (Bridgewater Treatise.) t Whether the earth is solid throughout or merely a spberlca.1 shell is a question on which the world of science is divided. The increase of heat as we proceed inwards aeems to indica.te that at no very great depth tlie hea.t must be so intense that all known substances would be converted into fluids. On the other band, Mr. Hopkins bas shown that the precession of thé earth's pole ia not such M it would be if tho ea.rth were a shell of such comparatively small thickness containing a vast fluid mass. Arguments of some force have also been urged to ahow that thé above-mentioned increase of heitt is not to be considered as an indication of a fluid nucleus; and it is certain that man bas penetrated the earth's erust to a distance absolutcly insignificant compared with thé dimensions of the earth's globe. Yet it seems clear that the balance of probability is largoly in faveur of a continuai increase of heat inwards, in even a greater ratio than that observed near thé surface. And it appears not improbable that at a depth of a thousand miles thé heat should be so intense that all known substances would at ordinary pressures be converted into vapour. But the pressure exerted by a vapourous nucleus on the surface of the fluid shell next to it, and by transmission on the solid shell, must bc so immense that the interior parts of the solid and liquid shells must owe their solidity and fluidity respectively to thé intensity of such pressure, and not to the insufficiency of tho heat in those parts to change respectively solidity into fluidity, and fluidity into gaseity, at ordinary pressures. Thus the thickness of either shell may bc far greater than would appear from any calculation ibunded on ordinary pressures. It is also coneoivable that thé immensity of the pressure exerted by the gaseous nucleus would be sufficient to modify thé motions of tho fluid shell, and that by combiningthe effects of sueh modification with the increased thickness of the-fl'ud crust deduced from thé consideration mentioned above, thé prec ion of thé earth's pole -might be accounted for as exactly as on thé supposition of thé solidity of thn whole mass of the oarth's globe.


at Saturn's poles than at bis equator. But even if it were proved that the former arrangement must inevitably subsist, what, after ait is such an arrangement but an almost exact counterpart of what is observed on our own earth ? It is true that tidal waves could not 8weep round such an ocean, as round the oceans tbat surround thé earth, but an océan whose tides are ruled by eigbt satellites, and restrained by the attractions of a stupendous ring, may require arrangements altogether different, in this respect, from those prevailincr on our earth. The appearance of Saturn, however, is not favourabie to thé supposition that the océan masses on his surface are confined to a single hémisphère for thé bright bands on This arrangement on the earth is modified by thé tendency towards the poles that might be expected from thé earth's form so that while the southern hémisphère (or more exactly thé hemisphere of wbich New Zealand forms the central région) is evidently that towards which the main body of the water is attracted, the northern polar regions are also occupied by a vast ocean, connected with thé southern ocean by 13ehring's Straits and the Atlantic. From this arrangement and the conformation of the land, it is obvious thitt at present thé centre of gravity of our globe lies nearer the southern than the northern pole. M. Adhemar haa suggested that this displacement of the centre of gravity from thé centre of figure is due to the vast masses of ice collected at the southern polo, and that as thé duration of thé antarctic summer is now continually increasing, those masses will diminish, and the frozen masses at thé arctic pôle increase, until the centre of gravity is nearer the northern than the southern polf, when the great southern ocean will rush northward. He conceives, in fact, tbat a vast flood takes place twice in every revolution of thé vernal equinox (that is, twice in 25,868 years), the ocean masses rushing alternately from polo to pole and he imagines that thé successive states of submersion and émergence undonbtpdiy passed through by every part of thé earth's surface may be better explained in this way than by the supposition of alternate élévations and dépressions from internai causes. Thé close observer of nature will not readily accept the idea of such cataclysmal floods, destroying ail living creaturf.s on thé face of thé earth at each eruption. It is not altogether improbable, however, that the ocean masses may oscillate from pole to polo in a more graduai manner, and that during such oscillations inundations migbt take place, insignificant when compared with thé uni versai floods imagined by Adhemar, but sufficient to constitnte tremcndous local catastrophes, and to leave lasting traces of their cffects. Thé results of such oscillations wonid di~ër in nn respect from those of élévations and subsidencf'.s of continents. It may be remarked tl)at while elcvations and dépressions of large tracts of the earth's surface have undoubtedly taken place, it appears improbable that whole continents should be so raised or depressed and the expression sometimcs met with in works on geology, that a. whole hemisphere may be elevated by internai forces while the opposite hemisphere is depressed, is simply an absurdity. Snch changes are inconsistent with thé simptest Ia.w of mechanies, that action and reaction are opposite and equal.' Forces temling to olevate one Iiemisphere must ~y ~~OM and therefore tend to elevate thc opposite hemisphere,-must tend, in tact, to lengthen that diamctcrof thé earth nlong wlticli their résultant acts.


Saturn's dise, which are probably vast belta of clouds drawn from oceans upon his surface, are found equally in the northern and southern hemispheres, and extend completely round Saturn's globe. The climatic conditions on the surface of Saturn undoubtedly differ in the most striking manner from those which prevail on the eartb. We may consider three points on which these conditions depend; namely:-the distance of Saturn from the sun the inclination of bis axis to the plane of his orbit and the respective lengths of the Saturnian day and year.

We have seen that Saturn's mean distance from thé sun is more than 9~ times as great as the mean distance of the earth. Thus thé diameter of the sun's dise appears less to the Saturnians tban to us in the proportion of 2 to 19; while the apparent surface of the solar dise, which varies as the square of the apparent semidiameter, appears diminished to about -~th part of the apparent surface of the dise visible to us. The quantity of light and béat received on any part of Saturn's surface is therefore only -g~th part of the quantity received on a part of the eartb's surface of equal extent, and equally inclined to the solar rays. In fact, notwithstanding the immensity of Saturn's globe, tbe whole of the light and heat received upon it, when Saturn is at bis mean distance from the sun, is considerably less than tbe light and heat similarly received on the earth. It does not necessarily follow, however, that the climate of Saturn is so bleak and frigid as that of thé earth would be under a corresponding diminution of the solar heat; for, independently of the consideration that the climate of any planet may be greatly affected by internai heat, there can be no ddubt that the amount and density of the atmosphere that surrounds a planet bas a most important influence on the climatic conditions tbat prevail upon its surface.* That Saturn has a very extensive, and therefore (at bis surface) a very dense atmosphère, seems probable from the appearance presented by his dise in powerful telescopes, as well as from bis vast absolute dimensions. Such an atmosphere can, of course, bave no effect in increasing the If the atmosphere of our carth were suddenly suhjected to such a change that heat radiating from the earth passed through thc air as freely as thé sun's direct heat, the earth would no longer be habitable by such races as now exist upon its surface.


amount of heat received upon auy part of Saturne suriace, or l'athée tends somewhat to diminish that amount but by preventing radiation, it may serve to maintain a mean température as high as the mean terriperature of our globe, or even considerably higher.* The amount of light received would not be increased by such an arrangement, except by the comparatively small amount refracted towards thé planet by thé atmosphère, and the consequent lengthening of the Saturnian twilights. That the surface of Saturn is illuminated with considérable brilliancy, however, may be inferred from thé brightness of his dise. Although it is less splendid than the dises of planets nearer the sun.f there is no approacli to thé sombreness and gioom tha.t o.newould expect from a diminution of thé solar ligbt to so smal) a fraction of that received upon our earth. It bas been calculated, however, that under such a diminution thé sun would still supply 560 times as much light as the moon at full-a calculation confirrned by the small loss of light in partial eclipses of the sun. There is therefore little reason for supposing that the quantity of light received by Saturn would be iusumcient even for such forms of life as are found upon our earth still less reason is there for supposing that no forms of life whatever could subsist on Saturn's surface.~ Mr. Hopkins bas calculated ttt~t if thé atmosphere of our earth were increased in hcight by about 40,000 feet, the earth would be maintained at its present température, ï/'e.rpo~~ only to the ~ai!K)7! of space, in ~e !'<x'~ <ï~~cc of the &M~. See Nichol'a Cyclopsedia, Appendix, Atmosphères of Planets.' This result, however, Cim h~rdJy be considered as satisfactorily established.

t Reference is not hère made to absolute splendour, which dépends on the magnitude of a. planet and its distance from thé earth, but to thn ïM~/7!SM brilliancy of the dise, which is independent of those relations. The faintness of Saturn's light compared with that of thé moon was vcry observable at t,he reappearance of Saturn on the mooc's bright limb after the occultation of May 8th, 1859.

It is probable that our own earth once received much less light than at present. This is indicated by the size of the eye-orbits in many extinct species of animais, and by the development attained by creatures of thé bat kind, which now furm an insignificant class of the earth's inhabitants. Thus, Hugh Miller, speaking of the remains.of animais of the secondary division, says, enormous jaws, bristling with pointed teeth, gape horrid in the atonf, under stajing eyf-sockets a full foot in diameter and again, here we see a winged dragon,' the Ptr'roda.ctylus Crassirostris, that, armed with sharp teeth and strong elaws, had careerod through thé air on leathern wings like a bat. Testimony of the Rocks,' Lecture III. Thé ptérodactyles of thé greeneand cxhibit not uncommonly a spread of wing of cigbt or nine yards Sen aiso Note D, Appendix I.

M


Saturn's axis is inclined at an angle of 26' 49' 28" to the plane of Saturn's orbit. Thus the Saturnian seasons, so far as they depend on this element, are not very different from those which prevail on the earth. In Table XI. (Appendix II.), the points of the horizon at which the sun rises and sets, the elevation of the sun at noon, the diurnal arc traversed by the sun, and the length of the Saturnian day, are given for the equinoxes and solstices of latitudes O", ô~ 10°, 60°, 65°, on Saturn's globe. These parts of Table XI. are calculatedjust as similar tables would be calculated for the earth. Thus:–suppose we require toobtaintbesearcsforalatitude of 42° upon Saturn's surface. Let n,z n, fig. 1, Plate XL, represent thé projection of the celestial hemisphere visible from a place in such a latitude (supposed north of Saturn's equator); n.o~beingtbe projection of the horizon-circle, whose south point is at H,, its north point at H~, its east and west points at o.* Then n.z is part of the meridian of the place; and p,, thé north pole of the beavens, is elevated above n, in an arc of 42~. Let o z be perpendicular to ir.H,, so that z is thé zenith. Draw o s perpendicular to o p, then o s is the projection of the sun's path at either equinox. Again, take arcs ss~ and s s", each of 26° 49~ 28~, on either side of s, and draw s~i and s~ parallel to s o. Then s~i and s~ are the projections of thé sun's path at thé summer and winter solstices, respectively: thus, the arcs ~s, i~ and ir,s~, give the 7~ altitudes of the sun at the equinoxes, at thé summer solstice, and at thé winter solstice, respectively. Now imagine the horizoncircle turned about the diameter ir~ so that the east point moves (along oz) from o to z; then the points at which thé sun rises at thé summer and winter solstices, respectively, move along the lines M~ and MW (parallel to oz) to the points and Thus the arcs n~ and n~ give thé c~m~s (measured from the south point) of the rising or setting sun, at the snmmer and winter solstices respectively. t Again, Ms~is the projection of part of a small circle of the sphere jr,zir.. If we imagine this circle turned about the line s~f, it would, wben fully open, Thé east point between o and the eye, the west point beyond o.

t Thé arcs z m and z~ are respectively the northern and southern oi the sun at the summer and winter solstices respectively.



appear as a circle about the point p as centre, and with a radius equal to p s'; the points corresponding to the rising and setting sun would move along a line through M at right angles to s~M, and tbis line would divide the circumference of the circle into two unequal arcs, the larger representing the ~M~?~~ the smaller thé ~oc~a~ ~'c traversed by the sun at the summer solstice. The lengths of the day and night are, of course, respectively proportional to the lengths of the diurnal and nocturnal arcs traversed by the sun and, furtber, thé length of the day at the summer solstice is equal to the length of the night at thé winter solstice, and vice

~<3T~.

Thé éléments considered in the preceding paragraph may also be determined for any given part of a Saturnian year. Thus, let A o B be the angle swept out by Saturn about the sun from the vernal equinox at the given period. Describe a circle M A M~ about o as centre, with o M or o M' as radius; let o B meet this circle in D. Then, if L'B L be drawn perpendicular to n,H, and L D s~ parallel to o s, LS~ represents the projection of the sun's diurnal path on the celestial sphere at the period considered, ir~ is the sun's m~ c~~M~, 11~ the sun's ~?~<- (measured from the south point) at rising or setting, and thé c~r~ arc traversed by the sun is obtained, as before, by supposing the circle of part of which L s~ is thé projection, turned about L S" A similar construction applies for all latitudes, and for all parts of the Saturnian year-the line o r,, assuming all positions from o H,, to oz, and the line o B sweeping from A through the complete circle of which M~A M is the senoicircle.*

Thefollowlng construction is more convcnient:–Letjp bo thé point in whieh o p, meets tho line s~M, and describe a cirele K~ with centre u and radius ojo; thenifon be drawn so that the angle D o c is equal to thé angto swept ont by Saturn about thé sun from the vernal equinox, s~D -L through D parallel to o s, and r, L' perpendicular to H, H, are the lines obtained by thé former construction for, if s~L (as before obta.ined) meets o ?“ in p~, we have o~ o p o L o M that is, o p' o D o L o B, or theright-angied triangles n o p' and BOL are similar, and the angle ODjp'is equal to thé angle 0 13 L, that is, the angle D o c equal to the angle DCA. When thé arcs corresponding to H, s' and H, L'are required for different latitudes, thé following is thé most convenient construction :–Thé circlû K D N is plainly a fixed circle for all latitudes (since s 8' is an a.rc of fixed length) thus, if E o be drawn so that thé angle s o K is equal to the angle D o c or A. o B, then E F perpendicular to o z gives the radius

M 2


Again, if the azimuth of the sun at rising or setting (in any given latitude) is known, it is easy to determine the rneridian. altitude of the sun. Thus, if the arc H,L is' known, we have only to draw i/L perpendicular to H,H~ and L s'" parallel to o s then n~ is the altitude required. Further, if L'L meets the circle M A M' in B, then A o B, or its complement, is the angle swept out by Saturn from the vernal equinox about thé sun. Similarly, if the altitude H s"' is known, then by drawing s'~L parallel to s o, and L L' perpendicular to H,n~ we obtain thé azimuth Ji,L', and the angle A o D, or its complément, as before.*

The Saturnian year, as already stated, contains about 29-~ of our years, or nearly 10,759~ of our days. The contrast between the Saturnian year and our own is rendered more marked by the shortness of the Saturnian day, of less than 10~ hours. Thus, thé Saturnian tropical year contains 24,618~ Saturnian days.t The most remarkable effect of Saturn's rapid rotation on his axis must be the rapid apparent motions of celestial objects. The diurnal motion of the sun, viewed from the earth, varies with the position of the sun on the ecliptic; at the equinoxes, when this motion is greatest, the sun moves over one degree of arc in 4 minutes of time, or over a space equal to his own apparent diameter in about 2 minutes. Viewed from Saturn, the sun (at the Saturnian equinoxes) moves over one degree of arc in about 1 minutes of time, or over a space equal to his own apparent diameter in abont 6 seconds. Ail the celestial objects .near the Saturnian

F o of circle G F.r, whose intersection (~) with n r~ determines the lines s~L and Li/ in whatever direction o r~ is drawn that is, for all latitudes.

It is assumed thron~hout that the diurnal path of thé sun is a decUnation-paraJIeï, which is not exactiy thé case, since the sun'a declination is continnally varying. In thé case of Saturn, however, the day is so short compared with the yettr, that thé s~n's daily path differs innppreciably from a declinatian-paraneL Thus the part of Table XI. wbieh states the meridian altitudes of declination-paraHeIs having given {tzimuths on the horizon, and the azimuths on the horizon of decUnMion-paraIlcIs having given meridian-altitudes, may be supposed to refer to thé diurnal paths of the sim at different seasons in given latitudes, w~e the given azimuths and a~«~o~ !M'M the range ~<McZ the ~MM the given ~M~M. See note (~), Table XI.

-)- The sidereal Saturnian ypar' contains 2~,620~ Saturnian days; but owing to :< slow precessional moyement of the Saturnian equinoctial points, thé tropical ycar is somewhat shorter. See Tables VII. and VIII., and thé explanation of thèse tabL's and of Table X.


equinoctial line, except the satellites, have about the same apparent diurnal motion. The diurnal motions of the satellites are diminished by their own motions round Saturn, which take place in thé same direction as Saturas motion of rotation upon his axis for instance, since Mimas revolves once around Saturn in about 22~ bours, the apparent motion of Mimas upon thé celestial sphere is little more tban one-half thé apparent motion of thé sun. The apparent motions of the satellites cômposing tbe ring (if these are separately visible) must be very slow, since tbese bodies revolve about Saturn in periods very little greater tban bis own period of rotation.

If our year and day were changed to the Saturnian year and day, respectively, the change in the year would undoubtedly produce far more important effects than the change in tbe day. The effects of the former change on the vegetable world would be not merely injurious, but destructive, except possibly within the tropics. Ail classes of animais, man included, would also suffer greatly in a winter or surnmer lasting nine years, and still more from the destruction of vegetables, plants, and trees. It is therefore probable that thé vegetable and animal worids on Saturn's surface, are, in general, very differently constituted from those which are found on our globe. Near the Saturnian equator there are two summers in each Saturnian year, and the variations of the seasons are not very marked. Hère, therefore, if anywhere, the races existing upon Saturn may resemble those found on our earth. We shall see also, presently, that thé intensity of the Saturnian winters in thé zones corresponding to our temperate zones, is aggravated by long eclipses of the sun's Hght by the rings, whereas near the equator the corresponding eclipses take place near the equinoxes and are of comparatively short duration.

Saturn's orbit is more eccentric than that ofthe earth, and consequently the light and heat received by Saturn vary in a more marked manner than with us. Thus, thé light and heat received by Saturn at perihelion, mean distance, and aphelion, are respectively as 46, 41, and 37. Let us consider the effects of tbis arrangement. The light and heat momentarily received by a planet vary inversely as the square of the planet's distance from


the sun. From the equable description of areas, it follows tbat thé momentary angular velocity of a planet about the sun also varies inversely as the square of the planet's distance from the sun. Thus, the light and heat momentarily. received by a planet vary directly as the planet's angular velocity about the sun. It clearly follows, therefore, that the light and heat received by a planet in any time are dir ectly proportional to the angle swept out about the sun in tbat time. Now, neglecting the precession of the equinoctial points, Saturn sweeps out the same angle about the sun (though not in the same time), in moving from the vernal to the autumnal equinox, as in moving from the autumnal to the vernal equinox of either hemisphere. He therefore receives the same amount of light and heat in each interval. Like our eartb, Saturn passes his perihelion near thé summer solstice of his southern hemisphere, and his aphelion near the summer solstice of bis northern hemisphere but the summer of the northern hémisphère lasts nearly sixteen years, thé summer of the southern hemisphere less than fourteen years. The difference of time exactiy counterbalances the difference of distance, so far as the light and heat received in the two intervals are concerned but this arrangement clearly tends to equalise the seasons of the northern hemisphere, and to make their contrasts more marked in the southern hémisphère.* It may easily be shown that the effect of the eccentricity of Saturn's orbit is to increase the total amount of light and heat S!r John Herschel in an article On the Astronomical Causes which may influence Geological Phenomena' (Geological Transactions, 1832), says, that thé corresponcling arrangement in the case of the earth exaetly pquidisps the seasons of either hémisphere. This is not the case, however the same amount of heat is received in the longer summer of the northern as in the shorter summer of the southern hemisphere but it no more follows that such a compensation affords to each hemisphere an equal and impartial distribution of heat' than it would follow thattwowinters are equivalent in their eRects to one summer because the same light and heat are received in tho former as in thé latter period. It is chiefly owing to the small fccentricity of thé earth's orbit that the seasons of the northern hemisphere resemble so closely thé seasons of the southern hemisphere possibly the great southern ocean bas a considérable influence in equalising the southern seasons. If the eccentricity of the earth's orbit were great the difference of summer and winter in the southern hemisphere would be greatly exaggerated; and the fact that the angular velocity of thé carth about thé sun varied aecordingly, would not render the effects of the intense heat of mid-summer and cold of mid-winter less distressing to the inhabitants of that hemisphere.


received in a sidereal revolution of Saturn about the sun. Thus, let us compare the heat received by two planets (which let us call p and r') revolving in orbits of different eccentricities, but whose major axes are equal. Let the minor axes of tbe two orbits be respectively b and b being greater than Then, since the periods of the two planets are equal (for their mean distances are equal), it follows from the equable description of areas about the sun, that thé area swept out by P in any time the area swept out by r' in the same time the area of P's orbit the area of r"s orbit, or (by a well-known property of the ellipse) b Now, suppose both planets to be at their mean distances from thé sun, that is, suppose they are equally distant from the sun then the area swept out by p in any time the area swept out hy P~ in tbe same time b b'; but considering the motion of each for a very small interval of time, it follows from the equality of the distances that thé area swept out by either varies as the angle hence, the angle swept out by r in any very small time the angle swept out by p~ in the same time b b'. In this time F and p' receive equal amounts of heat from the sun, since they are equally distant from him hence, from what was sbown in the last paragraph, it follows immediately that the béat received by p in a sidereal revolution the heat received byp~ in a sidereal révolution: & Or genel-ally, the -major axis of a planet's orbit remaining unaltered, the light and heat received in a sidereal revolution vary inversely as the minor axis of thé planet's orbit. We have seen, however (Chapter II.), that though the eccentricity of Saturn's orhit is very observable, the minor axis is very nearly equal to the major axis, and thus thé amount of heat and light received by Saturn is very little greater than it would be if Saturn revolved in a circular orbit at a distance equal to his present mean distance from tbe sun.

Thus :-Let A be thé heat received by P and in thé short interval of time considered a and a', the angles respectively swept out by r and P' about thé sun in that time H and H~ thé heat respectively recAived by p and ?' in a sidereal révolution then from what was shown in thé preceding paragraph, it follows that-

K A 4 rt. angles a

and H' a' 4 rt. angles

.(~pCT'i!.) H M~ a


Of the electrical conditions of Saturn, as of the other planets, nothing is yet known. It is not altogether impossible, however, that as we approach the physical interpretation of the phenomena of terrestrial magnetism–phenomena no doubt chiefly due to cosmical causes–'we may become acqua-inted with influences forming new and important bonds of union between thé members of the solar system.*

The connection between certain magnetic variations and disturbanees in tho solar atmosphere bas been placed beyond a doubt it remains, however, to be proved that the phenomena stand in the relation of cause and effect. Since it is highly probable tbat the solar spots affect the supply of light and heat, it is not improbable that they aiso influence electrical conditions. We may consider, therefore, tbat Humboldt was too hasty in contemptuously rejecting thé idea of such influence. Both sets of phenomena, however, may be duo to some cause yet undetermined. Thé correspondence of the decennial period of each with Jupiter's period of revolution bas been noticed. It may be remarked, however, that if the influence of Jupiter depended on any other relation than distance, such influence would operate twice in each sidereal revolution; and his variations of distance (from the sun) are so small that no great innucnec can be attributed to them. The greatest number of solar spots are found also in years when Jupiter is not near bis perihelion, as, for iustance, in the ycar 18-18, when he was nearer aphelion than perihelion. And, again, as far as terrestrial magnetism is concerned, we should expect any influence exerted by Jupiter to be greatest when he is in opposition, and no such variation has hitberto been noticed. It is not altogether impossible that in the successive conjunctions and oppositions of Saturn and Jupiter we may find a more satisfactory explanation of the decennial period in question; for thèse take place at intervals of about 3,627 days.or nearly ten years. It is conceivable that thé presence of both these planets along the same line through thé sun, whether in opposition or conjunction, would exercise a gréât influence over the zones of cosmical bodies revolving about thé sun, on whose motions, in ail probability, thé supply of solar light and heat in great measure depends (see Appendix II., Explanation of Astronomical Terms, Zodiacal Z~A<). It follows from thé results of Chapter VI., that tho conjunctions and oppositions of Saturn and Jupiter occur successively along lines inclined to each other at angles of about 58° 39', each line of conjunction or opposition falling by that amount bebind the preceding line of opposition or conjunction. Thus these lines complete thé circuit of thé two orbits in a retrograde manner in a period of about nftynine years. There must be a part of thé circuit in which the influence of the planets in opposition or conjunction is most effective; and we should therefore expect to flnd the successive maximum disturbances going through a series of variations in a period of about fifty-nine years. Observation appears to indicate that such -variations actually take place in a period of fifty-six years, though a long interval must elapse before the true period can be considered as established.

It bas long been recognised that the disturbance prevailing along the equatorial zone of thé sun's surface must be due to external causes, combining their effects with those due to thé sun's rotation, 1 which alone can produef no motions when once the form of equilibrium is attained.' External causes arc clearlyindieat.ed also bythc forms of the solar spots their widest openings are outwards, which would not, probabty, be thé case


The physical conditions and phenomena of Saturn's globe must be affected in a marked manner by the rings that circle about him. These serve to illuminate thé short summer nights, and to darken the short winter days of thé Saturnian. Let us examine thé nature of these effects, and thé manner in which they are produced.

In the first place, neglecting all consideration of the illumination of the system, let us consider what parts of the rings are above the horizon, and what are thé apparent outlines of such parts on the celestial sphere, for different latitudes on Saturn's surface. We may also, for the present, neglect the refractive effects of Saturn's atmosphere.

In fig. 2, Plate XI., let ~en'e' represent a section of the planet's globe through thé centre o and let N L i/N~ represent the corresponding section of the ring,–A A' being the sections of the division between the two bright rings, M L and M~i/ the sections of the dark ring. Let ~.jp. be the north pole and s.jp. the south pole. Thus if the figure be supposed to revolve about thé line r o P' it would generate surfaces representing Saturn's globe and rings. Now imagine a spectator placed at the north pole ~.p. :–thé pole of the Saturnian celestial sphere is seen at his zenith, in the direction p P his rational horizon is the celestial equator and it is perfectiy clear that the rings are altogether invisible to him whether he looks towards n or H~ or in any direction in the plane generated if thcy were due to internai action. The theory of thé dyna.mica.1 source of soln.r heat explains at once thé equatorial zone of disturbance, thé form of thé solar spots, and their spiral motions of rotation. A flight of cosmical bodies falling upon the sun would nccessarily be conA'erted by thé résistance of thé solar atmosphere into a spirally rotating whorl of intensely hot vapour. We may eonefive such a vapourous whiripool generating a rotatory motion in thé solar atmosphère and so causing vast depressions similar to those indicated by thé fall of the barometer in cyclones see Nichol's 'Cyelopeedia., Article Sun.' But a. more plausible explanation may, I thin~, be suggested. Where thé vapourous whorls approached thé surface of thc sun, their nerce heat would melt solid matter, turn liquids into vapours, possibly even vapours into some still more subtie form. The effects of such changes would correspond more closely than thé effects of mère depressions with observed appearances. Thé outlines of thé solar spots are shfu-ply defined, and thé spots change rapidly in form, especially before disappearing –pl~cnomena. which may not inaptly be compared to those presented when a stream of hot air is directed upon thé surface of a sheet of ice covoring water, till large hôte bas been mekcd completely through the sheet, the ice being thon allowed to form again.


by the revolution of B.n~ about the axis rp\ Suppose now that he advances along thé meridian ~e :-The point of the horizon towards whicb he is advancing becomes the south point as soon as he bas left the pole, and thé pole of the celestial sphere leaves the zenith-point towards what is now the north point of the horizon as he advances, the south point of the horizon falls lower and lower below the celestial equator, until he reaches the point n (in which a tangent from N meets the ellipse e n'e') when thé outer edge of the ring becomes visible at thé south point of the horizon. Continuing to advance, more and more of the outer ring becomes visible, the outer edge appearing as an arch in the southern horizon; and soon after he passes (on the northern arctic circle of Saturn's globe**) the inner edge of the outer ring becomes visible at the south point of thé horizon. Soon after, thé outer edge of the inner br ight ring appears; and when be reaches the point m (in which a tangent from M meets the ellipse ~en~) the inner edge of this ring appears. At thé inner edge of the dark ring becomes visible and after passing this point, parts of the complete system of rings are visible above the horizon, gradually rising higher towards the zenith, and extending farther and farther towards the east and west points of the horizon. Finally~ at e he sees thé inner edge only of the ring, extending as a zone of variable width on the celestial sphère the prime vertical t divides this zone into two equal parts, and thé width of the zone plainly diminishes from the zénith, where the ring's edge is nearest to the spectator, down to the horizon, where it is farthest from bim. If Thé point a is determined by an inclination of A, the tangent at to the ellipse ? e n~< at an angle of 26° 49' 28" to the line N o N' .? et le, the vertical :tt the point a of thé Satnrnian globe, is therefore inclined at the same angle to p o p~. lu like manner, the point t on the northern tropical circle of Saturn's globe is determined by an inclination of z the vertical at t, in an angle of 26° 49' 28~ to theline N o N'; T the tangent at t is therefore inclined at the same angle to POP~. The points t and u/ on thé southprn hemisphere are determined in a similar manner. It may be noticed that z k is parallel to t T, the tangent at t; and zg is in like manner parallel to a A, thé tangent at a. The vertical at any point of Saturn's globe meets e o </ farther from o as thé point is farther from either pole thus at a point very near e or </ the distance from o of tho point in whieh the vertical meets e o e', is ~yths of thé equatorial semi-diameter, or more than 6,000 miles, the compression of Saturn's globe being assumed at t At this time thé northern and southern pôles of thé heavens both appcar in thé horizon, towards and A respectively, and the celestial equator is tho prime vertical.


we suppose our spectator to advance from e towards the south pole, it is clear that the rings pass over to the northern half of the celestial hemisphere, falling gradually farther and farther away from thé zenith, and disappearing in an order the exact reverse of that in which they appeared. The same succession of phenomena would be presented if thé spectator travelled along thé other half of the meridian n e n'e', or along any other semi-meridian from the north to thé south pole. Thus, if we imagine ~<sn~ to represent, nota section, but a hemisphere of Saturn's globe, then ~andn~n'n~ represent halves of polar regions within -which the rings are altogether invisible <~ a'~ and n a a~ represent (approximately*) the halves of zones within which part of the outer ring only can be seen amm'c~ and a m mW represent (approximately) the halves of zones within which parts of both the bright rings can be seen, but no part of the dark ring; Z and 1 t t'l' represent the halves of zones in which parts of ail thé rings can be seen and finally 11~ represents one half of a zone witbin which thé inner edge of the dark ring appears above thé hohzon.f It is easy to determine bow much of each ring lies above the horizon of any point on Saturn's globe. Take, for instance, the point <x:–it is clear that thé horizon-plane at a (in other words, the plane touching the globe of Saturn at <~) intersects the plane of the rings in a line tbrough A; perpendicular to the line N0~. Let ng. 3 represent part of the ring-system on the same scale as fig. 2, but viewed from above the plane of the rings let o be thé centre oftbe system, and draw a line ON crossing the edges of thé rings at thé points L~, M~, and N, corresponding to the points r~ M, and N, respectively, in fig. 2. Then, if we draw AA~A' at right angles Thé tangent from thé inner point of the division at A fa.Us near a towards ?M. t If Satura were a perfect sphere it would be easy to détermine thé cxtent of these zones of his surface since the surface of a zone of a sphere to the surface of thé sphère (or four great cireles of the sphere) thé distance between thé planes of thé bounding circles of the zone thé diameter of the sphere. In thé case of :m obiate spheroid, zones parallel to thé equator bear a somewhat greater proportion than this to tho surface of a sphere of diameter equal to the equatorial diameter of the spiteroid the reader acquainted with the elements of conic sections will easily see that a narrow zone representedf by thé Une t a zone of equal width (measured from plane to plane of its bounding cireles) on a sphore of diameter e o e thé diameter conjugate to <! o t~ thé minor axis of thé ellipse e n~.


to o N, it is clear that A A~A' represents the line in which the horizon plane of the observer at 6g. 2, meets the rings' plane thus the segment AN A'lies above the horizon of the point Similarly we obtain thé segments MNM', L N L', and TNT~ lying above the horizons of thé points m, and respectively and corresponding lines and segments for any other points of Saturn's globe.* Again, it is easy to determine where an edge of a ring intersects the horizon of any point on Saturne globe. Thus, for thé point :–<~A, in fig. 2, is the distance of a from the line through A. corresponding to AA~ in fig. 3 hence, if, in fig. 3, we take A~~ equal to A in fig. 2, along N o, and draw the lines ~A and a A', the equal angles A a A" and A~ A" are plainly the azimuths (measm-ed from the south point) of the points at which the ring's outer edge crosses thé horizon. In a similar manner, by taking the lines M~, L' and T"t, in ng. 3, respectively equal to M m, L and T~, in fig. 2, we obtain the correspondino, azimuthal angles M M~ or M'm M~ L L" or L~ L~, and T T~ or T~ T". And if we draw ~u~u~ Y and t v', we obtain the azimuths of the points at which the inner edge of the inner bright ring crosses the horizons of thé points and t respèctively. We may obtain the corresponding azimuths in a similar manner for any point on Saturn's globe and for either edge of any ring.

It is also easy to determine the altitude of the point at which an edge of a ring crosses the meridian of any point on Saturn's globe. Take, for instance, the point t in ng. 2, and join N then the angle N t T at which t N is inclined to t T (the tangent at t to the ellipse e n~') plainly gives the altitude of the point at which the outer edge ofthe ring crosses the rneridian-in other words--of the point N. The angle z~N is the zénith distance of thé same point. If t s is drawn paral!el to NON', it is clear that thé angle s~T gives thé meridian altitude of the celestial equator above the horizon of t; hence s t N gives the southerly declination of the point N of the ring's outer edge. In a similar manner the altitude of the point in which either edge of any ring crosses the meridian of any point

on Sa,turn's globe may be determined. For a point on Saturn's equator we obtain tho line E xcx'E', cutthg off the Jargest segment of the system that can lie above thé horizon of any point on Saturn's surface.


Let us next consider thé form of the arched outline of the edge of a ring. If it were possible to view the rings from any point in thé line r o p', it is clear that all the edges would coincide with declination-parallels on thé celestial spbere, since the lines of sight from a fixed point in p o ?' to points in thé circumference of the ring's edge, would be inclined at a constant angle to the line r o r'. But since all thé points on Saturn's surface from which the rings are visible, lie at a great distance from FOP~, the edge of a ring (or, at least, that part of the edge which is visible) is viewed eccentrically. Now a circle viewed eccentrically from a point above its plane appears as an ellipse and the greater the distance of thé point of view from the perpendicular through the centre, in proportion to the diameter of tbe circle, thé more eccentric such ellipse will appear. Hence the outlines of rings will not appear to coincide with declination-parallels and the deviation will be more marked in the case of thé outline of an inner, than in that of an outer ring. It is easily seen that a declination-parallel through thé point in which an edge of a ring crosses the meridian, falls below the apparent outline of the ring's edge on each side of thé meridian, touching that outline on the meridian. Take, for instance, the point t, ng. 2, Plate XI., and suppose a perpendicular let fall from t on thé plane of the rings with the foot of this perpendicular as centre, imagine a circle described in the plane of the rings through the point N; this circle will fall within the outer edge of the outer ring, touching that edge at thé point N. Now this circle, viewed from t, would coincide with a declinationparallel on the celestial sphere and thé outer edge of the outer ring, viewed from t, would obviously appear to touch tbis circle, (and, therefore a declination-parallel) upon the meridian at N, and to pass above it on either side of thé meridian. Thé same may be proved of the other edges of the rings, and from whatever point of Saturn's globe thèse may be viewed, except, of course, from points on Saturn's equator. It follows that the visible part of a declinationparallel passing through the points in which thé outline of any ring meets the horizon, lies altogether above that outline. In Table XI. the relations hère considered are expressed for all latitudes within which any part of the rings can be seen. Thé


meaning of the part of this table baving reference to the rings may be shown as follows :-Take any latitude from the upper line, as, for instance, latitude 40° north, (corresponding nearly to thé latitudes of New York, Madrid, Bokhara, and Pekin, on our globe). It appears from the table, tbat. in tbis latitude the outer edge of thé outer ring crosses thé horizon at two points, 69° 36' east and west of the south point attains an altitude of 30° on the meridian, and an arc of 114° 2~–or somewhat less than one-third of the edge-lies above the horizon similarly the inner edge of the outer ring crosses the horizon 65°57~ east and west of the south point, and attains an altitude of 26° 11~ on the meridian, an arc of 104° 2~ lying above the horizon. Thus the outer ring covers two arcs of 3° 39' on the horizon and an arc of 3° 49' on the meridian. Although thé arc on the horizon is nearly as great as the arc on the meridian, yet it is easily seen tbat the apparent breadth of the arch presented by the ring is much greater on the meridian, for whereas the meridian crosses the arch at right angles, the horizon crosses it at an acute angle; so that the apparent breadth of thé arch near the horizon is much less than the arc of the horizon covered by it. Thus in north latitude 40° on Saturn's globe, the outer ring appears as a zone crossing the horizon towards the points E.s.E. and w.s.w.j attaining a meridian altitude of 30°; and this zone increases in width from the horizon to thé meridinn, where its width is about seven times as gréât as the apparent diameter of our moon. Sirnilarly it may be shown that thé inner bright ring rises as a much wider zone towards the points s.E. by E. and s.w. by w. of the horizon the upper edge of thé zone rises to an altitude bf 25° 22' the lower to an altitude of 12° 22~ only, on the meridian thus the greatest width of the zone is 13°, or more than 25 times the apparent diameter of thé moon. Thé great division between thé rings forms a zone between them, whose greatest width (where the zone crosses the meridian) is less than 49~ or about three The arcs of thé horizon and mcridina covcrpd by the rings arc somewhat greater than thé arcs given in thé table, and thé arcs covered by the division somewhat less ¡ fur thé thickness of thé rings bas not been taken into account in thé table. Thus in latitude 5° thé division between the rings would hardiy bc visible if thé thickncss of the system were 100 miles. Thé corrections due to this cause amount, howevt'r, only to a minute or two of arc in général.


semi-diameters of the moon. Thé dark ring covers nearly the whole space within thé inner edge of the inner bright ring for the inner edge of the dark ring crosses the horizon 13°5~ on each side of the meridian, and rises on the meridian to an altitude of only 46', so that only a narrow strip of sky about 28° from point to point and about three semi-diameters of the moon in width on the meridian, is left uncovered by the rings on thesouthern horizon. Again, it appears from the table that the meridian-altitude of a declination-parallel through the point (called A in thé table) in which thé outer edge of thé system meets thé horizon, is 34° 31~, or 4°31/ greater than the altitude of this edge where it crosses the meridian (atD) and that a declination-parallel through B crosses the horizon at distances 63°29~ on either side of the south point, or 6" 7' .nearer than A to the south point and similarly a declination-parallel through A~ crosses the meridian 7° 38~ above B~ and a declinationparallel through B~ crosses the horizon 1.2° 7~ nearer tban A~ to thé soutb point. Hence a star rising at A culminâtes3I/ above D; a star culminating at D is altogether bidden by the bright rings, except for a very brief interval when it crosses the division between thé rings; a star rising at A~ is altogether hidden by the inner bright ring, being 5° 22~ from the division between the rings even at culmination; and lastly, a star culminating at B is visible (through the dark ring) througbout its path above the horizon. Hence many stars must remain altogether invisible until thé slow precessional motions of Saturn's equinoctial points so far alter the declinations of such stars as to remove them from the invisible zone of thé Saturnian heavens.

In a similar manner the appearance of the rings for any latitude may be determined from Table XI. At Saturn's equator, the edge of the ring being turned towards thé planet, ib is probable, from the appearance of the rings when their edges are turned to thé earth, that an irregular zone of variable appearance ip turned towards the Saturnians. Assuming the dark ring to be on]y indistinctly visible, and thé inner edge of thé inner bright ring to be 100 miles in thickness, its appearance would be that indicated in note (3) Table XI. The width of thé zone thus presented wculd a.t the zenith be nearly two-thirds, at the horizon about one-fourth, of


the appa,rent diameter of the moon. Thé absolute extent of surface of the ring-system visible above the horizon is greatest for latitudes near the equator,* but the apparent surface of thé celestial sphère covered by thé rings attains its maximum extent in higher latitudes. It will be seen from Table XI. that thé arcs of the meridian covered, respectively, by the outer ring, the division between the rings, the inner ring, and the dark ring, attain their maximum values in about latitudes 45°, 40°, 32° 30', and 21° while the arcs of the meridian covered, respectively, by the system of bright rings, and by the complete system of rings, attain their maximum values in about latitudes 35° and 29°.

It is clear that the bright rings are plainly visible from parts of that hémisphère, only, of Saturn which lies above tbeir illuminated face. From the other hemisphere the rings are traceable in their effects in occulting the stars or other celestial bodies whose arcs above the horizon pass wholly or in part behind the ringa. These rings may also reflect a faint light received from Saturn's moons. The dark ring may possibly be visible in both hémisphères, since thé satellites composing it are probably separately visible from Saturn's surface. By day, the rings are either altogether invisible, or only appear as clouds of faint light below the sun's diurna! path. It might at first sight be supposed that the circumstance that thèse rings are composed of disconnected satellites, must have a marked effect, whether such satellites are separately visible or not; that the satellites in different parts of their revolution about the planet must exhibit such phases as our own moon, and tbat parts of the ring in which all the satellites are full' or nearly full, must present a much larger amount of illuminated surface to the planet, than parts in which all the satellites are new or nearly new. A little consideration will show that this is not actually the case. The appearance of the system shows that thé satellites composing it must be very numerous and closely packed thus the effects of mutual eclipses and occultations among the satellites counterIt is ensily calculated that thé surface of either face of the ring-system above the horizon at tho equator is pqnal to nbout y~ths of thé whole surface of either face, considered as extending from tho inner edge of thé dark ring to the outer edge of thé outer bright ring, without regard to divisions.


balance the éjecta due to their phases, and the question of illumination may be considered precisely as it would on the assumption that the rings are solid bodies. Now the brilliancy of an illuminated surface (beyond the earth's atmosphere) does not vary with the distance of the observer, nor with the angle at which be views thé surface thèse circumstances afFect'the apparent magnitude of the object, and, in the same proportion, the total amount of light received by the observer, but the intrinsic brilliancy of the object remains unaltered. The apparent brilliancy of an illuminated surface varies, however, with the angle at which the illuminating body is elevated above that surface.* Hence the apparent brilliancy of the rings at any instant is the same throughout their visible extent, and (co~e~a paribus) from whatever part of the hémisphère above their illuminated side they may be viewed; but such brilliançy varies with the sun's changes of declination, increasing gradually from the vernal equinox to the summer solstice, and thence decreasing to the autumnal equinox.

Between the vernal equicox and the summer solstice of either hemisphere, the shadow of the planet on the rings assumes sucIt appears from these considerations that Professor Challis is in error whon he states that a distant spherical body shining by reflected light would appear equally bright at all pointa of the dise' (Article on the Indications by Phenomena of Atmosphères to the Sun, Moon, and Planets, Reports of the Astronomical Society,' June 1863). A s&lf-Imninous spheric}d body whose surface is uniformly brilliant would so nppeaj, and therefore we may accept the diminution of brightness near the sun's periphery as an indication that the sun has an atmosphere but in the case of a sphere shining by light received from a distant luminous body, the illuminated hemisphere is not uniformly brilliant, and therefore the dise presented by it exhibits corresponding variations of brilliancy. An atmosphere surrounding a planet, by tending to equalise the illumination of the planet's surface, would diminish rather than increase this variation in fact, there is no resemblance between thn cases of a selfluminous sphere and of a sphère shining by reflected light, as regards the effects to ba attributed to the presence of an atmosphere.

Thé variation of brilliancy is suniciently conspicuous in the dises of thé planets Saturn and Jupiter and though these planète never present a gibbous appearance, yet there is a perceptible dinerencé in the illuminations of opposite aides of the dise when the planets are in or near quadrature; see the figures of Plate I. Similar variations of brilliancy are exbibited by Venus and the moon, when horned or gibbous. When the moon is full the variation is also traceable, but less clearly, owing to the irregularities of her surface. An examination of thé general brilliancy of dinTfrent parts of thé lunar dise confirma the views of the moon's form (as respects her visible hémisphère) presented in Note C, Appendix I.

N


cessively aIl the forms indicated in P]ate XII.* At the vernal equinox the edges of the sbadow are straight, as in 6g. 1 at and near thé summer solstice the outline of the shadow is part of an ellipse, an extremity of whose longer axis lies within the outer edge of the rings; in all intermediate canes thé outlines of the shadow are parts of an ellipse of considerable eccentricity. The interval of time in which the shadow changes frorn thé form indicated in one ngure to that indicated in the next is about 384 days. It is easy to détermine the mnnner in which tbe vast shadow of the planet sweeps over the illuminated face of the rings. At sunset, at and near either equinox, the rings are illuminated throughout their visible extent in all latitudes. Near the equator the shadow of the planet rises in the east, as soon as the sun has set,t eclipsing at once the whole breadth of the rings near the horizon in higher latitudes the shadow rises later, eclipsing first the outer edge of the rings. Later in the Saturnian year tbe curvature of the shadow shows its effect; the parallel of latitude witbin which the eclipse commences along the inner edge of the rings passing higher and higher, until it includes all latitudes witbin which thé rings are visible. Near the summer solstice the outer edge of the outer ring is not eclipsed at all. The shadow also rises later and later to midsummer; but as the nights grow shorter and shorter, and as in high latitudes this change takes place at a greater rate than the change in thé hour at which the shadow rises, it will happen that, in high latitudes, great parts of the ring are already in shadow when the sun bas set. In all latitudes and at all seasons the central line of the sbadow crosses the meridian at midnight. At this hour a very small part of the ring is visible, even from points near the equator, near the time of eithér equinox; but, for about three yea.rs, near the time of the summer solstice, the outer edge of the ring is not in shadow at midnigbt. At this time the system must present a magnificent appearance, as a vast double arch of light, indented by a broad elliptical shadow. Owing The point of view in these flgures is supposed to lie in the axis produced of the planet; the Unes A A', L L', M M~, T T' and B E', correspond to the lines similurly lettered in fig. 3, Plate XI. and the circips n n'n", a < J~ w~ t < and e to the lines eimilarly lettered in fig. 2, Plate XI.

t Owing to refraction the shadow doubtless rises before sunset, just as the eclipsed moon Is sometimes visible while the sun is yet appajently above the horizon.


L- i.: vo.


I.ntlrinI1:J.~)nr;n.1a-1i


to the refractive effects of Saturn's atmosphere, the outline of the shadow is probably fringed with a wide ruddy or copper-eoloured penumbra.* The central line of the shadow sweeps uniformly round the rings, thé shadow disappearing, at or before sunrise, in the west, in the same manner (at all seasons and in all latitudes) as it had appeared in the east. The changes taking place from the vernal equinox to the summer solstice are repeated in reverse order from the summer solstice to the autumnal equinox.

In his Outlines of Astronomy,' Sir John Herschel states that the regions beneath the dark side' undergo 'a solar eclipse fifteen years in duration.' Dr. Lardner appears to have imagined that Herschel supposed the whole hemisphere beneath the dark side of the ring to undergo a total eclipse fifteen years in duration; and, in a paper read before thé Astronomical Society in 1853, he endeavoured to show that by the apparent motions of the heavens produced by the diurnal rotation of Saturn, the celestial objects, includmg the sun and the eight satellites, are not carried parallel to the edges of thé rings; that they are moved so as to pass alternately from side to side of these edges; that, in general, such objects as pass under the rings are only occulted by them for short intervals before and after their méridional culmination that although, under some rare and exceptional circumstances and conditions, certain objects, the sun being among the number, are occulted from rising to setting.the continuance of such phenomena is not such as bas been supposed, and the places of its occurrence are far more limited.'f It will appear, however, on a more exact examination, that Lardner was in error on nearly every point he imagined he bad established. There are two methods by which astronomers determine the occurrence and nature of a solar eclipse. In one, the apparent paths of the sun and moon on the celestial sphere are examined for short intervals of time before and after the time of new moon and No attempt has been made in Plate XII. to indicate either the form of such penumbras or the twilight-circle bordering the parts of the planet in shadow. The extent of these depends altogether on the unknown extent and refractive powers of Saturn's atmosphere. The true penumbra, or that due to the apparent size of the sun's dise, is too small to be appreciable either in these figures or in the figures of Plate XIII.

t Dr. Lardner's 1 Museum of Science and Art,' vol. i. p. 69.

N 2


the moments of first and last contact and of central eclipse are thence deduced. In the other, a spectator is supposed to view from the sun the passage of the moon's dise across the larger dise of thé earth the manner in which the given place on the eartb's surface would appear to move, if viewed from the sun's centre during thé time of passage, is easilydetermined; and the moments of first and last contact, and of central eclipse, are determined from thé simple principle that if the given point on the earth is so situated that it would be invisible from a given point of the sun at any instant, then such point of the sun must also be invisible from the given point on the earth, or, in other words, is eclipsed. The application of the first method to the eclipses of Saturn's surface by his ring-system is simplified by the consideration that the rings occupy an invariable situation on the celestial sphere of any given point on Saturn's surface. At the autumnal equinox of either. hemisphere the sun bas at rising' an azimuth of 90° (in other words, the sun rises in thé east), and attains a meridian altitude equal to the complement of the latitude. After the autumnal equinox the sun passes to the south of the celestial equator in northern, to thé north in soutbern latitudes; and as his declination increases bis meridian altitude and azimuth at rising diminish. At length the sun crosses thé horizon at the points (called A in Table XI.) in which the outer edge of the outer ring meets the horizon. From this time the sun is eclipsed after rising and before setting for intervals of gradually increasing length, until he crosses the meridian at the same point (called B in Table XI.) as the outer edge of the outer ring. From this time the sun is eclipsed throughout the day (except, in certain latitudes, for two intervals of a few minutes, during which he is seen between the rings), until at rising and setting he crosses the horizon at the points (called A'' in Table XI.) in which the inner edge of the inner ring meets the horizon. From this time thé sun is visible (through the dark ring), after rising and before setting for intervals of gradually increasing length, until he crosses the meridian at the same point (called B~ in Table XI.) as the inner edge of the inner ring. From tbis time he is visible throughout the day (neglecting the partial eclipses probnbly caused


by the dark ring) until the winter solstice, and for a corresponding interval after the winter solstice. During the quarter of a Saturnian year from the winter to the vernal equinox a similar series of eclipses takes place in reverse order. In latitudes higher than 19° Ô(/ the sun does not reach thé point B~ so that in these latitudes eclipses in the middle of each day continue to the winter solstice. Again, in latitudes higher than 35° 52' the sun does not reach the point A', so that in thèse latitudes eclipses lasting throughout the day continue to the winter solstice.

The intervals during which eclipses of each kind are continued can be roughly determined by construction in the method indicated at page 164. The last section of Table XI. contains the more trustworthy results of calculation. From this table it will be seen that, even at the equator, the sun is totally or partially eclipsed for several days but that the periods of eclipse increase rapidly with the latitude. Thus, in latitude 40°, the eclipses begin when nearly tbree years have elapsed from the time of the autumnal equinox. The morning and evening eclipses continue for more than a year, gradually extending until the sun is eclipsed during the whole day. As the sun does not reach the point.A' in these latitudes, thèse total eclipses continue to the winter solstice and for a corresponding period after the winter solstice in all for 6 years <s, or <5~3'~ ~~rmc~ <~M/s. This period is followed by an interval of more than a year of morning and evening eclipses. The total period during which eclipses of one kind or another take place is no less than 8 yec~s <2P~.<~ days. In a similai. manner the eclipses for other latitudes are determined from Table XI. If we remember tbat latitude 40° on Saturn corresponds with the latitude of Madrid on our earth, it will be seen how largely the rings must innuence the conditions of habitability of Saturn's globe, considered with reference to thé wants of beings constituted like the inhabitants of our earth.

The second method of determining the extent and duration of solar eclipses-called the method of projecting eclipses-is less exact than the former, but better adaDj~ed for illustration. The figures of Plate XIII. represent Saturn as he would appear if viewed from the sun at the vernal equinox of thé northern hcmi


sphere (ng. 1) at the summer solstice of the same hemisphere (fig. 8) and at sixintermediateperiods.* These epochs correspond w.ith those of the figures of Plate XII., and, like them, are separated by equal intervals of 384 days. The arctic circles are represented by the lines a~a~ ànd a a'a", the tropics by the lines t t't" and tt~, the equator by the line 66~, and the north pole by the point p, in each figure (see Chapter IV. pp. 95-99) the rings are bupposed to be removed, and their shadows on the planet's dise thus rendered visible. t These shadows pass to the southern hemisphere at the autumnal equinox of that hemisphere, travelling rapidly southward at first., but more slowly as their width increases; and about two years before the winter solstice the lower edge of the black shadow passes beyond the lower edge of thé dise. The five dotted parallels of latitude in each figure (except ng. l)represent:–Thé parallel just reacbed by thé lower edge of the black shadow; a parallel passed over by this edge a parallel just within the upper edge of the black shadow a parallel just clear of this edge and a parallel just clear of the dusky shadow of the dark ring. Now, owing to the rotation of Saturn on his axis, any point on his surface would appear to an observer in the sun to travel along alatitude-parallel, appearing on the left edge of the dise (the moment of sunrise at the place), and disappearing on the right (the moment of sunset at' thé place). Hence, a place between the lowest pair of dotted parallels in any figure (that is, at the epoch represented by such figure) would be in shadow in the morning and evening, dipping below the shadow in the middle of the day a place between the second and third dotted parallels (counting upwards) would be in shadow throughout the day a place between the third and fourth would not be in the black shadow in the morning and evening, but would dip witbin it in the middle of the day and, lastly, a place within the two upper dotted parallels would not be in the dusky shadow in the morning and evening, but would dip within it in the middle of the day. These results correspond with those already Fig. 1 corresponds to Satu~h's position on the 18th of May, 1862; fig. 8, to bis position in March, 1870.

t To avoid confusion the line of light corresponding to the division between the rings is omitted in the ûgnies of Plate XIII.


obtained, and the figures of Plate XIII. suSiciently indicate thé vast extent attained by the shadow near the time of the winter solstice, and the consequent long duration of eclipses, in latitudes not very near the equator. The shadow of the ring passes through the same changes of form in inverse order between the winter solstice and the vernal equinox of the southern hemisphere but the pole of the planet passes to the left, so that at the latter period fig. 1 'M~67'~ represents the dise of the planet. The other figures inverted indicate the manner in which the shadow sweeps across the northern hemisphere, to the winter solstice of that hemisphere. The shadow, in returning, passes through the same changes, but in inverse order, and sloped towards the left instead of towards the right. Thus, at the end of the Saturnian year the appearance of the dise is again as in ng. 1.

Ail objects whose declinations are variable, such as the planets and tlie outer satellite, undergo a similar series of eclipses. Thé extent and duration of such eclipses for any celestial object will vary with the range of the objectas changes of declination. Thus the outer satellite, whose declination never exceeds 15° north or south of Saturn's celestial equinoctial-line, may be totally eclipsed during thé whole time it is above the horizon only in latitudes lower than 25° north or south; since the point B of thé ring is more tban lô° from the equinoctial in higher latitudes. ~ince the seven interior satellites move very nearly in the plane of the rings, it is clear that in places very near Saturn's equator thèse satellites can only become visible when they reach their greatest departure from tbe plane of thé rings. In all other parts of Saturn's surface these satellites can never be eclipsed by the rings. Their orbits being (approximately) circles concentric with the rings, would, like thé edges of the rings, appear as ellipses to the Saturnians, and would lie altogether clear of the rings-just as the outer edge of a ring lies altogether clear of the inner edge. The apparent magnitudes of the satellites vary with the point of Saturn's surface from which tliey are viewed, and with their own motions. The following table will serve to give an idea of the relations among the satellites in the latter respect thé satellites are supposed to be viewed from a place near Saturne


equator in higher latitudes the satellites vary similarly in apparent magnitude, but within a narrower range of variation, as they traverse the sky from horizon to horizon:-

Apparent Diameter Same, mean diameter Disc, mean dise of

Assumed Dise Moon'a dise as 1 Moon as 1

Namo Diameter

inmilea on the at the onthe atthe onthe atthe

Meridian. Horizon Meridian Horizon Meridian Horizon

Mimaa 1000 43' 27" 31' 24~ 1-396 1-009 1-950 1-019 Enceladus 1000 30 44 23 57 0-988 0-770 0975 0-593 Tethys 1500 35 3 28 42 1-126 0-922 1-269 0-851 DIone. 1500 27 20 23 15 0-879 0-747 0-772 0-558 Rhea 2000 23 34 21 7 0-757 0-679 0-574 0-461 Titan 4000 19 0 18 7 0-610 0-582 0-373 0-339 Hyperion 800 3 7 3 0 0-100 0-096 0-010 0-009 Japetus 3000 4 45 4 40 0-153 0-150 0-023 0-023

The eclipses of the satellites by the planet, and of the planet by the satellites, may be determined by the methods applied to the rings. These eclipses have been considered in Chapter IV. Of the planets only Jupiter and Uranus are visible to the Saturnians supposing their eyesight as ours. Jupiter is an inferior planet; and its phases, viewed from Saturn, resemble those of Venus viewed from the earth. Although Jupiter approaches as near to Saturn, when in conjunction, as to the earth when in opposition, he is, in the former case, invisible to thé Saturnians, since he rises and sets with the sun. Since in other configurations Jupiter is at a greater distance from Saturn than from the earth when in opposition, and since, fupther, only a part of his illuminated face is turned towards the Saturnians, he can never present an appearance even approaching in brilliancy the appearance he presents to the earth when in opposition. His mean synodical period with respect to Saturn is 7253'445 days. Uranus is a superior planet to Saturn, and must be distinctly visible when in opposition, being then removed by a distance only one-half that by which he is removed from the earth when in opposition. But before reaching quadrature Uranus must become invisible to thé Saturnians, supposing their eyesight as ours. His mean synodical period with respect to Saturn is 16568-295 days.


The result of the examination of the probable physical conditions and phenomena subsisting on Saturn does not appear to faveur the supposition that the planet is a suitable habitation for beings constituted like the inhabitants of our globe. Thé variation of gravity, the length of the Saturnian year, and the long-protracted eclipses caused by the ring, are the circumstances that seem to militate most strongly against such a supposition. Over a zone near the Saturnian equator these circumstances have less eifect/'however; and it is not impossible that arrangements unknown to us prevail on Saturn which may render other parts of his surface habitable as we should understand the term: The very combinations which convey to our minds only images of horror, may be in reality theatres of the most striking and glorious displays of beneficent contrivance.'

On the general question of the habitability of the system that circles about Saturn, we hâve no means of forming an opinion. From the analogy of our moon it appears highly probable that no part of the system is habitable by such creatures as inhabit our earth. t

Hcrsehers Outlines of Astronomy,' p. 286..

t See Note C, Appendix I., Habitability of the Moon.


APPENDIX I.


NOTE .A.

CMALD~EAN ASTRONOMY.

The Planetary Five

With a submissive reverence they beheld ¡

Watched from the centres of their sleeping flocks

Those radiant Mercuries, that seemed to move

Carrying t-hro~gh œther in perpétuai round

Decrees and resoLu fions of the gods.

'WORDSWORTH.

IN many parts of the East astronomical systems are found which bear obvious traces of a common origin. We find in ail the same duodecimal division of the Zodiac the week used as a division of time the planets associated in the same order with the days of the week and the hours of the day;t and other points of resemblance, sufficiently marked to leave little doubt that they are not accidental.

Meagre and imperfect as thèse systems now appear, there can be little doubt that the system from which they sprang was founded by astronomers of great ability, close observera and careful iriterpreters of nature. The origin of the system must be placed in a remote antiquity. The Egyptians, to whom the invention of astronomyis sometimes attributed, in all probability derived their system from a more ancient nation. The claims of the Chinese may be dismissed at once, if we consider the character of that people-apt to imitate but slow to invent. When we examine the claims of the Indians, Persians, and Babylonians, we are met by a singular circumstance :–7'Ae!r systems of a~?<ro?!0~ belong to a latitude c~s~6ra&~ higher </<a?t the ~~M~cs q/'J5eM~?'6S, ~rseyo~, or Babylon. For the Brahmins teach in their sacred books that the longest day in summer is twice as long as the shortest day in winter, winch is not thé case in any The signs of the Zodiac are not the snme in all the Systems. The signa we usethe Ram, Bull, Twins, &c.-appear to have been derived from the Dodecatemoria of the Chaldseans the Chinese name the signa as follows :–Thé Mouse, Cow, Tiger, Hare, Dragon, Serpent, Horse, Sheep, Monkey, Cock, Dog, and Bear.

t This order is as follows :–The Sun, the Moon, Mars, Mercury, Jupiter, Venus, and Saturn for the days of the week Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and the Moon for the hours of the day,-the first hour of each day being associated with the planet that ruled the day.


part of India se also Zoroaster taught thé Persians and Ptolemy obtained ancient Babylonian records of star-risings, and these belong to latitudes certainly not lower than the 40th parallel. In the measurement of the earth's circumference adopted by ancient astronomers, we have a singular confirmation of this circumstance. It corresponds to a latitude of about 45° and taking into account errors of observation, we must yet place thé latitude of the country in which the measurement was effected somewhere between 35° and 55° north.

Struck by the singular circumstance that these nations should employ a system of astronomy with which the celestial phenomena visible to them do not even approximately correspond, Bailly was disposed to ascribe the invention of the system to an extinct race, whom he called the Atlantides. He placed the seat of this race in Tartary or Siberia; but the cradle of thé race,–an< indeed, of mankind-the Atlantis of Plato's TimaBUS, he placed somewhere near the north pole.' Uncertain whether Iceland, Greenland, Nova Zembla, or Spitzbergen, were the true Atlantis, he avowed a preference for Spitzbergen as nearest to the pole.' He pleaded thus plaintively for these cheerless regions: Are not these countries misérable enough, deserted as they are by the sun covered with ice which grows thicker every year left desolate by the emigration of their inhabitants ? Shall w~, too, abandon them ? Should we not rather console them for the lossea they have sustained, and for their present state, by praising their former condition ?' Accordingly he proceeded to claim so high a value for the scientific attainments of the race, as to give use to the remark of D'Alembert, that the race appears to have taught mankind everything except their own name and existence.'

There is no occasion, however, to seek in these uninviting regions either for the origin of the human race or of science. We may accept the traditions which point to the Chaldœana as the first people who dwelt in cities and formed a nation. AU that is necessary to reconcile their claim to the invention of astronomy with the facts stated above, is to suppose that they were not originally settled in Mésopotamie where they afterwards appeared, but near Mount Ararat, and that the race spread themselves so far north as thé Caucasian range. It would be easy to account for their removal from these regions. They were subd-ued by tlie Assyrians, and by the Babylonians and the deportation of conquered races was the common practice of both these nations: Chaldœan astronomy was already famous, so that it is in no way improbable that the monarchs of Assyria and Babylonia, anxious to attach the crédit of so much leaming to their own courts,* would remove the Chaldaeans (even from such distant regions) In the time of Daniel we find the Chaldœans set apart as a. race devoted to the study of the stars and laying claim to the possession of magical powers. It was part


successively to Nineveh and Babylon. That Mesopotamia was not the original aeat of the race is evident from the words of the book of Judith (undoubtedly written by a person well-informed respecting thé Chaldaeans) _< This people' (the Jews) is of the offspring of the Chaldaeans. They dwelt first in Mesopotamia, because they would not follow the goda of their iathera, who were in the land of the Chaldœans Judith, v. 6. Two arguments have been urged by Bailly against the claims of the Chaldœana to the invention of astronomy. They were acquainted with the fact that cornets are wandering members of our system, and Bailly finds a difficulty in understanding how thé Chaldaeans should discover what Hevelius denied ail his life, and what Cassini long considered doubtful. He does not tell us why the Atlantides should be better informed than the Chaldseans. Possibly he considered that, having gone to the Poles to invent a nation, he could assign to them what attributes he pleased or he may have wished to console them for their present state by praising their former condition otherwise, there is no nation of antiquity for whom comprehensive views of nature and a high amount of mental culture might t be more justly claimed than for thé Chaldœana. Dr. Prichard, the celebrated ethnologist, considered that the Syro-Arabian or Semitic branch of the human &mily has at all times equalled in mental development the most favoured races of the Indo-European branch. Thé Semitic nations,' says Humboldt, anbrd evidence of a profound sentiment of love for nature and in another place he aays, a grand and contemplative consideration of nature was an original characteristic of thé Semitic races.'

Secondly, Bailly argues that the Chaldœans were not sensible of the true value of the system they used. In support of this statement he urges that, although we leam from Berosus that the Chaldseans were acquainted with the period of 600 years, which Cassini thought so perfëct,* they made little use of it. Now, whatever the advantages of the period of 600 years-and Cassini greatly over-rated them-it is slightly cumbrous, and we cannot wonder that the Chaldœans should employ their convenient Saros of 18 years, rather than a period of as rnany générations.

It may, however, be admitted that the Chaldœans, subdued successively under the despotic control of Assyrian, Babylonian, and Persian rulers, gradually lost the skill that had distinguisbed them in their days of freedom. The decay of science that usually follows the subjection of a nation, was hastened in the case of the Chalda?ans by other circumstances. Poetical, of their servitude to overawe thé ignorant Babylonians they revenged themselves by deceiving their equally ignorant rulers.

Six hundred years,' Cassini wrote, is the finest period that erer waa inrented ¡ for it brings ont the solar year more exactly than that of Hipparchus and Ptolemy, and the lunar month within one second of what is determined by modern astronomers.'


fanciful, aiid, like ail eastern nations, quick in tracing ianciml analogies, the genius of their race led them early to choose the heavenly bodies as types of- thé divine attributes, and, in later times, as objects of adoration. The planets were regarded with peculiar reverence, and the later Chaldœans reposed undoubting faith in thé influence of these orba on the destinies of men and nations.~ Such views must have proved a serions check upon their progress. Astronomical discoveries came to be jealously guarded as sacred secrets, to be revealed only to the initiated, and to them only by symbols. The spirit of inquiry and speculation began next to be viewed with suspicion and distrust astronomers contented themselves with handing down the records of observations, without discussing how far these tended to support or to modify the systems they had been taught. Expenence has repeatedly shown that the effects of such a course are not merely repressive, but destructive. Men can no more succeed in stereotyping a system of science than they can arrest the development of a tree without destroying it.

On the whole there appears to be no valid reason for rejecting the traditions which attribute the origin of astronomy to the Chaldœans, and which assign a high value to thé system they founded, and to the accuracy and extent of their observations. The records that have been handed down to us are mixed up, however, with much tliat is false and exaggerated we have such fables as the tale of Ctesias, that the observations of the Chaldœans had been continued for 470,000 years, during which time they had calculated the nativities of ail the children that were bornt they believed, also, we are told, that the earth is formed like a boat that thé. earth would be overwhelmed by a flood when all the planets were conjoined in Capricorn, and destroyed by nre when such a conjunction took place in Cancer and many other such fables have been handed down to us. On the other hand, many accounts of their observations, the periods they empluyed, and the discoveries they enected~ agree very closely with the discoveries of modern times and it is not probable that these accounts were invented by the writers who relate them-often themselves ignorant of astronomy. Thus we learn from Diodorus Siculus, and Apollonius Myndius, that the Chaldœans maintained that cornets are bodies travelling in extended orbits, and were able to predict the coming of some of these meteors.i They were acquainted with the precession of the equinoxes, The Chaldseans asserted that astrology was founded not in renson and physical contemplations, but in the direct expérience and observation of past ages.' Bacon'a AdvMcement of Lca.ming,' Book III., chap. iv.

t This fable is referred to by Cicero, lib. ii., de Divinat. c. 97. Other accounts make the number of years 270,000. P?-oc~ r~<sM, lib. i., p. 31. Diog. Laert. P7-oa"7M. t Thé account that the Chaldseana were able to predict earthquakes and inundations


making use of a tropical year of 365 days, 5 hours, 49 minutes, 11 seconds (only 25 seconds too great), and a sidereal year of 365 days, 6 hours, and 11 minutes (not quite 2 minutes too great). The Chaldœans were also acquainted, long before the Egyptians and Greeks, with thé art of dialling. But thé most remarkable evidence of their skill and ingenuity is undoubtedly the invention of thé period called Saros* (or Restitution), by which they were able to predict lunar eclipses, and announce the days on which eclipses of the sun might be expected. This period is still used by astronomers, and is thé best period of the kind ever invented. Ite nature may be thus stated :–Eclipses of the sun and moon can only take place when the moon is new or full, and near one of her nodes thus thé recurrence of eclipses depends chiefly on the common and nodical lunar months but the apparent magnitude of the moon, and her position in the sky, must plainly affect the nature and visibility of an éclipse so that thé recurrence of eclipses depends in part on thé anomalistic and sidereal lunar montbs. Now, the Saros contains 223 lunar months; falls short of 242 nodical months by about 39 minutes, and of 239 anomalistic months by less than 5 hours; and lastly, exceeds 241 sidereal months by less than a da.y. Thus eclipses very nearly recur, take place nearly in the same .part of the celestial sphere, and the magnitude of the moon is very nearly equal, in the corresponding eclipses of each successive cycle. Modem astronomers calculate the length of the Saros to be 6,585 days, 7 hours, 40 minutes, and 38 seconds; the Chaldœan value of the period was 6,585 days, 8 hours, exceeding the true period by only 19 minutes, 22 seconds.t

There are good reasons for supposing that the Chaldœans were acquainted with the true system of the universe. It bas been mentioned in Chapter II. that the ancients were acquainted with the relative distances of the planets, a. knowledge which could only have been obtained from considerations s ibunded on the true system. Again, though Hipparchus had thé advantage of Cbaldœan records with which to compare his own observations, he deduced thé tropical and sidereal years-in other words, calculated thé precession of the equinoxes-with less correctness than thé Chaldaeans. is possibly fabulous. It is not altogethcr impossible, however, that, close observers as they were of nature, and able to devote their whole time to watch her operations, they noted and recorded Wtt.rmng signs that escaped the notice of thé less observant. .BEesychius says, 2{~oî aptCjuJy T~ ircpà B«~3u~<oyfoty. The ancients were not wall acquainted, however, in general, with the nature of the Saros. Abydenus and Berosus estimated the Saros at 3,600 years Euseb. Chron., lib. I.' p. v. 13, and p. vi. 37. Suidas came nearer thé true value, estimating the Saros at 18~ years. t They trebled thé period to make the nnmber of days exact, so that eclipses happeued nearly at the same hour of the day in each successive triple-Saros.

0


Hence we may conclude that such accurate observers were not unacquainted with those irregularitiss which the Epicyclians were Ibrced to explain by means of epicycles, eccentrics, and oscillating planes. Now, it was a part of the Greek character to n'ame systems on insufficient knowledge, and to explain false systems by false hypothèses,–

Collecting toys

And tri Ses for choice matters, worth a sponge ¡

As children gathering pebbles on thé shore.~

'We can understand, then, that thé Greeks should make the earth thé centre of ail celestial motions, should suppose these to take place necessarily in circles, and the like. But we hâve no reason for supposing that the Chalda2ans, close and patient observers of nature, and disposed, like all the Semitic races, to seek grand and simple interpretations of natnral phenomena, would make the earth the centre of motion, when observation had once proved that such a System could only be maintained by cumbrous and complicated hypothèses. On thé contrary, from the reverence with which they regarded the planetary bodies, it seems little likely that they imagined thèse bound to move about a terrestrial centre.

It may be urged that, if the Chaldaeans considered the sun to be thé centre of the scheme, they must either bave adopted some such modified system of epicycles and eccentrics as Copernicus, or else have preceded Kepler in the discovery of the elliptic motion of the planets. It appears, indeed, highly probable that their observations were conducted with sufficient accuracy to enable them to detect thé ellipticity of the planetary orbits.t The account given by Philolaus of the opinions of Pythagoras seems clearly to point to knowledge of this kind. We have seen that the Chaldseans regarded the planetary motions as sacred secrets, not to be spoken of save in doubtrui mysterious terms. Further, in thé time of Pythagoras they were subdued under Cyrus so that, fëarrui of offending the Fireworshipping Persians, the Chaldaeans would conceal their own religious opinions-or, in other words, their system of astronomy. If the opinions attributed to Pythagoras by Philolaus were really derived from Cbaldaaan Greek natural philosophers,' says Humboldt, were but little disposed to pursue observations, but evinced inexhaustible fertility iu giring thé most Yaried interpretations of half-percelved. facts.' Thé Greeks,' wrote Bacon, by only employing the power of the understanding, bave not adopted a fixed rule, but have laid their whole stress upon intense meditation, and a continuai exercise and perpétuai agitation of the mind.' t Callisthenes,' says Porphyrius, sent to Greece observations of thé planetary motions t~ea by thc Cha.ldaeans for 1,903 years before Alexander's entry into Babylon.' Aristotle, speaking of an occultation of Mars by the moon, adda, Such observations hâve been mnde on thé other planets for many years by Egyptian and Babylonian astronomers and many of thèse ha.ve come to our knowledge.'


astronomers, they effectually att<uned both ends by simply telling him that the earth and planets move in oblique circles about Fire.' Philolaus adds, as thé sun and moon do,' from which we may conclude that he, at least, was not acquainted with the true system nor is it probable that Pythagoras was better informed but the very circumstance that Pythagoras probably knew little of astronomy makes it thé more remarkable that he ahould not only attribute motion to the earth, but assign elliptic orbits to the earth and planets.

There is no evidence that Chaldœan astronomers were acquainted with the nature of gravity. They may have conceived the idea that the sun and planets exercise attractive influences varying with their distances and volumes, but there is no reason to suppose that they were able to deduce from the motions of the planets the manner in which such attraction varied, still less that they were acquainted with thé general principle now known as universal gravitation. Dr. Gregory, however, considered that either Pythagoras himself or the astronomers from whom he derived his system were acquainted with the law by which gravity varies with distance. He observes that these philosophers spoke allegorically when they asserted that Apollo touched the seven-stringed lyre, which he supposes to represent the sun and the seven planets, and to indicate that the former retained the latter by attractive forces in harmonie proportion and, because the tones obtained from chords of equal thickness are inversely proportioned to the squares of their lengths, he infers that the harmonie proportion alluded to is the inverse duplicate of thé squares.' We may adopt the opinion of the author from whom thé above passage is derived, that the doctrines of Pythagoras did not lie quite so deep and it is little likely that the Chalda~ans concealed real knowledge under so obscure and fanciftil an image.

Mr. Layard has shown that the Assyrians and Babylonians were skilful mechanicians, and particularly well acquainted with the nature ofthe various metals, and the best methods of working and alloying them. There can be little doubt from the account handed down to us in the Book of Daniel of the state of the Chaldœans under their Babylonian masters, that neither wealth nor skill was spared in erecting buildings that might serve as observatories, and in supplying these with astronomical instruments of the best workmanship. The terrace and pyramid of Belus, for instance, were used for astronomical among other purposes here thé Chaldœan astronomers pursued their labours, and thence they proclaimed the hours of the night. We leam from Callisthenes and Epigenes that they recorded astronomical observations on bricks and tiles. Many such tablets, Thé Earth and its Mechanism.' By H. Worms. Pp. 9, 10.

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formed of clay, and bea~ing inscriptions in cuneiform characters, have been discovered by Mr. Layard and other eastern travellers. Thé inscriptions appear to have no reference to astronomical observations. Across the tablets, however, while yet moist, engraved cylinders were rolled, and the impressions thus stamped appear, in general, to be records of celestial phenomena. It may be conjectured that one of thé duties of the Chaldœans was to superintend the construction of cylinders, thé symbols on which should seive to indicate to thé initiated the date corresponding to each tablet.* r~ n

When we consider thé marvellous exactness with which thé Chaldœan astTonomers calculated the several periods their determinations of which have reached us, the question suggests itself whether they could possibly have attained such exactness without the aid of the telescope. The art ol making glass was known to the Assyrians, who were also suihcientiy acquainted with the science of optics to construct lenses. Sir David Brewster, speaking of a plano-convex lens of rock-crystal discovered by LayardatNimroud, says: The convex side is tolerably well polished, and though uneven from the mode in which it has been ground, it gives a tolerably distinct focus, at the distance of 4~ inches n-om the plane side he adds 'It could not have been intended as an ornament we are entitled, therefore, to consider it as intended to be used as a lens, either for ma-~niMng, or for concentrating the rays of the sun.'

If we were better acquainted with thé nature of the Chaldœan system of mythology, and knew the planets with which their various deities were associated, we might be assisted in the inquiry whether they used telescopic aid in examining the celestial bodies. It is clear that little connection exists between thé Assyrian and Greek systems of mythology. Npw and then some attribute of an Assyrian reminds us of a Greek deity but when ~e proceed to consider other attributes no further resemblance can be traced.tVarious opinions have been expressed as to the celestial bodies with which the deities were severally associated the most probable arrangement appears to be thé following :-Nisroch, the great triune deity, was associated with the planet Bel with Jupiter; Merodach with Mars; Mylitt~ It is doubtful whether aIl the symbols on thèse cylinders are astronomie or or!y thèse te principal figures and in the background. It has been suggested th.t the principal figures may represent constellations. Among symbols a representi.g the ~n moon, and stars, Dr. Birch has detected figures corresponding to ten of thé

Zodiacal constellations.

~1~ chief gedd~f Assyrians, ~e of ~1 (chief of the twelre great gods presided over by.Nisroch), corresponds so far with Hère, but in her other attributes more nearly resembles Aphrodite.



with Venus; Nebo with Mercury; Ishtaj with the moon; and Shamash with thé sun.*

Fig. 1, Pht-te XIV., represents oneoftheibrms in which the deity Mylitta appears in Assyrian sculptures. In her lelt hand she bears an emblem resembitng the symbol still used by astronomers to represent thé planet Venua '}' in her right hand she bears a staff tipped with a crescent. Now, with moderate telescopic power, Venus is thé only planet that ever presents thé crescent fbrm, Mercury only assuming th.at form when too near thé sun to be seen without telescopes of great power, properly mounted, and directed to the calculated place of' the planet on thé celestial sphere. It may therefore be noticed as, at the least, a singular coincidence, that thc crescent should be found associated, not with the deity representing the moon, but with thé deity representing a planet whose appearance never a.:Hbr~}s any indication to the unaided eye of thé crescent form,

Bel or Baal is variously represented in Assyrian sculptures. Among thé winged globes, which probably syrnbolised at the same time a deity and the planet with which he was associated, we find one in 'which the central globe is surrounded by four others this may possibly indicate tbe system of satellites attending on Jupiter. Bel is aiso represented with four horns and a figure in Assyrian sculptures with four star-tipped wings probably represents the same deity.

Nisroch or Asabur (among other attributes) was the time-god or yearIn one of the Phœ~icmu dialects the sun is called Cam~sh, a term probaLly identical with the epithet Chomeus of Apollo. E~mbolfit mentions in his Views into Nature' that Camosi is a. South-American word for tbe sun.

t This symbol ( )somewhat resembles the Egyptian symbol of life (thc c~M~), which consista of a straight rod and circle separated by a cross-bar,–emblematic (I suppose) of temporal and etemal life separated by denth. Mylitta. was somctimes represented with the waters of life flowing from her breasts see La-yard'a 'Nineveh and Babylon,' p. 606 note also the first figure on page 605. The figures of Plate XIV. are taken from the above-named work, and from Layard's 'Nineveh and its Rcmains.' The astronomical symbols of thé planets have been derived, in nM probability, from Chaldsean and Assyrien sources. The symbol of thé planet Mercury ( $ ) is thé <M~Mc<s, which, like the pe~<M< is an emblem of eastern ongin. The symbol of Mars ( J ) represents a shield and spear-the former being thé circular shield with which Assyrian spearmen are constantly represented' (Layard's 'Nineveh and BabyJon,' p. 194). Tbe symbols of Jupiter and Saturn ( and h ) are moro doubtful a resemMa.nce bas been traced between the former and the initial Ictter of the Greek Zeus it appears to me far more probable, however, that the symbols of Jupiter and Saturn are simply the Syro-Arabie forms of thé numbers.4 and $, indicating thé positions of thèse bodies in thé scheme of the Planetary Five. The syrnbol of thé earth ( ) is simply the inverted emblem of life, and possibly bears some reference to terrestrial corruption and decay.

If thé Chaldseans used telescopes fTcn of moderate power they must hâve been acquainted with the vastness of Jupiter's bulk, i~-nd would therefore, in all probttInJity,


god, beneath whom were the twelve great goda presiding over the twelve months of theyear; and beneath these again some 4,000 deitîes who ruled over the days of the year and the various phenomena of nature. If the Chaldœan astronomers were acquainted with tHe &ct that Saturn is girdled about by a ring, they could have chosen no more suitable representation of a deity who was supposed to sway thé circHng seasons tend thé flight of time.' For among all nations and in every age the ring bas been chosen as the aptest emblem of time; and such names as a/MM~, ~~oc, ~oe E~tct~roc, ~e~, &c., indicate that the ring has been considered an especially appropriate emblem of the simplest and most marked recurring period known to man. Thus we find the serpent-ring among other emblems of Cronus or Saturn and Homer constantly applies to Cronus the epithet (t-u\r~c, an epithet plainly connected with ttie influence of this deity over the year.t

We have seen that Galileo was able to detect a peculiarity in Saturn's figure with a very low telescopic power. In the clear skies of eastern climes, it is probable that the same or even less power would distinctly exhibit the form of the ring. But, further, if we suppose, as we are justified in doing, that the changes observed in Satum's rings during the 200 years that have elapsed since their discovery, form part of a progressive series of changes, thé rings must have been very much narrower-and, therefore, assign to him a proportionately vast attractive influence. Possibly some tradition of such knowledge Is embodied in the well-known passage

Ef y ~e, we<p~<rao'0€ 0<o~, ?~ 6~8<T< wa~rey,

~€<p~ ~RUO~f OUp~~Cc~ /fpt~Mt<rayT<t,

11~6? 5' ~tHrTtO'9e 06ol, w5<J~ T€ 0«tt!<tH'

'A~.À' ou« &y epu~cuT' oupa~JCe~ Tr<S(Of3e

Z~ StroToy ~o'TMp', o&8' e! ~~Ot wuAÀa Ka~otTe' 'A~Â' ~r< 5-~ Kal 6~ TfpJ<pp<ff ~cAo~t ~~<ra<, AuTp <ce~ Ya~ ~~<ra<jn', aurp Te 6<tÀa<r<rp'

Setp~y /*e~ Kef ~retïa Wtpt p~oy O~Â~wofO

A~a~7)~' Ta Se ?' eS-re ~6T~op<t w~ïa 'y6M(To. Hiad VIIj[. 18-26

Compare also line 451 of the sama Book, and PIato's Theœtetus,' i.153. The image in the above passage seems singular~y infelicitous unless interpreted in some such way as is indicated above such an explanation appears more natural than that commonly oiïered, which refera the image to subtle dogmas of physical m~uencea and powers, associating together the various parts of the universe.

From ~a, to surround.

t The later meaning of the epithet appears little suited to a deity represented as a semi-idiotie old man swallowing stones for chiidren. As the epithet jBoM~ty of Heré was probably derived from the worship of the eastern original of Heré under thé form of a cow (Muller Scient. Myth. p. 202), so the epithet a-yK~o~T~y either refers, like the mythological account of Cronus, to his rule over the seasons, or is derived from the form under whieh the eastern original of Cronus was worshipped. See figs. 2 and 3, Plate XIV.


their ring-form much more easily detected-three or four thousand years ago titan in Galileo's day.* It certainly does not appear incredible that mechanicians so ingenious as thé Chald~eans, and not unacquainted with the laws of optics, should hâve been able to construct telescopes as powerfui as Galileo's and, with such telescopes, they could not have failed to detect Saturn's rings. It is certainly a singular coïncidence that thé god Nisroch should be represented in Assyrian sculptures M~ a ring (see figs. 2 and 3, Plate XIV.); and it secms difHcult to accouut for thé selection of such a remarkable figure to represeut thé suprême god, unless we suppose thé Chddœans acquainted with thé peculiar conformation of tlie planet they associated with that deity. On such a supposition, howcvcr, one can readily understand, that tliey should conceal their I~nowledge under such mystical symbols.t In fig. 3, the deity is represented as triune, a figure which may liave reiërence to thé triple attributes of thé god; though it is not altogether impossible that the triplicity observed in several representations of this deity, may have reference to a tradition of some such imperfect discovery of Saturn's ring as Galileo effected.

The use of engraved cylinders by Chaldœan astronomers bas already been noticed. Fig. 4, Plate XIV., represents a tablet stamped froni such a cylinder. The figures in the background represeut the sun, thé crescent moon, a star, and a ~y. Thé opening of thc ring is rather less than thé full opening of Saturn's ring, and thé breadth of thé ring corresponds with the breadth we may imagine tlie ring to have had three or four thousand years ago. The figure of a ring is met with in other engraved tablets, the breadth being about thé same in ail, but thé opening varying. In a cylinder, represented at page 343 of Layard's < Nineveh and Babylon,' thé sun and a bh-d (probably a constellation) appear above a ring nearly closed thé principal figures ofthis cylinder represent Dagon the Fish-god, another deity, and a crowned figure in the act of adoration before an object resembling ngures 2 and 3, Plate XIV., but thé human figure and ring are repl&eed by an open eye. It may he noticed tliat when Satm'n is viewed with a télescope of small power, thé rings bcing open to their full extent, he presents anappearance somewhat resembling an open eye: the resemblance is, at least, sumciently close to attract the notice of an imaginative and poetical race like thé Chalda-ans.

It is probable that thé researches of travellers in tI~e East will, before It is not altogether impossible that some of thé inner sat(~IUtes Imve been formed from outer rings about Saturn within the interval of time mcntioned. t The mysterious precept ofrythttgoras, 'Thou shalt not represent thé deity within a ring,' proba~ly has reference to such figures. His travels, therefore, may be presumed to ha-ve extended into Assyria and Babylonia. Like many others of his precepts, this one probably refera to religious ubs'rvances and rites that had como under his notice during his travels, but which wcre unintelligible to him.


1 ong, afford us more accurate information of the history, language, and arts of Assyria and Babylonia than we now possess. Thus a meaning may be found iïi symbo~ and inscriptions which are at present unintelligible and we may thenoe obtain some idea of the methods of observation employed by Chaldœan astronomers, of thé manner in whioh they recorded, and of the system by which they explained, astronomical phenomena.


No part of the solar system affords so.striking an argument in favour of Laplace's Nebular Hypothesis as the Saturnian system of rings. A brief examination of some objections that have been urged against that theory will therefore not be out of place in the present work. The hypothesis itself is so well known, that it is unnecessary to enter into any lengthened description of it.

The planetary system presents certain points of uniformity for which the law of gravity does not accoiint; thus :-The planets revolve in the same direction about the sun, in orbits nearly circular, and nearly in one plane they also rotate on their axes, and their satellites (excepting those of Uranus, and possibly Neptune's satellite) revolve, in thé same direction ail thé known asteroids also revolve in the same direction. That this uniformity is not thé effect of chance, will appear from a single example :-The probability that the 83 known asteroids, if projected. in thé sa-me plane but otherwise at random, should ail revolve in one direction, is less than 1 in 4,835,700,000,000,000,000,000,000.

The uniformity here considered may, undoubtedly, result from design in original creation; but, on the other hand, the idea that the solar system has been developed under the operation of uni~brm laws, is no more opposed to just conceptions of the wisdom and power of the Creator, than is the idea of the development of a tree or of an animal.* The solar system and This view has been objected against as atheistical but thé objection is founded on thé atheistical assumption that the minor developments referred to are not parts of thé scheme of thé Almighty. It is also urged that to suppose the human race so insiguificant a. part of the universe, as it would appear (to our conceptions), from thé

NOTEE.

LAPLACE'S NEBULAR THEORY.

This world was once a fluid haze of light,

Till toward thé centre set thé starry tides,

And eddied into suns, that wheeliug cast

The planets. TBNNYSON.

T~t~ Traira K~J~oy ~o~frc~ <! S~/tfoup'y~ o~ ~cp<y~ &A.Âà A~y~.

MERCURIUS T~tJSMEOISTUS.


the whole portion of space falling within the range of human observation, form, necessarily, infinitely minute parts of the space over which the operations of thé Almighty Mind extend-that is, of inimité space and thé time within which our system has been created, and during which it wiU continue to exist, form necessarily innnitely minute parts of the time during which thé operations of the Almighty Mind have been and will be in action-that is of eternity. We must, then, seek infinitely iarther back for the operation of a First Cause, than merely to the origin of our system, vast as it may appear to merely human conceptions. We are e therefore at liberty to seek or adopt any theory which explains thé existing state of our system by the operation of uniform laws.*

Laplace conceived that the solar system may have been ibrmed by the graduai cooling and condensation of a vast rotating nebulous globe tliat in the process of contraction successive rings were tlirown off, to ibrm in one case a zone of small planets, but in général to break up and ibrm each a single globe that in the formation of such globes a similar process was repeated, encling in the formation of satellites, and in a single case of what we now know to be a ring of small satellites.

Modern science is opposed to thé idea of a vast nebulous globe, maintained in a state of extreme tenuity by intense heat.t But, on thé other hand the laws of Thermo-dynamics supply a satisfactory explanation of the original process of formation. If we conceive the distribution imagined by Cliladni (see Explanation of Astronomical Terms, JM'e~07'c Stones) to extend throughout the interstellar spaces, then all the results auggested by Laplace would follow from the agglomération of vast numbers of cosmical bodies, gathered from vast distances t under the influence of their own attractions, or of the attractions of a central body; and the heat generated by the loss of vis viva at the formation of each planet or satellite, would be above view, is to suppose thé inanité wisdom and goodness undoubtedly disph~yed towards thé human race bestowed on an unworthy object aji objection founded on thé erroneous notion that we are to conceive otherwise of the infinite wisdom and goodness of the Almighty than as bestowed on each the minutest (or to our view the most insignificant) of His works, and on each thé minutest interval of time. See Bacon's Advaaceinent of Learning,' Book I., § 1, and Book III., chapter iv.; and Hooker's 'Ecdesiastical Polity,' Book I., chapters ii. and iii. Compare Nichol's 'Cyclopœdia of the Physical Sciences,' Article 1 Nebular Hypothesis;' und WI~ewelFs 'Astronomy and General Physics,' (Bridgewater Treatise.)

t It vas in illustration of this part of his theory that Laplace referred to Hersehcrs Neb~ar Theory. (See Explanation of Astronomical Terms, 2~&M~r 2%eo~, Z/er~cAf~s.) It is a mistake to suppose that the overthrow of the latter theory carries with it Ltiplace's Nebular Theory, thé main points of which are in no way connected with Herschel's.

Distance is an important element in snch a process. See Explanation of Astronornical Terms, Vis ~~<ï.


sufficient to account for the obvions signs that the planets, and, in a less degree thé satellites, were originally in a state of intense heat. It has been considered by some that the motions of the satellites of Uranus are altogether opposed to thé theory of Laplace. It has even been atated tliat Laplace himself, had he lived to thé present day, would have abandoned his theory as untenable on this account alone-which will hardly appear probable when we remember that Laplace survived the cider Herschel more than four years, and published the first and fifth editions of his Système du Monde' nine and thirty-seven years, respectively, after the discovery of two of the satellites of Uranus.t In -fact, the motions of these satellites are not so utterly opposed to the theoty as might at first sight be supposed. Satellites travel, in général, nearly in the equatorial planes of their primaries, and these planes hâve very various inclinations to the ecliptic.~ Assuming that the inclination in thé case of Uranus was originally very nearly 90°, it is conceivable that external disturbing causes § (to which Uranus must have been exposed for a longer time than any planet within his orbit), may have carried the inclination ~0 and ~OM~ thé right angle so that, instead of saying that the satellites of Uranus move It is possible that in such considerations we may find an explanation of the peculiarities of form and rotation observed in the moon. (See Note C. )

t It has been argued that Laplace considered his scheme a mere conjecture' (see Science and Scripture,' by Professor Young, p. 14). It is true that I~apL).ce presented his hypothesis as an hypothfisis, and not as a scientifie doctrine; speculations on past processes traceable only in their results must always be imperfect and uncertain or, to use Laplace's own words, everything not resulting from obsen~ation or calculation rnust,' to a certain extent, inspire distrust.' But it is alao true that Laplace formed a high estimate of thé probability of the hypothcsis. He speaks of it as 'une hypothèse qui me paraît ~'M~e?', avec M~e ~raM~e w<ïM<W!M~Me<' des phénomènes précédents mais que je présente avec la défiance que doit inspirer tout ce qui n'est point un résultat de l'observation ou du calcul.' Professor Young mistranslates the c!osing words of the passage into that distrust which should inspire everything which is not thé result of observation or calculation,' possibly gathering from this singular sentence his idea a that Laplace attached a low value to thé Nebular Theory.

It may be remarked that Laplace's theory, as originally presented, offers no satisfactory explanation of this diversity of inclination. In the successive collisions through which each globe may be conceived to have been formed (on the altered theory suggested above) we appear to have a sufficiently plausible explanation of thé peculiarity in question.

§ We appear to have an indication of the operation of such causes in the peculiar distribution of the perihelia of the planetary orbits alluded to at p. 37 (note). If we suppose, for instance, that our system had passed through a region of the interstellar spaces in which cosmical bodies were distributed with a. density varying according to some uniform or tolerably uniform law, and that such passage occupied an interval of time in whieh thé most distant members of thé system completed several revolutions ¡ then it is certain that after the passage the aphclia of ail the orbits would be f~und on that side of the system which had passed through the most densely-crowded part of the region.


in a retrograde manner in a plane inclined 78° 58' to the ecliptic, we might more correctly say that they move in a direct manner in a plane inclined ~01° 2~ to thé ecliptic, Thé same considerations apply to the case of Neptune's satellite, incrcased distance aiding us to interpret what (on thé assumption we are considering) would be increased disturbance of inclination. Owing to Neptune's immense distance, however, and his slow motion in his orbit, it is not probable that thé direction in which his satellite moves, can have been satisfactorily established in the short interval that elapsed between thé discoveiy of the satellite and thé announcement of its retrograde motion. In any case we do not require absolute affirmation or negation, even in universal propositions if the exceptions be singular or rare, it is sufficient for our purpose.'t

The theory of Laplace is perfectly reconcilable with the Scripture account of création. It is only necessary to assume that in the first chapter of Genesis the sacred penman has recorded a series of visions, in which was presented to him all that the Almighty saw fit to reveal to mankind of the former condition of our globe. That Moses, like Jeremiah, Ezekiel, Daniel, and Zechariah, received inspired knowledge specially by means of visions, seems suggested by the injunction that the ark and its appurtenances should be made after their pattern which was showed' hirn-or, more correctly, which he was caused to see in the mount. The words of the second verse of the Bible seem to confirm this view The earth was without form and void the earth must have had form of some kind, regular or irregular, and though thé expression may be interpreted to signify merely that the earth was without regular form, it seems little likely that reference is here intended to the present spheroidal form of thé earth but assuming that Moses describes a vision that passed before him, the words which immediately follow explain the true meaning of the expression The earth was,' that is appeared, without form and void,' because darkness was upon the face of the deep.' Now, if the earth in tracts of fluent heat began as would follow from the theory we are considering, and as geological evidence appears clearly to establish-the whole of the waters now forming our oceans must have been suspended round thé earth in the fbrm of a dense vaporous envelope through which no ray of thé sun's light could peneIt is clearly only by thé change in the position of the prunary that thc direction of a satellite's motion ca.n be determined.

t Ba.eon's 'Novum Organum,' Book II., aphor. xxxiii.

t Exodus xxv. 9 and 40; xxvi. 30 and xxvii. 8; see also Numbers viii. 4 Acts vii. 44 and Hebrews viii. 5. Compare the mode in which David received the pattern ail this,' he says, thé Lord made me understand in writing by his hand upon me' 1 (1 Chron. xxviii. 11-19).


trate.* But in the course of âges, thé heat of thé earth's globe would diminish until it became insumcieut to maintain masses so vast in thé fbrm of vapour: then light-but not as yet thé source of light-began to penetrate the earth's cloudy envelope

Forthwith light

Ethereal, nrst of things, quintessence pm'e,

Sprang from thé deep, and from her native east

Tojourney through the aery gloom began,

Sphered in a radiant eloud.

We are thus able to explain the recurrence of day and night before thé appearance of thé sun, without having recourse to thé Aurora Borealis, to successive electric flashes, to~sustained disturbance of tlie aether pcrvadhig space, or to any of thé other contrivances that have been invented to cxplain away the diniculty.

With the further diminution of thé overhanging cloud-massea, a firmament, Expansé of liquid, pure,

Transparent, elementul air,

began to appear between the waters on thé earth's surface and thé vaporous envelope. And next, the dry land appeared, heaved up by volcanic action following thé precipitation of such vast masses of -water on thé as yet lately formed crust of the earth.~ The land thus upheaved became covered with dense forests and abundant végétation, nourished by internai heat, while i

From thé earth a dewy mist

Went up and water'd ail the ground.

Venus and Mercury appear to be still surrounded with such dense vaporous envelopes thé true surfaces of thèse pl:mets huve probably never been seen, and, possibly, bave never yet received a ray of tbe sun's Hght.

t It seems clear that the word (ro~a), translated firmament (the o-Tcp~tt of tho Septuagint), means merely the variable transparent expanse above the earth at any time [Compare Gencsis i. verses 16, 17 and 20.] It seems equally clear tbatby thé waters above the firmament' clouds are signinpd. During many ages after the change recorded in Genesis i. verses 6 and 7, and even after the appearance of thé heavonly bodies. tbo waters above thé firmament' must bave constituted an important part of ail the waters of our globe. The notion that thé waters above thé firmament arc waters above the stellar npaces is too absurd to need serious réfutation. Compare Genesis vii. 11; viii. 1-3; Job xxvi. 8-11, and xx.xviii. 8-11 and Proverbs Yiii. 23-29. It may be remarked that nearly all thé active volcanoes on our globe are found near the sea. Even tho volcano Pe-schan, noted by Remusat as an exception to this rule, is found near a région probably at no very distant date covered by an ocean of vast extent. From Capes Blanco and Vcrd to thé sea of Okotsk thc traces of such an ocean run in an uninterrupted series, which includes the desorts of Sahara, Ara.bia, Shamo, and the Russian stoppes thé Mediterranean, Black, Caspiau, and Aral seas and tbe Iakes Bal-kash, Isse-kul (notvery far from Pe-schan'), and Bai-kal. Probably the ranges of mountains running across Central Africa and


At length the heavenly bodies appear. First the mid-day sun breaks through the cloudy envelope still surrounding the earth not until many ages have elapsed appears The moon

The moon

Globose then ev'ry magnitude of stars.*

In this manner may be explained those passages in the Scripture account of creation, which (literally interpreted) appear most opposed to Laplace's Theory, and, I think; to any rational conceptions of the former state of our earth or of the solar system. Into the other difficultics which attend the literal interpretation of that account, or, on thé other hand, into the singular correspondence exhibited between the features of the successive days of Creation, considered as visions, and the main features of the successive geological epochs, I do not propose to enter on these points, the reader is referred to works especially treating of those subjects.'t'

It may be noticed in conclusion, that in Sat~rn's ring-system we seem to see the processes conceived by Laplace going on before our eyes so that it is not impossible that in thé course of time we may obtain evidence founded on observation and calculation of the truth of that theory which Laplace despaired of seeing established on a finner foundation than that of stron"probability.'

Asia. formed the southern limits of a vast northern ocean, a series of promontories pointing nortliwards mai'king the outline ofa vast southern continent. Miller (spf~ following note) fails notice the correspondence between the order in which the heavenly bodies are mentioned (Genesis i. 14-18), and the order in which they must successively have appeared. He describes thé stars as appearing before tho sun.

t See Miller's Testimony of the Rocks Lectures III. and IV. and authors referred to by him in those lectures.


NOTE C.

HABITADILITY 0F THE MOON.

THE question of the moon's habitability–intereating to astronomers on its own account-acquires an additional interest if we consider that on its solution depends thé opinion we shall fbrm of the habitability of the important secondary systems attending on Saturn, Jupiter, and Uranus. I propose to consider in this note sorue points conn~cted with the inquiry. The physical conditions and peculiarities of the moon are undoubteclly in striking contrast to those prevailing 0~1 the earth. The lunar year consists of little more than twelve lunar days, ca.ch day lasting more than four of our weeks. Our seasons, due to an inclination of 23 degrees, are also very different from the lunar seasons due to an inclination of 1~ degrees if, indeed, we can apply the term seasons to intervals in which the sun rises and sets only three times. Again, our earth (considered as a satellite of the moon) is altogether invisible to three-sevenths of the moon's surface; to the remaining four-sevenths the earth does not rise and set as thé moon does to us, but moves within narrow limits round a fixed point on thé celestial concave, such motions being thé exact converse of the lunar librations; the earth also passes through all her phases in a lunar day and night, the half set of phases passed through in thé lunar night varying for each point of thé moon's surface.

That the moon has not an atmosphere corresponding in extent and density to our own is undoubted it has not been considered so certain, however, that the moon's surface is absolutely devoid of atmospheric envelope. Thé first and most obvious argument against the presence of a lunar atmospliere, is that the lunar dise, even when examined with the most powerful telescopes, exhibits no indication of clouds. Owing to the slowness of the moon's rotation we should hardiy expect that belts of clouds would be formed, as on the swifûyrotating planets Saturn and Jupiter, but irregularly dispersed clouds, even if not separately visible, must produce effects very easily traceable from the earth. The distinctness ofthe outlines ofmountains, plains, and valleys, on the moon~s surface, would varywith thé aggregation and dispersion (due to variations of température) of clouds


and mists about them. No such changes are obsei-vable as long as the clearness of our own atmosphere remains unchanged, the irregularities of the lunar surfàce are seen with unvarying distinctness. It appears reasonable, then, to conclude that the visible lunar hemisphere is either devoid of air or of water.

Secondiy, if the moon -were sun-ounded by an atmosphere, even of limited extent, the effects of refraction could not fail to be traced in the occultations of stars. The refractive effects of the atmosphere surrounding Saturn are, as we have seen, traceable from the earth, which is removed fully 3,500 times as far from Satum as from the moon-a disproportion in thé distances that would compensate an immense disproportion in the extent and density of the atmospheric envelopes surrounding the two bodies.* Lastly, there is not the slightest trace of a twilight-circle on the moon, nor do the horns of the new moon extend beyond the semicircle. When it is considered that Venus, though removed so much farther than the moon, and though she is one of the most difficult objects of telescopic observation in tlie heavens, distinctly presents bôth these phenomena, their absence in the case of thé moon appears the more remarkable. If the moon had an atmosphere, even of small extent and density, the powernd telescopes that have been directed towards her could not have failed to exhibit the phenomena considered. On the other hand, arguments are not wanting in support of the hypothesis The stars are not a.Iwa.ys instantaneo-usly occulted by the moon. Some disappear by sudden diminutions of brilliancy (as the star « Cancri)-a phenomenon that may be accounted for by supposing such stars to be close double or multiple stars others after disappearing, reappear for a brief int~rval–a phenomenon that appears to indicate the existence of T.tst irregularities upon the moon's surface. But the phenomena that would result from the presence of a lunar atmosphere are altogether différent. Thus, suppose an observer on the moon to witness a central occultation of a star by the earth :-The star as it entered (apparently) the confines of our atmosphere would move more and more slowly; instead of appearing as a point it would assume thé form of a circular arc gradually extending farther and farther round thé earth's dise and when actually behind the centre of the earth, the star would appear as a cirele of light concentric with the outline of the earth's dise. Passing beyond this point the star would present similar appearances in reverse order. That even in such a central passage a star would not be actually occulted, is clear from thé considération that the horizontal refraction of the earth's atmosphere is upwards of 33', which would be doubled for an object seen beyond the earth from thé moon but tho earth's semi-diameter seen from thé moon subtends an arc of only 57' 6". Since thé moon's semi-diameter viewed from the earth never exceeds 16~ 45~ it is évident that au atmospheric envelope of much less extent than that of the earth would suffice to render thé occultation of a star by the moon impossible.

In the article rffprred to at page 177, note Professor Challis omits to notice the phenomena considered above. It seems clear, however, that they would be the most marked phenomena attending an occultation, if thé moon had an atmosphere. In a similar manner it may be shown that the phenomena attending an eclipse of the sun would be \'ery diiïerpnt from those actually presented, if thé moon had an atmosphere.


that the moon has an atmosphere. In thé first place, we might inier from the analogy of our earth, and of the larger planets, that all the members of thé solar system are surrounded by atmospheres of greater or less density and extent. In the second place, thé traces of past volcanic action on the Junar surface, leave little doubt that while such action went on the moon must have had an atmosphere capable of stipporting combustion and further, must have been enveloped by the gases distributed during tremendous and long-continued eruptions.

An attempt has been made to reconcile these contradictory evidences by the hypothesis that an atmosphere originally surrounding the visible lunar surface has been attracted to the opposite hemisphere.

The moon's centre of gravity is undoubtedly nearer to us than her centre of figure. In the first place, we have in such a displacement the only possible explanation of the peculiarity of the moon's rotation referred to at p. 50.* Secondly, Professor Hansen has proved that an observed discrepancy between the actual lunar inequalities and tlie results of the theoretical examination of the lunar motions, is removed, if the centre of gravity of the moon is assumed to be 33~ miles fartber from thé earth than the centre of ngure. This result bas been confirmed by the comparison of photographie pictures of the moon, taken at the times of her extreme eastern and western librations. Iu the year 1862, M. Gussew, Director of the Imperial Observatory at Wilna, carefully examined two such pictures taken by Mr. Delarue. The result of the examination may be thus stated :-The outer parts of the visible lunar dise belong to a sphere having a radius of 1 082 miles, the central parts to a sphere having a radius of 1,063 miles; the centre of the smaller sphere is about 79 miles nearer to us than the centre of the larger the line joining the centres is inclined at an angle of about 5° to the line from the earth at the epoch of mean libration thus the central The question of the moon's rotation has frequently aroused controversy. Bentley and Keill disputed over it in 1690, and so recently as 1855 the columns of the daily press were occupied with its discussion. Thé question is altogether a verbal one. The moon's motions may be described as being compounded of a motion of revolution around the earth and a motion of rotation in the same time about an axis through the moon's centre (the moon not being a spheroid it is incorrect to speak of thé moon's own axis'). Now, if it were not for certain irregularities we might simply say that the moon rotates about an axis near the earth, just as a. globe rigidly attached to an arm moving on. a central stem would be said to rotate about the stem, though to an eye from which stem and arm were concealed the globe would appear to revolve around a centre and rotate in thé same time about its axis. In the case of thé moon's motions no such simple rotation exists but it is a question whether the lunar movements would not be expressed more simply, and (taking dynamical considerations into account) more accurately, by saying that the moon rotates about an axis near the oarth, and that this axis is subject to such and such motions, than by the mode of expression generauy adopted.


part of the moon's dise is about 60 miles nearer to us than it would be if the moon were a sphere of the dimensions indicated by the disc's outline. Ifwe suppose the invisible part of the moon's surface to belong ta thé larger sphere, and thé density of thé moon's substance uniform, it would follow from this conformation, that the centre of gravity of the moon is about 30 miles nearer to, the earth than is the centre of the larger sphère–that is, than is the centre of thé moon's apparent figure.

But although thé moon's centre of gravity is tlms displaced, it is very doubtful whether we have in such displacement a satisfactory explanation of thé observed peculiarities of the lunar dise. The visible hémisphère in all probability was originally clothed with an atmospher e and partially covered by oceans.* .Now, it is hardly conccivable that a displacement of the moon's centre of gravity should be followed by thé departure even of all the inelastic fluids from thé nearer to thé further hemisphere, far less of aU thé elastic atmospheric envelope. Assuming, however, that thé atmosphère had thus been displaced, and the fluids dissipated by evnporation vacuo irom ail the depressions on the visible lunar smface, it is inconceivable that no traces should be visible of thé atmosphere and thé oceans thus collected on the iurther lunar hemisphere. Even if thé exact half of the moon's surface were invisible to us, some of the oceans would extend into the cavities and depressions visible round thé edge of the lunar dise, and the.atmosphere would be traceable (by its effect in occultations) completely round that edge and when we consider that owing to the moon's librations only three-sevenths of the lunar surface are actually hidden from us, we are compelled to reject thé notion that thé distribution of air and water on the moon's surface is such as bas been suggested. It appears to me that the simplest of all the phenomena presented by the moon–namely, her c~MM–will serve to g-uide us to an explanation of thé contradictions we are considering. Imagine our earth stnpped of air and water, and ail verdure destroyed from its surface what would be tl~o appearance of such a globe removed to the distance of the moon? Bathed in the sun's light it would doubtless be a brilliant object, but its brilliancy would differ altogether from thé silvery effulgence of the moon. The various strata which rise to thé surface at dînèrent parts of the earth might not, in gênerai, be separately visible; but thé commingling of thé cblours that mark such strata would certainly produce warmer tints than are observed on any part of thé lunar dise. The vast déserts, steppes, llanos, savannahs, and prairies of the earth would be distinctly visible as streaks and patches of uniform colour. The icy polar regions and thé That oceans once covered parts of the visible hiï~r hemisphere seems evidenced bf the traces of past volcanic action upon thé moon's surface. See note t, p. 205,


snow-covered momtain ranges would alone reflect the kind of light that we receive from the moon.*

But now let lis imagine our globe subjected to another change. We Lave plain evidence that thé climate of thé earth was in past ages far wurmer than at present. Animais and plants now found only in thé tropics were fbund in the temperate zones, and rnany forms of life existed on thé earth for which even the tropics would now fbrm but a bleak and unauitable résidence. It seems rcasonable to conclude that this change of climate is due to the loss of' internal heat by slow radiation, and that thé change is still proceeding.-j- Now, imagine this cliange to proceed until thé whole of thé water on thé earth's surface should be fiozen. Then if this dismal globe were removed to thé moon's distance, its brilliancy would no longer present a very marked contrast to thé lunar light. The frozen surface of thé ocean would present precisely such vast level tracts as thé so-caUed lunar seas j; thé glacial regions on land would resemble thc rough and n-LOuntainous districts of the lunar surface; while, if we conceive thé continents on our earth gradually covered with snow as the process we have imagined went on, they would correspond exactly to thé vast tracts of brilliant white so conspicuous upon thé lunar dise.

It is obvious that some of the dimculties before considered disappear if we suppose all nuids on the moon's surface to be frozen. As thé atmosphere would in such a case be perfectly free A'om clouds or mists, ail the irregularities of the lunar surface would be distinctly visible, and such distinctness would not be liable to any perceptible variations. Yet, if the lunar atmosphère bore any proportion to the atmosphère of the earth as regards extent, thé outlines of the lunar irregularities would be softer than Even at thé immense distances to whieh the planets are removed the colours of their surfaces can be traced whenever the actual surfaces are visible, as in thé cases of Mars, Jupiter, and Saturn. When a dense atmosphere supports hcavy masses ofvapour thé light reflected is brilliantly white, as in the cases of Mercury and Venus, and thé white belts on Saturn and Jupiter. Such whitcness, however, obviously diffërs altogether from thé surface colours of thé moon.

f Such a change would be accompanied by a graduai diminution in the dimensions of the earth, and it bas been argued that since the pci-Iod of thé earth's rotation has not perceptibly altered during three or four thousand years, no such change can be taking place. It may be remarked, however, tbat periods of ten or twenty thousand years are but as seconds when compared with thé interval necessary to effect perceptible changes of climate in the manner considered. That the dimensions of the earth were once far greater than at présent seems evidenced by thé cumbrous forms of the animais and reptiles that inhabited it of old. Such animais could hare movcd with ireedom and activity only under thé diminishcd attraction of gravity resulting from greater dimensions of the earth's globe.

Indepcndently of their colour these level spaces in thé moon seem scarcely explicable on any other supposition than that they are frozcn seas, for while absolutely level they are clearly solid. In cvcry respect save in fluidity they correspond to our terrestrial system of océans.

p 2


they actually appear. Thé clearness, also, of such an atmosphère would only serve to render the phénomène attending an occultation more distinctly visible; and we have seen that such phenomena would be sufficiently marked.

Let us imagine, however, the effects of a further diminution of température. It is well known that when subjected to a loss of heat suniciently gréât, many gases, elernentary and compound, are reduced successively to the liquid and solid ibrms. Hitherto no process bas enabled the chemist to convert oxygen, nitrogen, or hydrogen~ into either the liquid or solid Ibrms; but there is no reason for supposing that they form exceptions to the général rule, that, under suitable variations of temperature, ail substances in nature may assume any one of thé three forms-gaseous, Mquid, and solid. Now, it is probable that the variations of température with which we are 'fami!iar include but a small part of thé range of possible variations. Thus it is conceivable that a planet parting with its heat by slow radiation might after thé lapse of many ages have lost so much heat that ail the gases upon its surface would be condensed to the liquid or solid ibnns. The length of time required to effect such changes would depend on the mass of the planet's globe-a large planet would obviously require a longer time to part with its internai warmth. than a small planet. What relation such time would bear to the mass of a planet could not easily be determined, but it is certain that some such relation exists. Now, on Laplace's hypothesis of the development of the solar system, the moon was ibrmed belbre thé earth and the mass of the moon is little more than ~yth part of the earth's mass. Thus it is conceivable that the moon's mass may have become so intensely cold that thé atmospheric envelope once clothing it has been condensed into thé liquid, and thence into thé solid form. It need not necessarily be assumed, however, that ail the gases on the moon have been thus solidified. Small seas of liquefied gases may exist upon thé moon's surface and, again, some of the phenomena that have been supposed to indicate the presence of an atmosphere may be due to gaseous envelopes of small extent still uncondensed. We may imagine, for instance, that hydro~-en would resist an intensity of cold that would liquef~ or solidify all other gases. On these points we can only form vague conjectures, since as yet the more important gases have defied ail attempts at lique&ction or solidification.

A gas may be eonverted into thé liqmd a~d solid forms either by loss of temperaturo or by pressure. A combination of both processes is generallyadopted to condense n gas into the liquid form then part of tins liquid being allowed rnptdly to résume the gaseous form, thé rcmainder is solidified, owing to the loss of latent heat.


APPENDIX II.



TABLAI.

C'e/M~ ~'0~7' /7/<

Grcatest apparent diamoter (viewed from thé earth) 32' 36~'41 lIIean apparent diameter (viewed from thé earth) 32' 3~-64 Least appircnt diameter (vtewed from tho earth) ..31' 31"'79 Greatest a.pparent dtamcte.).' (viewed from Sutuni) 3' 33"'61 Nen.n apparent di~meter (viewed from Saturn) .3~ 21~-66 Lpust appa.rc;nt. dmniptpr (viewed from S<t.turn) .3~ 1(~-98 Equ~toriid horizont~d pM:diax at mean distance from the earth 8'~776 8"-91.59 Volume (eM-th's as 1) 1,415,225 1,260,160 Ma~(carth'.sasl) 354,936 316,047 Density (e.u-th's as 1) 0'250 0-2~0 Diamcter in miles 888,646 854,928 Gravity ut equator ~S'7' 27'6 In one second of time bodies fall in fcct 4G2-07 444-54

TABLE IL

C'C~~ 7~/K~S 0/' ~<?-<A, J~

1~, 18G5.

Mean distance from sun in miles (sun's pquatorial

parallax 8~5776) 9.),274,()00 Mean distance (sun's eq~atorial parallax 8"'0159) 91,669,000 Greatest distance (mean distance 1) 1-0167G05 Leastdistance(samcunit) 0-9832395 Mean sidereal révolution (mean solar daya) 36o'~ 6'' 9m 9"6 Mcan tropical révolution (mean solar days) 3Gô" 5" 48m 46"6 Mean Miomalistic revolution (mean solar days) 366~ 6'' 13m 49"3 Eartb's motion in pci'IheHo in ~me~n solar day 1° 1~ 9~'l Earth's mean motion in mcan solar day 0° 59~ 8 '9 Earth's motion in aphelio in n. mean solar day 0° 57~ 11~8 Earth's meau motion in a mean sidci'eal day 0° ô9~ 59~-0


Eecentricityoforbit. o-016760o AQnualTanationofsamo(decreasp). 0-0000004161 Deasity (water's as 1) ô-67-t7 Polar diameter in miles ,y ~a

~,ouo

Mean diameter in miles 7, D 16 Equatorial diameter in miles 7 9-~4 Bodies full in one second of timo in feet 1~.1 Centrifugal force atpquator -00345

TABLE III.

Elements q/S'~r~ <ï. ]& 1865.

Greatest distance fromthe sun (earth's mean distance as 1) 10-072533 Mean distance from thé sun (same unit) 9-5388.50 Least distance from the sun (same unit) 9-005167 Eccentricity of orbit (semi-major-axis as 1) 0-0559484 Annual variation of same (decrease) 0-000003125 Sidereal revolution in days 10759-2197106 Synodical revolution in days (at epoch) 377'767 Meansynodical revolution 378-092 Longitude of the perihelion .90° 23' 36~-4 Annual variation of same (increase) 19~-31 Same variation referred to ecliptic (fncrease) 69~'41 Longitude of the aseend!ngnode[~]~ 112° 29' 18"-20 Annual variation of same (decrease) 19~-54 Same variation referred to the ecliptic (increase) 30~-56 Inclination of orbit to the ecliptic[t'.] 2° 29' 26~-15 Annual variation ofsamp(dper€as(i) Q/Daily motion in orbit, in perihelio 2' 15~-3 Mean daily motion in orbit 2' o/~ Daily motion in orbit, in aphelio l' 40~.0 Inclination of axis to the plane of Satum's orbit 63° 10' 32~13 Annual variation ofsame(decrease) 0~391 Inclination of axis to the ecliptic 61° 49~ 38~-05 Annual variation of same (increase) 0~-350 Time of rotation on axis 10" 29m 17. Apparent equatorial diameter, at mean distance from earth 17"-05 Same, Saturn in opposition, in per)hplio 20~-31 Same, Saturn in opposition, at mean distance from sun 19~-04. Same, Saturn in opposition, in aphelio 17~.09

The symbols thus braeketed refer to thé corresponding symbols in Table" VII andVIII.


Same, Satum in conjunction, in périhélie 16~25 Same, Saturn in conjunetion, at mean distance from sun lô~ 43 Same, Saturn in conjunction, in aphélie 14~-68 Light received at perihelion (earth's at mean distance being 1) 0-0123315U Light received at mean distance (same unib) 0-01099021 Light received at aphelion (same unit) 0'0096ô6ôl Greatest distance from the sun in miles 969,650,000 923,238,000* Mean distance from thé sun in miles 908,804,000 874,321,000 Least distance from the sun in miles 857,958,000 82~404,000 Equatorial diameter in miles 75,100 72,250 Polar diameter in miles 68,270 65,680 Polar diameter (equatorial diamcter as 1) -909 -909 Compression JL Equatorial diameter (earth's mean diameter

bMngl) 9-4871 9-1271 Polar diameter (same unit) 8-6246 8-2974 Volume (earth's being 1) 776-432 691'362 Massorweight(parth'sbeingl) 102-683 91-433 Density (earth's being 1) 0-132251 0-132251 Same(den8ityofwaterasl) 0-750482 0'7o0482 Surface (unit 1,000,000 square miles) 16,655 15,415 Same (earth's being 1) 84-54 78-25 'Weightofaterrestrial pound, orgraTity, ut pole 1-239 1'192 Weightofaterrestnalpoundatequator 1-041 1-002 Centrifugalforcoatequator 0-1706. 0-1641 Bodies fall in one second of time, in fect, at pole 19-95 19-19 Bodies fall in one second, in feet, at cquator 16-76 16-12

TABLE IV.

Elements of Saturn's Rings, Jan. ls<, 18G5.

Longitude of ascending node of ring on the ecliptie [S] 167° 43~ 28~'93 Annual variation of same (decrease) 3~-638 Same variation rcferred to the ecliptie (increase). 46~'4G2 Longitude of rising node of ring on Sittorn's orbit [A'] 1710 43' 3,5~-06 Annual variation of same (decrease) 3~-134 Same variittiou referred to the ecliptie (increasc) 46~'966 Latitude of rising node of ring on Saturn's orbit [~3']8~ 2ô~'88N Annual variation of same (inerease) C~'235 Inclination of ring's plane to the ecliptie [:] 28° 10' 21~'9ô Annual variation of same (decrease) C~'350

The first column eorrfsponds to an equntorial ]torizont:d solar parallux of 8"'ô776 the second to an equatorial horizontal solar parallax of 8~-915 9.


Inclination of ring's plane to the plane of Satm'u's orbit

[l'] 26°49'27"'87 Annual variation ofsame(increase) 0"'321 Arc from rising node of Saturn's orbit on thé ocliptic to

rising node of ruig's piano on Saturn'a orbit [S'] 69° 15' 12~-49 AnnualA'ana.tionofsame(incrcasc) 16~'SUo Annutd precession of the rising node of ring's plane on

Satm'n's orbit (or, annual precession of the vernal equinox

ofSahu'n'snorthernhpmispbpro) 3~'1'io Complete révolution of cithcr fiquinox in years, about 412 080 Exterior diameter of the outer ring (in miles) 173,500 166,920* Interior diameter of thé outer ring 153,o00 H7 670 Exteriordiameterof thé inner ring 160,000 144,310 IntcriordiamRterof thé inner ring 113,400 109,100 Interiordiameterof the dark ring 9o,4()0 91780 Breadth of thc outer bright ring 10,000 9,625 Breadth of the division betweel) the rings 1,750 1,680 Brcadthof the innerbright ring 18,300 17605 Breadth of thé dark ring 9,000 8,660 Breadth of the system of bright rings 30,0.50 28 910 Breadth of the entire system of rings 39,050 37 670 Space between the planet and the inner edge of

the dark ring 10,150 9,760

Thé first colurnn corresponds to an equatorin.1 horizonhd solarp<).r:dl:txof 8'~776 thé second to an equatorud horizontal solar parn.U.t.x of 8"'91ô9


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N Log.tanI § S t I M

N S J I w

0 R

j ° 0 0 o o 1860 125 35 15-76 9-0970522 167 30 3C-62 28 10 23-70 7 7 38-45 23 27 27-070 1861 125 37 25-99 ~g~ 9-0967958 1G7 40 23-08 28 10 23-35 7 7 23-45 23 27 26-594 1862 125 39 36-30 g ~.gj) 9-0965393 167 41 9-54 28 10 23-00 7 7 8-45 23 27 26-1] 8 18(!3 j 125 41 46-60 9-0962827 167 41 56-01 28 10 22-65 7 6 53-45 23 27 25-6-i2 '86.1 i 125 43 57-17 9-0960260 ~g 167 42 42-47 28 10 22-30 7 6 38-46 23 27 25-166 1865 125 4(! 7-74 9-0957692 ~g ) 167 43 28-93 28 10 21-95 7 6 23-48 23 27 24-C90 1866 125 48 18-40 9-0955124 167 44 15-39 28 10 21-60 7 6 8-50 23 27 24-214 1867 125 50 29-16 2 ~.g~ 9-0952555 167 45 1-85 28 10 21-25 7 5 53-53 23 27 23-738 1868 125 52 40-02 9-0949985 167 45 48-32 28 10 20-90 7 5 38-56 23 27 23-262 1869 125 54 50-99 2 ~g 9-0947415 167 46 34-78 28 10 20-55 7 6 23-GO 23 27 23-786 1870 125 57 2-07 9-0944844 167 47 21-24 28 10 20-20 7 5 8-65 23 27 22-310 1871 125 59 13-26 ~.g~ 9-0942273 167 48 7-70 28 10 19-85 7 4 53-70 23 27 21-834 1872 126 124-57 g~ 9-0939701 2572 1674854-16 281019-i0 7 438-76 232721-358 1873 126 3 36-01 9-0937129 ~g 167 49 40-63 28 10 19-15 7 4 23-83 23 27 20-882 1874 120 5 47-58 2 ~.y~ 9-0934556 g~g 167 50 27-09 28 10 ;!8-80 7 4 8-!)0 23 27 20-406 1875 126 759-28 ~.gg 9-0931983 ~g 167 51 13-55 28 10 18-45 7 3 53-98 23 27 19-930

1S76 126 10 11-11 ~.g~ 9-0929410 g~g 167 52 0-01 28 10 18-10 7 3 39-07 23 27 19-454

1877 126 12 23-07 9-0926837 ~yg 167 52 46-47 28 10 17-75 7 3 24-17 23 27 18-978 1878 126 14 35-16 2 9-0924264 g~ 167 53 32-94 28 10 17-40 7 3 3-27 23 27 18-502 1879 126 16 47-38 ~g 9-0921690 167 54 19-40 28 10 17-05 7 2 54-38 23 27 18-026 1880 126 18 59-73 j~g 9-0919116 167 55 5-86 28 10 16-70 7 2 39'49 23 27 17-550 1881 126 21 12-21 2 9-0916542 167 55 52-32 28 10 16-35 7 2 24-61 23 27 17-074 1882 j 126 23 24-82 9-0913968 1675638-78 281016-00 7 2 9-74 232716-598 18S3 j 126 25 37-56 ~.gy 9-0911394 167 57 25-25 28 10 15-65 7 1 54-88 23 27 16-122 1884 j 126 27 50-43 2 9-0908820 167 58 11-71 28 10 1S-30 7 1 40'03 23 27 15-646 1885 126 30 3-43 2 ~g.~ 9-0906246 167 58 58-17 28 10 14-95 7 1 25-19 23 27 15-170 1886 j 126 32 16-56 ~g. 9-0903670 g~g 167 59 44-63 28 10 14-60 7 1 10-35 23 27 14-694 1887 1263429-82 ~g.~ 9-0901095 168 031-09 281014-25 7 055-52 232714-218 1888 126 36 43-21 2 13'52 9-0898520 g~ 168 1 17-S6 28 10 13-90 7 0 40-70 23 27 13-742 1889 12~ 38 56-73 jg.~ 9-0895945 g~ 168 2 4'02 28 10 13-55 7 0 25-89 23 27 13-266 1890 12<J 41 10-38 jg.yg 9-0893370 168 2 50-48 28 10 13-20 7 0 11-09 23 27 12-790 1891 I2C 43 24-16 ~g.~ 9-0890795 g~g 168 3 36-94 28 10 12-85 6 59 56-29 23 27 12-3J4 1892 1264538-07 214-04 ~'0888220 g~ 168 423-40 281012-50 66941-50 232711-8~8 1893 126 47 52-11 2 9-0885645 168 5 9-87 28 10 12-15 6 59 26-72 23 27 11-362 1894 I2G 50 6-28 ~.gp 9-0883070 168 5 56-33 28 10 11-80 6 59 11-95 23 27 10-886 1895 126 o2 20-58 2 ~g 9-0880494 ~g 168 6 42-79 28 10 11-45 6 58 57-18 23 27 10-410 1896 126 54 35-01 ~.gg 9-0877918 ~g 168 7 29-25 28 10 11-10 6 58 42-42 23 27 9-934 1897 126 56 49-57 2 9-0875342 g~g 168 8 15-71 28 10 10'75 6 58 27-67 23 27 9-458 1898 126 59 4-27 ~.g~ 9-0872766 C) 168 9 2-18 8 28 10 10-40 6 58 12-93 23 27 8-982 1899 127 1 19-11 n .ng 9-U870190 168 9 48-64 28 10 10-05 6 57 S8-20 23 27 8-506 1900 127 3 34-09 9-0867614 168 10 35-10 28 10 3-70 6 57 43-48 23 27 8'030 *SecNotep.216.

.~or De<ey~ the j4/?~6a)~~ce q/ /S~< ~t'M~, ~'c.*

TABLE VII.


S!

gS û Q' Log.sinI' l' § t" 1'

a" S

'-? R

-i

o I ll 0' l N 0' Il o I l~ 01Il n 0' l Il

18CO 112 26 44-40 59 14 20-21 9-6544178 2 29 26-90 ni M 40-23 2 8 24-70 2(! 49 26-27 1861 112 27 15-96 59 14 36'91 9-6544192 ~g 2 2') 2fi-75 171 40 27-20 2 8 24-94 26 49 26-59 1802 1122746-52 59 14 53':30 9-6544205 22!'26-60 1714114-16 2825-17 264926-91 1863 112 28 17-08 59 15 ') 9-70 9-6544219 13 2 29 26-45 171 42 1-13 a 2 8 25-41 26 49 27-23 1864 112 28 47-64 59 15 26-09 9-654-1232 14 29 26-30 171 42 48-09 2 8 25-64 26 49 27-55 1865 112 29 18'20 59 15 42-49 9-6544246 ~g 2 29 26-15 171 43 35-OG 2 8 25-88 26 4!) 27-87 1866 112 29 48-76 59 15 58-88 9-6544259 2 29 26-00 171 44 22-03 2 8 26-12 26 49 28-19 1867 112 30 19-32 59 16 15-28 9-6544273 13 2 29 25-85 171 45 8-9!) 2 8 26-35 2C 49 28-51 1868 1J2 30 49-88 59 16 31-67 9-654428C 13 2 2!) 25-70 0 171 45 55-96 2 8 26-59 26 49 28-8" 1869 112 31 20'44 591648-07 9'6544299 14 2 2& 25-55 17146 42-92 2826-82 264!) 29-15 1870 1123161-00 5917 4-46 9-6544313 ~g 22925-40 171 47 29-89 2827-06 264929-48 1871 112 32 21-5C 59 17 20-86 9-6544826 14 2 29 25-25 171 48 1G-8G 2 8 27-30 26 49 29-80 1872 112 32 52-12 59 17 37-25 9-6544340 ~g 2 29 25-10 171 49 3-82 2 8 27-53 26 4!) 30-12 1873 112 33 22-68 59 17 53-65 9-6544353 13 2 29 24-95 171 49 50-79 9 2 8 27-77 2G .1 30-44 1874 112 33 53-24 59 18 10-04 9-6544366 2 29 24-80 171 50 37-75 i 2 8 28-00 26 40 30-76 1875 1123423-80 591826-44 9-6544380 13 22924-65 1715124-72 2828-24 264931-08 1876 112 34 54-36 59 18 42-83 9-6544393 14 2 29 24-50 171 52 11'69 2 8 28-47 26 49 31-.IO 1877 112 35 24-92 59 18 59-23 9-6544407 2 2!) 24'35 171 52 58-65 2 8 28-71 26 49 31'72 1878 112 35 55-48 59 19 15-62 9-6544420 14 2 29 24-20 171 53 45-62 2 8 28-94 26 49 32-04 1879 112 36 26-04 59 19 32-02 2 9-6544434 13 2 29 24-05 171 54 32-58 2 8 29-18 26 4!) 32-36 1880 112 36 56-60 59 19 48-41 9-654.1447 ~g 2 29 23-90 171 55 19-55 2 8 29-41 26 49 32-69 9 1881 112 37 27-16 59 20 4-81 9-6544460 14 2 29 23-75 171 5R 6-52 2 8 29-65 26 40 33-01 1882 112 37 57-72 59 20 21-20 9-6544474 13 2 29 23-60 171 56 53-48 2 8 29-88 26 49 33-33 1883 112 38 28-28 59 20 37-60 9-6544487 2 29 23-45 171 57 40-45 2 8 30-12 26 49 33-65 1884 112 38 58-84 59 20 53-99 9-6544.501 jg 2 29 23-30 171 58 27-41 2 8 30-35 26 4!) 33-97 1885 112 39 29-40 59 21 10-39 9-6544514 13 2 29 23-15 171 59 14-38 2 8 30-58 26 49 34-29 1886 112 39 59-96 59 21 26-78 9-6544527 2 29 23-00 172 0 1-35 28 30-82 26 49 34-61 1887 112 40 30-52 59 21 43-18 9-6544541 13 2 29 22-85 172 0 48-31 2 8 31-05 26 49 34-93 1888 112 41 1-08 59 21 59-57 9-6544554 13 2 29 22-70 172 1 35-28 2 8 31-29 26 49 35-25 1889 112 41 31-64 59 22 15-97 9-6544567 14 2 29 22-55 172 2 22-24 2 8 31-52 26 49 35-57 1890 112 42 2-20 59 22 32-3G 9-6544581 13 2 29 22-40 172 3 9-21 2 8 31-75 26 49 35-90 1891 112 42 32-76 59 22 48-76 9-654-1594 14 2 29 22-25 172 3 56-18 2 8 31-99 2G 49 36-22 1892 112 43 3-32 59 23 5-15 9'6544608 ,g 2 29 22-10 172 4 43-14 2 8 32-22 26 49 36-54 1893 112 43 33-88 59 23 21-55 9-6544621 13 2 29 21-95 172 5 30-11 2 8 32-46 26 49 36-86 1894 112 44 4-44 59 23 37-94 9-6544634 2 29 21-80 172 G 17-07 2 8 32-69 26 49 37-18 1895 112 44 35'00 59 23 54-34 9-6544648 13 2 29 21-65 172 7 4-04 2 8 32-92 26 49 37-50 1896 112 45 5-56 59 24 10-73 9-65-14661 13 2 29 21-50 172 7 51-01 2 8 33-16 C, 26 49 37-82 1897 112 45 36-12 59 24 27-13 9-6544674 14 2 29 21-35 172 8 37-97 2 8 33-39 26 49 38-14 1898 112 46 6-68 59 24 43-52 9-6544688 13 2 29 21-20 172 9 24-94 2 8 33-63 26 49 38-46 1899 112 46 7-24 59 24 59-92 2 9-6544701 14 2 29 21-05 172 10 11-90 2 8 33-86 26 49 38-78 1900 112 47 7-80 69 25 16-31 9'6544715 22920-90 1721058-87 2834-09 2G 49 39-11 See Note p. 216.

TABLE VIII.

~'o?' Ca/cM~M~y the Elevation o/~ Sun above < Plane o/</<e7?~ ~'c.*


U.U.;AT L~QUAUTY Ot- JUPITER -1/ alU.~T I~QUA~-Y 0F SAT.J~~

Equation DUTcrcncea Differetices EQ"~tion Equ&tion First Second 'quatlOn pirst Second

First

1550 -014-IG +048-7'J </

151r)o -0 1 4')7 + ¡ 18'73 + 048,71) 314,07

+~ 7 -0-1<; -8 8 .0~ 0~ 1 ~8-84 341..0 1 s~7 31~13 1~0 4.8.05 ,,o.77 ]610 7 :li'Hl r~ 1.7.43

'~1 1 1-~ 1810.07

2..26 1 21 7.88 ~30 1 7'16 0 ,,o.~ "t0 10M..M ;3 2.~ 0,~ ~8.. 6'39 l.~ 1. 0.87 1 ~24-70 0 7-88 ~0 ,? 3~ 31.

,,70 1~78 0 ~30

]680 1<1 6;)'85 r, 0 M'07 }J'fi7 :14 17'85 2 22'30 8'55

1CSO 14 M~ ~-0 2~.17

~0 1.4~7 0..

1700 16 *29-92 0 4fj'95 4'17 38 34'30 2 3'28 9'89

1700 1629-93 04S-95 4'32 ~n?~ 1M-S8 ]

l~ 1711.M 041.63 ~~S i~ 10.95

1' ~11~ n.n~ 4'M 42 9-11 10'95

1720 1748.58 037.03 4-CO 42 9-11 i 30.46

1~ 18 .~f- 032-28 43 39 .,7 1 30',j6 11.95

1~0 182086 0 27'34 ~~g 118~1 11'05

1740 1848.20 0~34 1 G.L6 12-25

1750 19 10',19 022"-)o 5 0;-), 46 4'34 1 G'6 12'2Õ

17.0 1910.49 0 0,~ 12'61

1760 1~7.60 0 040.69 1

1170 19 ~19-46 0 11'86 .5*25 47 88'G8 0 40'69 ] 2'96

T".0 19 39-46 n 11 ~o St! ~'SS 486-16 o 27-48 13.26

1780 194.~4 0 ~8 014.22 1790 1947.04 +010 -00.85 13'37 1800 1.42.76 -04.~ +01.2.67 1810 1933.01 0~ 0 20.12 2

1820 1.17.S. 0 039.49

1830 18 fJ7'37 0 20',j8 à-82 47 2'95 0 3!N9 13'37

ic"~ iR'.T-t? 020.48 052.68

1 sîlo 0~.79 i r., 13-03 ~0 ~31..8 8 0-~ 1 5.<1 13'03 ~0..7 0 118.35 1800 1724.51 0 130.78

1870 ~643.59 0~ 142.71

1870 r, 43o 045,65 4'73 40 :12'ï2 1 42'71 11'93

1S80 1.57.94 04~ i~, 10-86 1890 1. 7.78 0 0. 6 ,.io 1900 1413.2.5 14 054-53 17-89 2

6~'<?~ /< of ~~Mr/Z and ~~2'~r.

TABLE IX.


Face of Ring I

Yenr Dlonth 1)ny Civil Time illumillated Pime at pns~ngc

Ycur Month Day Civil Tin ie dSi~'i~er~I rhascat passage betwecn patauges

h.m.

1612 Deccmbor 28th ) 3'.M. Disappcarancc Southern

1G26 Scptembcr 15th 11 A.M. Rcappcarat~cc Nortitern

1M2 June 18th 5 ~.M. Reappcarance Southera

1G!)S Mardi Srd 7 f. Rcappcarance Nortiiern

](:71 Dect-mber 5th 9 -A~[. Disappe:)mnce Southern

1G85 August 20th 12 ~oon Di~appeamneû ~forthern

U01 May 23rJ 7 r.~r. Renppcara~RC Southcru

1~5 February Cth 1 r.M. ReappCHrance Northern

1730 November 7th 11 A.M. Di~appcarMice Sontl)0'n

U-14 July 23rd 6 r.~r. Northern Disappearatice ~7GO ~prn 24th 4 Reappcarancc Southern

1774 January 7th 1 A.~t. Reappcarancc Northern

1789 October 7th 12 muln. Disappeara~ce Southern

]803 June 2~rd 10 U A.M. DisappcaraTtce Northcrn

)8)f) March 2:!rd 7 T.~[. Rcappcanmco Southcrn

1832 Deccmbcr 4th 9 p.M. Reappcarancc Northern

1848 September 3rd 3 26 t'.M. Rcappcai-ance Southcrn

18()2 May 18th 8 30 A.M. Disn.ppcaraj)ce Northcrn

1878 February 14th 2 P.~[. Disappcaj'a~cc Southern

1891 October 29th 1 A.M. Reappcurancc Northcm

1907 July 29th 3 A~t. Rcappcaranec Southcrn

1921 April lOth 4 A.M. Disappearaoce Northem

1937 January Cth 4 r.M. Disappettrajtcc Southem

]950 September I!)th 1 r.M. Rcappearancc Northern

I9CG June 17th 2 P.M. Rcappcaranec Southcrn

1980 rebruaiy 28th 3 p.~[. Reappcarancc Northcm

i9M November 2Cth 5 A.M. Dif=appca.rfU)co

-1.

TABLE X.

jP~es o/ tlie 7i'i:'y~& Plane /Aro?/ the ~'M~ ~~<cc~ /e ~er/7's 1GOO ~<UOO.


<M

c* 3

='. r,j

f1J

ëë'

=~

~M

5~.3~

«} ?- d o

UJ

~~Sg 5~ d

O ro,s

53~~ 's~~a i~~

5 S

~S

!j'! ~i~ ~~s 3~~

~M

d

5 S H ~j 6~

3: § o

S~ti-~

~~3 °'6 S~

0~'s~

~a S

~~3 &S

~S~'C

CQCS'3

.~i~

.S~S

~S ~J.f

h

~ii

~!I

i

S

T3

o 9~9 =' '=' ? =- o. <.

°s ) ° > &.O~ 4'~ ÕOÕ o c- C- ) ) '.?. f~ e~ j t

'S' s~ §S=- S' S'' '~?!

IQ~ 1 (.:>oo.c a <1 (;'f ;1"'1 O r-.

_h~ ;='

S 9~~ S ? e s 5: "H! S

S 3 5~ g g g 4: t ~t

c1~ "H 'n i. O M N O t~ r-~ er H ~p ~1 M G9 ^ll n r~ V ci

g CJ~ CI ~f7 G9 C: 1l' r1 ^i ,V .1_ r·l C1 CI dl

S~~ 9°~ 1 ~?p ~.< a <=. o

°-, 0 r CI c9 <<M C!-)r-tr-< r-<T)f-< ~M,

10 ~O~ GO ri 4'J Cn C1 O ~?I ~s~ g.:g: c:

gg~ M SS~ c-o ~SS W S~!9'' ~SS ~«~

.<)~ (.:>~ et l` u~ .N 4'J IQIQ

S~S 9°~ ~~S ? ? =: S S =. <= e,

0 o 0. CI:I -<)<~ 4'7 -t'~C~ r-)e-)r-< <1 -0'~) <:) C) r-t,

S Sg~ ~yl ë93 rM·1 ~ëg Ô r~~ SSS~' 1 ~~S~~iS C~ ~33~' 1

~<)~ Ci r·~ rH K7 ~rJ M ~1 4y rr r·1 n

o S~?! r-i 9~ r~ ~°~! d~ ~?' .d, ~S~S" p S~SS~S :M Me-t~M"

p Ci ~N r··l VI 4D 8-1-- M M 4'J M M w'7 r~ r~ a~ M

a§§ o ~9 S fp ~S3 C.'i î~ .ni se S S' ~-S~~S S 33~'

d' ci v~ 4-~ r. vm, î_ 4~ .o e~a e°~ c~rJ `r r` ci M ci éô c4 c.

~S 9~~ 3~~ Go ~S°°SS S93SS5! -=~!S~~

p o .c~ r1 et C~ n .~J M VI .N CI 'dl ~r Ci Ci eJi

J cD O C'9 Cl:>0C? O O L'i ~1Q1Q0)~ ~OIQIQOIQ 0<:)1Q~0

S § 3 S g S! ~§S M s3S9~ n ~°S~S3 v0 ~S~S~

S~S 9'=~ S°~ SSS~~ S~ ?3~

o r. o v ao _O~ ~Oc)t- INO~OIQIQ co~~c.o~-

S§S S S S ~S~ S S 35~ ~~SSS~ SSS~~

M C4 ~IQ~ N t` c. 4~ :9 n CI n M m

3!~S 3~ S~ <='<SM ~C~MC' MMOM~ o~ec~io

0 g Ci e~M)~ t~~ o<M}r<'0?< o

M ?!SS S§S 3S'S ?' 3:-<'M~'o e~oei~e-)~) eooot~~t

~0)M.) CC~M &0-<t< t~t-t-t ~r-.M ~0:MC<r-.

gcco f4 .-1 S°~! d~ 7'?? 53<ac't- e~<oo)-~r-r-< r-tcst-t.

n rH r-1 V~ M à- t'J O t` CI N~ Ci .!1 t~. r-1 rr O 1~ 1~

1 C'f 0 00 0" <:> 0 0 è);) co 0 t- co CI) .t 0 1. IQ

s s§§ ss~ ~ss -ID s~ss s.

C"f ,1 C) co c.o co Ci r·~ rl u~ u~ dl t` t` t·. CD 4~ n n .r~ d~ M n

S!S co '-<o~ ~o~ ~.y~) !booo)o cac'f-'pt~ta et-~t-to

-3 Ci CI C4

S ~gs SS~! §SS sgS~ë S ~9~

C"f Go t- CI r·-1 r-1 co ~1 ~D IQ~IQ~~

S°~ ~~S g~S ~~S~SS SS~S~

4~ rl M CI if l u~ .~1 M CI n ~O r~ r~ M .rJ aJ n r-.

~-O" SS°S SS~ 3' ~M~COM r~OM~MtO ~MMMO

'-< ~t- 3SS '&us~ OOOOOOt-t- < tSSSSM

~D O dl r~r O rr ~N O C^J t.~ t` Ç~ C!~ Ci ~M M C~ ~t~ r..m~ t0 G9 w'i e~ M

0 l e-t-~<~ l 'O'Mr-t ~~M~f ~~SS"

3 s g 3 SS3 SSS ~SSSS -=~ S ~~3 3

n C) co t- 00 IQ r.~ r.. r-1 IQ W Go oo a0 h. ts t~

VI r-t VI ~t<t~ ~~SS9 1-4 S'?!~§~3 c> S'S~

Sa 1 ~'C'M SSS SSS! So~t-<:S-f OOr-tf-M ~c.t~o ~0}<a <acCMa rH ~:M9m u7 OOQOQOQOM 000}M~.K

oe'<=- &<p<p &<=.c'c.<=' <=,oe'oo

3 g 3 3§3 SSS §S§§g ggg~g

C)C)C)C)~

'&

y v

s.?.

"'s"<J~

ë

ta ~c: "1:<

3 ''S~ S

E-< £ \:1. 51-

ë 3 .j~ .a~~g'

j s ~sss~s~ s~sgsgg

¡; s ~ç:;¡:¡:;ç:ç: i~, ç:;

.!<'O; ,1 .s ~C~pJ Éj .!4

g' ~SS S'ë~~S'~

~s~~s~g s~ëc~~p~ .§~ëê~~o

V 8 B 8 O U w w w w w 1:: '& .0 .0 .0 w

~J! §Ë~§S~§-iTgS~~ ~'3'ë'ë'ë'ë~ H J S~

p =~ t9 ] S 'a .3 g t9 'a r9 "g. g r.n co g¡, ec g¡, w rn -5 gj¡ to

àj r$ s ri u r$ 1 s 0 æ

;;j ~aihs~aj. ~ëj~ ~ë~ëë~ë~S is-~ëëëëë .gg-g.S5a's.g-gg'3.g~§'s.g-s~ë-gga~§~g~~s~~g-gHg â 5~g~-§~a~ F~a~'S~S~ 2<§~ÔS~O~O~O~~

-S .2 § -S S

0 ~) -!]


?. c-S: &) T3 S o o S S -a

8, .SS S 9 g S S- g~ë s s ~H ~g~ M ~<S '5.K s

u~ < a t-· t- a a n & Ç~ < ? e?'=.T;C' &S=e'S~

iS~S.SS M S- S "1 8 g <= s~~ ~~g~

Vol O et 1 tC CI CIO. 1 cc 1- 1 r~1 8"= 8!:=:

'.<. g:99 S J~~ .'j

co n .p o ô G. Ul -o~'a..cs

–r– ".T" a & a~

~~s, ~) s j 1 s ) s s sjë~

C':) G 1- C'I COI Oc0 oot' r- Ct 0 ~CJ)CH 8 i~ p,p,= æ

~s s s s' s .s~~ ~j .ra

99 s s" s~' 'S

~=~~S~ oj4 §SS~! "1 S~ S 3 l dr ë~§ j~~ ~4'f

GO O r~ i~ 0 CO C'I C'I Il) O C7 m 1:" c.> C7 in M r·+~ 4J ¡:;

co ~~Je' a ~~co" ~s

s~MS~9 c. =-. g s ë'sSa.'c~Sg

M<BM<C'-M CCt-M t-t 0)CO :1' ri 'i" M 1 ~~SC~SM~B ,S ~~3~ !i!. ~ë~Bg~~S.~h -s"=–r'8,'Ss'3~~gihM.g 99<=~ r~ ~-ë~- S- 2 S = ~.S~TJi-~ "cg~ ~sgës ~s s~ ~ii.

n r~ r-. ct o o co r~ co cmo m r.r c.m d~ c' ~~¡;¡'kas 8. p) v

MM~~s~ ~w ~M ~=. ? °° ? S~S~~S

5~M~C< r-<.S 1 g 0 jg ~SB~~CO~S ~3SS Co:> S§ë~9 CIJ CI) 59 '? ~~g~.

n. r-i rr C0 O O 1" V~ eN CI Co:> '<il rr r."I rr atl C ~ro d 9 00 '0 0 CI)

a> s~-ss 0 s~ ë~ e~ g s'T'TT ~~i~ +,

~.3 3~ S CI> s S 5~~ 0 ~S ~9 3 .gg~~ ~ë~~ a –?–5–– SM>.g'2 S~Q~~

ss°°~~ ° S S S ~.S~~S.s~SS

r<~g~ -M r<r. g g g ~'S~qi'S-C~

Vol o et .a <:> aa IQ .er co Ci IQ e:> re~ m m ct ct t- .N ,g ¡r;"t1 en Itj æ] 51:>

s~~ss s~ ~s ? ~~gi~

(~ b t~ ~o- -=.=.E:> e:: n w g rQ ·O

~9 ~~3 1 s s 00 g. ~~Mi

IQ C'I: g~.@g.s .8~ â

"3S CI e~~SSë vu 3S !~S V O dr

s s s s s s ~~s~~ s~ g g g

VoIO<:>C>~ao COC'lco~Co:>I '0 M GV 6V Ct t~ t;-I r·`1 8:S

~=-3~8 s~S~~ S~ S S JS

n r-~ CI y-r O~ tr G~ eJ M 1 M O O C7 m 8~ .e

S ë M~

~=~S SSSS~ S~ S~ ~H~ ~2

.0r-lG 00~~1Q"¡< V .'T1 CO:> .V rr CI;Q. a¡'g UJè>

n Cl .r Cr t~ t~ t~ bD t~ O O rH G~7 :8

~s7"s~~9 ~s s !s~

0 o M ca ·r r., m o~ <:> II;) CQ. t.~ co Vol c "i' t" '8 uc alq!8!A !}OU sa nî a

OOM<f'~<~ S~SSS t- So3 ~o 6oS oo -B S~

0 0 <=) <S r- .~0

~g MM&oMtio 'S~

) t ) i dt o0 O O O j j j ) -3§' (=!~p=!~E S.S

1 1 00. t- <D 00 0 <:> 1 1 1 1 1 ~}: y, ¡:

'')!tt aB~Ot-tO <='<= 'S 'ë[S t<<-f)-<~ S..n

–r~ <§~J!~

g s~ s § ~s a ~.j ~ë-s-s gj. ~i c aoc éo S -ë~ .§S ë .t S 's~ SSëS~ ST. __i § i. `''3 ~g~~

,?Ht' !:jt"~ .s :}!?!<!

i1"!< !~M !{! 6~6 c~ e~ ~u ° 'S'S'S~'S ~g. -g~ ëi~~ ~c~ §a Ëssaunloq~osuois~S .ct

8 S: · 'J:: w w w w w a¡' Ca E-I E-I lJ '08u!!JQa¡8au PU1J,¡ ô

g f:l) bD p U1" '8 g, -ô âi S 1) ë r.. g¡:: ô 2 r S 88üT aq':J JOSUO!S CI)

-~ë'~ë'? §)&§,&§) ~?°6 .ëëi~~ëë§ë~j g ~-uorn~p pooms~ «

~a§i!g~ s~~ss ~§i§~~

~1 â, ~j!~ o" 3 § -.S ~63 5~ J J

~i ~1 1=1 '1 S


EXPLANATION OF THE TABLES.

TABLES L, IL, and III. have been calculated for the most part irom < Madier's Elements.' Thé dimensions of Saturn's globe, as of the rings in Table IV., have been selected ibr reasons mentioned in Chapter 111. Thé gravity of Satum has been calculated, for the equator and poles, from approximate formula (~ Todhmiter's Analytical Statics,' art. 217.) TABLE IV. The quantities S, I' and been calcul~ted <rom thé Ibrm~œ given in the explanation of Tables VII. and VIII. Thé variations of ait thèse quantities, except /3', are nearly ~miton~ for long intervais of time, and have been determined irom the values of thé quantities for thé years 1800 and 1900. The annual variation of /3' is not unifbrm for that interval, ranging from 0~-239 in thé year 1800, to 0~-234= in thé year 1900.

TABLE V. Except the 4th, 6th, 7th, and 8th columna, ca.lculatcd by myself, thé elements of Table V. are Miidler's, corrected in places irom the best modern déterminations.

TABLE VI. Except the column of meau hourly motions, this table is thé samc as Table XXXIII. of Loomis' Practical Astronomy.' 1 have addcd thé honriy motion of Neptune to thé hourly motions ofthe other planets.tal~en n.-om Hind's < Introduction to Astronomy.' The equatorial horizonttd parallax of thé sun at his mean distance is assumed to be 8~-5776 throughout this table.

TABLE VII. bas been calculated by means ofthe -fbilowing ibi-mulac* Let S represent thé mean longitude of the ring's ascending node in tlie .ecliptic at time t..

i, thé mean inclination of thé plane ofthe ring to thé ecliptic. I, the mean inclination to thé equator.

N, thé mean position of thé ascending node in thé equator. (j, thé obtiquity of thé ecliptic.

See Nautical Almanac' fur 1838, préface, p. vin. and pr~facf-s to latfr Na~ical Almunacs.


Then adopting Beaael'a détermination of s and i, viz. S=166°5~ 8~-9+46~462 (<-1800~

!'= 28° 10~ 44~-7- 0~350 (<-1800j

and assuming tan ~==tan i cos

tan N=-tan Q tan I-+~. ta n N sin(~+~) tan 1- cosN

The table is applied to the determination of the appearance of the rings, by meana of the following ibrmulœ

Let a represent the major axis of thé ring at the planet's mean distance.

the apparent outer major axis of the outer ring)

ail, the apparent inner major axis of the inner ring

b', the apparent outer minor axis of thé onter ring)

& the apparent inner minor axis of the inner ring~

the elevation of the earth above the plane of~

the rings t

l', the elevation of the sun above thé plane of t

the rings j

jp, the inclination of the northern semi-minor axis of the ring to the circle of declination.t

a, the geocentric right ascension Il

the geocentric decHnation

p, the distance from the earth of the planet.

thé heliocentric longitude P~

/3, the heliocentric latitude

?', thé mean distance from the sun J

Then, adopting Bessel's value of a and Bouvard's value of ~=39~308; r=9'54301; Iog(ar)=2-5741663;

and assuming tan Q==tan 1 sin (a-N)

~) (a-N); tan ~tan (Q-S) cos~;

ços 0 )

sin ~=sin i cos /3 sin (\- Q)-cos i sin /3

~=~; ~=~x-665; ~==a/sin~ ~=~x'665.

P

~a:a~Required to determine e~ b', & p, and l for June 22nd, 1865, at mean noon

M. MMadi, in 1716, determined a =166° 20'; and (see Table VIII )=d69° 48' 30": these values agree well with the values and variations given in the text t b', b", and are considered positive when the north surface of the ring is visible, otherwise négative; is considered positive if the sun is above the northem surface of the ring, otherwise negative p is considered positive if the nort~m semi-minor axis of the ring is inclined to the east of thf decHnation.circ~, otherwise negative.


These values correspond very well with those given in thé Nautical Almanac' for 1865, p. 486, viz.

p=- r38'-4; ~= 40~23; ~= 26~75;

~=+13° 4~-4; ~=+ 9~52; ~=+ 6~33.

The value of l' may be more conveniently calculated from Table VIII. than irom the formula given in thé Nautical Almanac.'

TABLE VIII. The elements in this table are those referred to under thé same symbols in Table IV. The value of ~may be determined from thèse elements as ibilows

Let À be Satum's heliocentric longitude.

/3, Satum's heliocentric latitude.

Then, assuming

cos ~/=cos (\) cos /5

we obt;<un sin ~=sin (~) sin Il.

We obtain from Table VII.,

N==125° 47~ 9~7; andlogtanl==9'09o64=72

Agam a=202° 49' 21~-0; ao(i ~=6° 46' 14~ 5 s.

Thuaa–N= 77° 2~11~-3; and the calculation proceeds as follows:-

logBm(a–N)~= 9-9887877

log tan 1= 9-0956472

Q= 6° 55' 31" log tan Q= 9-0844349 ~=- 6° 46' 14" log sin Q~ 9.08~563 Q-~= 13°4r45" Iogcot(a-N)= 9-3621013 19-4433576

logcos(Q-~)= 9-9874723

~==-1° 38' 14" log sin~= 8-4558853 logtan(Q-S)= 9-3868543

log cos~== 9-9998227

~=-t. 13° 41'26" log tan l= 9-3866770 log (a r)= 2-5741663

log p= 0-9696225

~=40~229 log ~= 1-6045438 log sin ~= 9-3741578

~=+ 9"-521 log b'= 0-97-87016 a"= 40"-229x'665= 26"'753

&"=+ 9~521 x-665= + 6"-332


Thus for June 22nd, 1865, at mean nooii

We obtain from Table VII.

~= 112°29'32~-7; s'=59°15'50~3;~dlogainr=9-6544253 Again \= 209° 8' 3~-9; and ~=2" 28' 19~2.

Thus À–~= 96° 39~ 2~-2; and the calculation proceeds as follows

The < Nautical Almanac' gives l'= +15° 54'-].

Madier'a values of t~ and i' have been adopted in Table VIII. Bouvard's values differ slightly A'om those of Madier. Thus, for the year 1900, the values of v and il, according to Bouvard's Tables, are respectively 112° 47' 20"-7 and 2° 29' 20"-4. In Table VIII., and i' are respectively 112° 47' V'8 and 2° 29' 20"-9. Adopting Madier's values, the ~ormulse for $3' and F are as follows

8~=58° 57' 56~8+16~395 (t-1800);

F=26°49' 7"'0+ 0~-321 (<-1800).

Adopting Bouvard's values, we obtain thé formulae

6~=58° 58° 1~9+16~201 (<-1800);

F=26°49' 7~-2+ 0~317(~-1800).

The hour at which the ring's plane passes through the sun may also be determined from Table VIII. Thus, for the passage in May, 1862:From the table we have for May, 1862, V==171° 41' 32~-4;

and Saturn's heliocentric longitude being 171° 39' 47~1 at mean noon of May 17th, and his daily motion 2' 3~*4, it is easily calculated that his heliocentric longitude was 171° 41' 32"'4 at 8h. 30m. A.M. of May 18th, 1862, at wnich time, accordingly, the plane of the rings passed through thé sun. In a similar way, it may be shown, that the passage ofthe ring's plane through the sun in 1848, took place on September 3rd, at 3h. 24m. p.H. It may be mentioned. that /3' deduced from the table is not necessarily the same as Saturn's heliocentric latitude at sucb- a. passage, since Saturn may be (through perturbations) above or below his mean orbital path. It may be mcntiûncd that (~- a~) Is Argument X~IL of Bouvard's Tables of Saturn.


TABLE IX. combines parts ofBouvard's Tables (XI. of Jupiter aud Satum), the French measures being converted into Enghsh. A word or two may be required m exy)Ianation of thé table. Take thé inequality of Satnm Thé équation of Saturn for 1550 is +48~-79,–by this is to be understood that (so far as the great inequality is concerned*) Saturn at dus time was 48~'79 in advance of his mean place in longitude the équation for 15CO is negative,-or in 15CO Saturn was behind his mean place. At some intermediate date, then, he must have been in his mean place, and it is ea.sily seen that this must have happened in the year 1552. Froni this time Saturn lagged more and more behind his mean place, until, between the years 1780 and 1790, his équation attained its greatest négative value. Th:s bappened about the beginning of the year 1786, Saturn being then about 48~ behind his mean place in longitude. From this point his distance û-om his mean place has been continually diminisiling, being now about 41~. This diminution will continue till lie reaches his mean place in thé beginning of the 21st century; lie will tlien pass in advance of lus incan place, tijl in the middle of thé 23rd century lie will be about as much in advance as he was behind in 1786. Now, it is clear, from thé considération that Satum was iaUing iartiier and ~rther behind his mean place irom 1552 to 1786, that dm-ing ail that tirne he was moving with a motion less than his mean motion and further, it is clear that thé same was thé case befbre the year 1550; for before that year he had been gradually falling back to his mean place, from a place about 48~ in advance of it. Thus, from 1552 to 1786, and for about as long an interval before 1552, Saturn's period was greater tlian his mean period. And it is clear that Satum's period bas been less tlum lus mean period û'om 178G to the present time. It will continue less till thé middle of the 23rd century. Thé column of first diirerences indicates thèse changes more clearly. It exhibits thé amount of longitude lost or gained by Saturn in each decennial period. It appcars that thé loss was greatest when Saturn was near his mean place irom which we learn that Saturn moved more slowly at that time,–or, in othcr words, that his period was then greatest.~ ShniJarly, we learn that Saturn's period gradually diminished, until in 1786 it p:tsscd through its mean value, and that it bas continued to diminish ever since. Thus Sa.turn's period attained its maximuni when the inequality vanished, and passed through its mean value when the inequality obtained its maximum négative value; and similarly Saturn's period attains its Throughout the expl:m~tion these words mustbe understood; other perturbations operate to diminis!i or mcrt'asc tlie departure of Saturn from his mean place, t By tbf period of a ptanct at any instant' is to be undcrî-tood tlie pcnod in which thé planet woutd accumptish <). sidcreal résolution about thc suu if undisturbcd from that instant loy the attractions of other bodic's.


mmimum value when the inequality vanishes, and retutns to ita mean value when the inequality attains its maximum positive value. Lastly, the column of second differences enables us to estimate the rate at which the period diminishes or increases. It appears from thia column that the period varies most rapidly when it is passing through its mean value. The inequality of Jupiter may be interpreted in precisely the same manner. If the two columns of third differences be drawn out, they will be found less regular than the columns of first and second differences appear to be. We have in this irregularity the first indication of the variation in the disturbing actions of the two planets, arising from the variable relations described in Chapter VI.

TABLE X. gives the days on which the plane of Saturn's ring has passed through the sun from the time of the discovery of the ring to the end of the 20~h century. The passages have been calculated from those of September 3rd, 1848, and May 18th, 1862. The only corrections applied have been those due to the great inequality, and to the precession of the nodes of the ring's plane on Saturn's orbit. Thus, for the calculation of the ring's disappearance in the year 1789 :-This disappearance must be calculated ~rom September 3rd, 1848. Saturn's mean sidereal period contains 10759-2197 days, but in each year the nodes of the ring regrede through an arc of 3~145 and therefore in Satum's sidereal period thé nodes of thé ring regrede through r 32~-6~ Now Saturn's mean daily motion at the part of his orbit in which the passages we are considering take place-in other words, at the autumnal equinox of his northern hemisphere-is l' 59~-0 thus the time occupied in passing over an arc of 1' 32~6 is 0-779d., and by this amount Satum's mean sidereal period must be diminished to obtain his mean tropical period for the part of his orbit in question. The latter period is therefore 10758-441 days; and this interval contains 7 sets of four years (one year in each set being leap year), one common year, and 16Gd. 10h. 35m.; therefore two such periods contain 14 sets of four years, and three common years, wanting 32d. 2h. 50m. Now, if we calculate such an interval backwards n-om 3h. 26m. r.M. of September 3rd, 1848, remembering that 1800 is a common year, we arrive at October 5th, 1789, 6h. 16m. p.M. But from Table IX. we find that for September 3rd, 1848, the inequalityis-43' 56~-6, and for October 5th, 1789, thé inequality is-48' 21~-4 thus Saturn was 4~ 24~-8 farther behind his mean place in October, 1789, than he was in September, 1848, and therefore the ring's plane passed later through the sun by the time in which Saturn with a daily motion of l' 59~-0 passes over an arc of his orbit of 4' 24~-8 or by 2d. 5h. 24m. so that thé corrected date is October 7th, llh. 40m. the nearest hour to which is 12 midn., October 7th.

Siitum's mean period contains 29-4578 tropical, or 29-4566 sidereal years.


For -passages* calculated irom May 18th, 1862, the excess of Saturn's tropical revolution over 7 sets of four years and one common year, is 166d. llh. 16m. This may easily be verified in the manner ahown above, remembering that Saturn's mean daily motion near the vernal equinox of his northern hemisphere ia 2~3~-4.

The autumnal equinox of' Saturn's northem hemisphere is continually receding from, and the vernal equinox approaching, the perihelion of tlie orbit, by an arc of 19~31+3~145, or 22~-455 in each year, or by 11' r''5 in each mean Saturnian period. Owmg to this variation Satum's tropical periods, measured irom the vernal equinox, succesaively increase by about 21 seconds, while those measured from the autumnal equinox successively diminish by about 20 seconda. Another small correction ia due to the same variation of motion applied to the correction for the great inequality of Saturn.

Thé table can be applied to determine approximately the dates of the passages of the ring's plane through thé earth. Thus, take the passages of the year 1789 the ring's plane passed through the sun on October 7th, when the earth therefore had passed the autumnal equinox by about 18°; thus the earth was between thé autumnal equinox and E (ng. 1, Plate VIII.), very near the point a,t which q' 7 crosses the earth's orbit. At this moment Saturn was near the point M, but had not quite reached that point for thé nodal line of the ring's plane on Saturn's orbit advances 46~-966 yearly in longitude, and therefore in 1789 thé point corresponding to M was nearer m" by an arc of 58~ 54~-2 and similarly the nôdal line of the ring's plane on the ecHptic was very nearly in direction s R, but passed nearer ?' by an arc of 58' 16~-3. Thua it is very easily seen that before the passage of the plane of thé ring through the sun the earth had passed twice through the ring's plane, both passages occurring when the earth was very near thé point e', or in Midsummer, 1789. During the short interval of time that elapsed between these passages the earth and sun were on opposite sides of thé plane of the ring, which was therefore invisible. It was during the reappearance of the ring in the summer of 1789 that the elder Herschel determined the period of rotation of the outer parts of the ring. After thé passage of thé ring's plane through the sun on October 7th, 1789, the ring was invisible for more than three months, reappearing when thé earth was very near the point E', or early in February, 1790, after which the ring continued visible for 13~ years. Table X. can also be applied to determine approximately the appearance of the ring viewed from the earth, and thé elevation of the sun above the rina~s plane. Thus :–We may assume without important error that Saturn moves with uniibrm angular velocity about the sun between thé successive passages tabiilated. On this assumption the arc swept out irom P or M


(fig. 1, Pinte VIII,) at any given time 180°: the time êlapsed since the preceding passage tabulated the complete interval between that passage and the next.* Thus Saturn's position on his orbit is approximately determined. The earth's position in her orbit at the same time is determined in a similar manner. Thus we can determine the required elements by construction, marking down the positions of the two bodies in a figure (asng. 1, Plate VIII.), and thence determining the angles at which thé sm and earth are respectively elevated above the plane of the rings, as shown in Chapter IV., page 80, note* or we may obtain the required angles hy a simple trigonometrical calculation

TABLE XI. exhibits the general features of the Satlunian heavcns for those latitudes within which any part of thé rings can be seen. Of thé manner in which this table is to be interpreted cnough has been said m Chapter VII. The table bas been calculated as iuHows The azimuths of the sun at sunrise and sunset at thé winter solstice in any latitude are obtained n-om thé ~rmula_

cos azimuth=sin F sec

where I' is the obliquity of the Saturnian ecliptic (or 26° 49' 28") and the saturnicentric latitude. The supplément of thé angle thus obt<~ined is the correaponding azimuth at the summer solstice in latitude At thé equinoxes the coiTesponding azimuth is 90° for ail latitudes.

The meridian altitudes of the sun at thé winter and summer solstices in any latitude are obtained by subtracting and adding, respectively, 26° ~9' to the meridian altitude at either equinox-that is, to the complement of the latitude.

The diurnal arc traversed by thé sun at the winter solstice, in latitude <~ is given by thé formula-

cos (diurnal arc) = tan F tan

360°, diminished by the arc thus obtained, is the correspondmg arc at the summer solstice also the noctumal arc at the summer is equal to tlie diumal arc at the winter solstice, and vice t;~a. The length of the day follows at once irom thé length of the diurnal arc since-

length ofday lOb. 29m. 17s.: diurnal arc 360°

,The length of the day at the winter solstice is obviously equal to the length of the night at the summer solstice, and vice ~6r~.

For the appearance of the ring we have thé following formula;The interval from the passage in May, 1862, to thé next passage (in February 1878~ being o751~ days, Saturn's average daily Mgtdar velocity ia this interval is l''o'?~-7 The following interval (to thé passage in October, 1891) contains 500~ days i/tJus interval, therefore, Saturn's average daily motion is 2' 9~-5..


Let reprisent the saturnicentric latitude. ?', thé semi-diameter of an edge of a ring.

s, the equatonai semi-diamcter of Saturn.

s~ the polar seïni-diameter of Satum.

a, tlie azimuth of the ring's edge where it.crosses the horizon. the a-ltitude of the rmg's edge where it crosses thé meridian. -y, thé arc of the ring's edge above the horizon.

Put

cet O.=~cot ~=s sec S ~=~ sin~ cosec

s "t'

Thon

thé upper or lower sign to be taken in the last formula according as (?') is greater or less than The latitude in which the edge of a ring disappears is obtained by putting ~==r, whence we get

cot d) == ~'+5) (~–s)

The arcs of the horizon or meridian covered by a ring or division are obtained by takiag thé diSërence of the azimuths or altitudes, respectively, of the inner and outer edges oftiie ring or division.

Thé parts of thé table reffn'mg to dectma.tion-paraU~a through the points A, A~, B and B~ hâve been calculated from thé following Ibrmula! Let A represent thé azimuth of thé point A) latitude c~.

~ibr latitude <

B, the meridian altitude of the point B J \.lor a lue <p.

P, the meridian altitude of a declination-parallel

through A.

Q, thé azimuth of thé point of intersection with thé

horizon of a declination-parallel through B.

Then,–

cos (~-t-P)==cos A cos

and cos Q cos ~=coa (B+~).

And substituting A' for A, and B' for B, thé same formulas are used to détermine the altitudes of corresponding parallels through A~ and B'. For those latitudes within which thé sun reachcs the points A~ and n', thèse parallels represent thé sun's diui'nal paths at that part of the Sutur-


nian year in which the sun passes through the points A, A~, B, or B'. Thua we can determine the intervais contained in the last section of thé table, as follows:-

Let L be the angle awept out by Saturn about the sun from the autmn.nal equinox, when the aun's meridian altitude is M, in latitude ô Then,-

sinL=~~+~;

sin F

and, if we suppose Saturn to move uniformly with his mean motion, thé interval ironi the equinox in which he would sweep out the angle L about the sun is ~days. For one degree of arc the

Saturn'e mean daily motion

time is 29-9 days, for one minute of arc the time is 0-5 d. From these &)rmulœ and values the intervals of total and partial eclipse hâve been calculated-a suitable correction being introduced for the sun's apparent diameter (assumed to be 3' 20~) viewed from Satui-n. These results are not affected by the refraction of Saturn's atmosphère, for when the sun is eclipsed by any part of the ring refraction elevates the sun and that part of the ring by the same amount. The other elements tabulated are affected by thé refraction of Saturn's atmosphere. Thé effects of such refraction are :-To inerease altitudes and azimuths, especially the latter to increase the diurnal arcs traversed by the sun, the lengths of the Saturnian days, and the arcs of the rings' edges above the horizon and, in general, to diminish the arcs of the meridian and horizon covered by the rings; but when the outer edge only of a ring is visible thé arcs of the meridian and horizon covered by that ring are increased by refraction.


EXPLANATION OF ASTRONOMICAL TERMS USED IN THE BODY OF THE WORK.

~g/ra~'o~An apparent displacement of any celestial object, due to the progressive motion of light. Aberration is caused in two waysfirst, by the orbital motion of the earth, secondly, by the motion of the observed celestial object. Aberration due to the first cause is constant for ail celestial objects except the moon. Aberration due to the second cause is common to ail celestial objects, but varies with their distances and rates of motion where these are known the aberration can be determined. The aberration of the fixed stars due to this cause is not determinable but the distance between the real and apparent place oi* a star must in general be very great. For instance, light is 14 or 15 years travelling from Sirius to the earth, and in this interval Sirius no doubt travels many millions of miles. The earth's axial rotation also causes a small change in the apparent positions ofall celestial objects this is called the ~M/r~ a~mx~'o~. ~E'~gr.–See Medium, ~.SM<ï'

Altitude.-The angular distance of a heavenly object from, the horizon, measured in the direction of a great circle passing through the object and the zenith. See A~M~.

Altitude ~M~ /~<)'M~eM<. See J.~M~/i.

Amplitude.-The distance of a celestial object at rising or setting, n'om thé east or west points, respectively, of the horizon.

~y~ar Velocity.-The angular velocity of one body about another is the rate at which angles are described by thé radius vector of the former body. See jRa~ïMS F~c~r.

J.7ï07MŒ~<:c J~ë~o~Thé time of revolution of a planet or satellite in référence to the line of apsides of its orbit. The period will vary according as thé nearer or farther apse is chosen aa the starting-point :-Thus, in the case of the earth the line of apsides is continually advancing, so that the anomalistic period exceeds the sidereal period by the time in -which the earth passes over the annual arc of advance traversed by the line of apsides and the earth will plainly pass over this arc more rapidly when near perihelion than when near aphelion.

Ansce.-Handles a term applied to thé apparent projections formed by the ring on each side of Saturn's globe.


238

SATURN AND ITS SYSTEM,

Al)helion.-The point in thé orbit of a planet or cornet which is fat-tlicst from the sun.

~osf~M~n'?<H~Thé point in a satellite's orbit ~arthest from Saturn. ~pa~o~o~Thé motion of the celestial bodies viewed from the earth. The term is sometimes applied to the daily motions of thé celestial bodies caused by the diurnal rotation of thé earth, at others to thé motions ofthe céleste bodies on the aidereal sphère,–that is, among the fixed stars. .4;M! Z~e o/The imaginary line joining thé apses ofthe orbit of a planet or satellite more strictly, it ia the line joining what would be thé apses of the planet's path if thé planet moved undisturbed through a complete revolution from the moment considered.

Apse or Apsis.-The point of the orbit of a planet or satellite at which it is farthest from, or nearest to the sun or primary, respectively or, more correctiy, the points of such orbits at which the direction of motion is at right angles to the line from the centre of motion.

J~-c of J~'o~ess~The arc passed over by a planet when its motion is direct, or in the order of the signs.

Arc q/7'o~Y~!OM.The arc passed over by a planet when ita motion is retrograde, or contrary to thé order of the signa.

Aries.-A constellation but also thé first sign of the Zodiac. The commencement of this sign is called ~6~< point of ~s it is thé point in which thé ecliptic and the equinoctial line intersect, the ecliptic passing from south to north of the equinoctial line. The sun's centre occupies this point at the vernal equinox of the northern hemisphere and from this point longitudes are measured along the ecliptic in thé order of the signs, and right ascensions upon the equator from west to east. The constellation Pisces at present occupies the sign Aries. At the vernal equinox the earth's heliocentlic position corresponds to the first point of Libra.

~ce~~y ~o~e.–See 2~o~.

Ascension, ~7~Thé right ascension of a celestial body is the angle between two planes, one passing through the pole of the heavens and thé body, the other through thé pole of thé heavens and the first point of Aries. Thé method of indicating the position of a celestial object by assigning its right ascension and declination maybethus illustrated :-Suppose a télescope so constructed as to be moveable about an axis directed to thé pole of thé heavens, and also about an axis at right angles to the former and to thé axis of thé télescope let the telescope in the first place be directed to thé first point of Aries then thé telescope may be directed towards any celestial object by two movements-the first round the polar axis of the instrument (from west to east), the second about the other axis (towards or-from thé north pôle) tlie angle through which the telescope is swept about thé former axis is the aame as the Right ~c~~ of the object. the angle


through which the telescope is swept about thé latter axis is thé same as thc <7c<~Mf~~ of the object; and thé declination is ?M?'<A or ~OM~A accordi ng as thé latter motion of the telescope is ~ï~cM'~ or~'o~ thé north pole. A telescope so mounted is called an ~~f~o~'M~. (Thé refractive effects of thé atmosphere are neglected in thé preceding lines; slight corrections are due to those effects.)

~Is~yo~s.–Thé minor planets which revolve between the orbits of Mars and Jupiter. Axis <?/ p/<x~<Thé imaginary line upon which thé planet rotates. Axis of an orbit.-The major-axis of the orbit of a planât is the apsidal line the minor-axis is a line at right angles to the former through its middle point.

Axis o/M?'e.–If the surface of a body may be supposed to be produced by the revolution of a plane curve about a straight line, the body is said to have a ~M~cc of revolution, and thé straight line is called the axis. q/~M?'e of thé body. Neglecting minor irregularities, thé planets are sucli bodies, the generating curve in each being an ellipse, and the minor axis of such ellipse the axis of figure.

Axis o/o~<o~Any straight line about which a body revolves in the same manner as it would if thé parts of the body were rigidiy connected with thé Hue, in called the axis of rotation of thé body. In the earth and planets the axis of rotation coincides with the axis of figure. ~4~M~Thé azimuth of a celestial body is the angle between two planes, one passing through the zénith and thé body, the other passing through thé zénith and thé north and south points of thé horizon. Azimuths are measured through 180°, and in general from the north or south point of the horizon according as thé north or south pole of thé heavens is elevated. Thé method of indicating the position of a celestial body by assigning its altitude and azimuth may be thus illustrated :-Suppose a telescope constructed so as to be moveable about a vertical axis and also about a horizontal axis at right angles to the axis of thé telescope let the telescope be directed in the first place towards the north point of thé horizon then thé telescope may be directed towards any celestial object by two movements–thé first about thé vertical axis, the second about the horizontal axis; thé first movement directs the telescope to the point clirectly below the object, and the angle through the telescope is swept is the same as the <m/~ of the object measured from the north point the second movement raises the telescope till thé object is in the field of view, and the angle through which the télescope is swept is thé same as the f{/(!<~ of the object. A telescope so mounted is called an a~M~6 and ~M~ MM~-M~ (The altitude alone is affected by tlie refraction of the atmosphere. Compare ~sc6M.9M~ ~)


J9e/<a.–A name applied to the faintly coloured streaks crossing the dises of Satum and Jupiter:

Circle of tlte celestial ~Ao'c.–A circle in which any plane meets the imaginary sphere caled the celestial sphere. Planes passing through the centre of this sphere meet its surface in ~ea< c~'c/es–as the ecliptic, pr~e ~e/ca~, ~e?'</MM, and the like planes not passing through the centre meet the sphere in ~e~/ circles; these are sometimes termed ~arcf~e/s. See jPa~'a~. Where the word circle is combined with another term, as declination, latitude, or the like, the circle referred to is a circle on which thé element mentioned is measured. Thus, a c~cZ!'7M<ïo?t-c~'c~ is a circle passing through the poles of the heavens, on which, therefore, declinations are measured.

<7o-M~Thé complement of the latitude, or the angle by which the latitude ialls short of 90°.

(7o~M?'e, ~Mï'Moc~<ï/A great circle passing through the poles and the equinoctial points.

(7o~M7'e, <S'o/s~'<!a~A great circle passing through the poles and the solstitial points.

Compression o f a ~~6<Thé amount by which the polar axis falls short of an equatorial diameter. It is generally expressed by the ratio it bears to an equatorial diameter :–thus, if the compression of a planet is said to be ~yth, wh~t is mcant is that the excess of an equatorial over the polar diameter is equal to -~yth part of an equatorial diameter. (7o~fM?'a~'o~Thé relative positions of stars or other celestial bodies. Conjunction.-Two bodies are said to be in conjonction upon the celestial sphere when they have the same longitude. When a planet is simply said to be in conjunction, it is to be understood that the planet is in conjunction with the sun. Since the planets are always near the ecliptic, a planet in eonjunction with the sun haa very nearly the same right ascension as thé sun. The symbol expressing conjunetion is d

Constellation.-A number of stars included within an imaginary figure for the sake of easier identification.

<7M~M?Mï~o~Thé passage of a heavenly body across the celestial meridian of a place.

Cycle.-A period within which a series of celestial phenomena recurs. (7ycZ6 of Eclipses.-See Saros.

D~c/<:oy:Thé angular distance of a celestial body from thé equator, measured along a great circle passing through thé body and thé pole of the equator. See JB: Ascension.

JD6cJ:'?M<oM-C!rc~See Circle.


.Dcc~'M<OM-p<xr~See Parallel.

2)~re6.–Where the sexagésimal division of the circle is employed, a degree of arc is the 360th part of the circumierence a degree of angle is the 360th part of four right angles the degree is divided into 60 minutes, the minute into 60 seconds, after which, in general, decimals are employed. In the centésimal division of the circle, a degree or grade is thé 400th part of the circunuerence, and is divided into 100 minutes, thé minutes into 100 seconds, and so on continually.

Descending Node.-See Node.

Diameter, Apparent. The angle subtended by the diameter of a heavenly body, viewed from thé earth.

Z)~c.–Thé visible surface of the sun, moon, or planets.

Eccentricity of an o?'&Thé distance of the centre of an elliptie orbit from either focus. It is generally expressed by the ratio it bears to the mean distance or semi-major axis of the orbit :–thus, when the eccentricity of an orbit is said to be O'OJ, what is meant is that the distance of the centre of the orbit from either focus is equal to T-o-th part of the semi-major axis of the orbit.

Eclipse.-The concealment of a celestial body in the shadow of another body, or by the interposition of another. In speaking of the satellites of Jupiter or Saturn, the term eclipse is confined to the former class, a concealment due to the latter cause being called an occM~a~OM. ~c~<c.–Thé great circle of thé heavens along which (approximately) thé sun's centre appears to move in the course of a year.

Ecliptic, Obliquity of ~e.–Thé angle between the planes of the equator and thé ecliptic; or, in other words, the complement of thé angle at which thé earth's axis is inclined to the plane of thé ecliptic.

Elements of an 07~:<Quantities whose determination defines the path of a celestial body in space.

Ellipse.-A closed curve produced by cutting a cone obliquely. If a cone be cut obliquely so that the resulting curve is open with one branch only, thé curve is aparabola; if the resulting curve is open and has two branches, the curve is an hyperbola. In the last case, the cone must be what is commonly called a ~OM~6 cone, but is strictly speaking understood by the term cone.

~o~a~'OM.–Thé angular distance of a planet from the sun, or of a satellite from its primary, viewed from thé earth.

jE~ocA.–Thé moment of time to which given numbers or quantities apply.

jE~Ma~'oM.–Any mimber or quantity that has to be applied to thé mean value of another number or quantity to obtain the true value.

R


~~or.–The equator of a planet is the circle in which a plane at right angles to the polar axis, and half-way between thé poles, intersects the surface of the planet. This plane is called the plane of the planet's equator. The term is, in général, confined to the equator of the earth, and the intersection of the plane of the earth's equator with the celestial sphere, is called the Celestial Equutor, and sometimes the Eq-uinoctial. Equatorial r~esc<?pe.–See Right ~sc<~SK~.

~or~~ ~?~o~ Solar P~The angle subtended by the earth's equatorial semi-diameter from the ~u when the earth is at her mean distance from the sun. From observations of the transits of Venus in the years 1761 and 17G9, this angle has been estimated at 8~o776. it appears probable that this value is too small, and therefore the sun distance determined from it too gréât. The best modern observers determine the angle at about 8"'9 the value assumed in the body of this work is 8"-9159 The problem of the sun's distance awaits a more satisfactory solution from observations of the transits of Venus in the years 1874 and 1882. See .P~'a~ac~'c 7~e~a~, AfooM's.

Equinoxes.-The points in which the equator of a planet intersects the plane of the planet's orbit about the sun. The term is generally confined to the intersection of the ecliptic and the plane of the earth's equator. For the northern hemisphere, the point at which the ecliptic passes to the north of the equator, is called the Vernal J~~ thé opposite point, where the ecliptic passes to the south of the equator, is called the < Equinox. For the southern hemisphere, these terms are interchanged.

Field of ~The part of thé celestial sphere visible at any instant in a telescope. The greater the magnifying power applied to a telescope, the smaller is the field of' view.

j~- of ellipse.-Two points on thé major axis of an ellipse equidistant from the centre, and whose distances from either extremity oi thé minor axis are equal to the semi-major axis of the ellipse. If two lines be drawn from thé foci of an ellipse to any point of the curve, the sum of their lengths is equal to thé major axis they are also equally inclined to thé tangent at that point.

G~~n-c.–As supposed to be seen from thé earth's centre. C~c~c Longitude and jM~See Longitude and Z~ 77~~c.As supposed to be seen from thé centre of the sun. 7~r~0ne half-(bounded by a gre.t circle) oi the surface of a sphère.


J~<)?'t'2'OM, ~yM~e.–Thé circle in which a tangent-plane to thé earth at any point meets the celestial sphere, is called the sensible ~or~o~ of that point.

~b~o~, 7~o~«/Thé circle in which a plane through thé eartli's centre, parallel to the plane of the sensible horizon of any point of thé earth's surface, meets thé celestial sphere, is called thé ?'a~'o~<x/ or true ~oy'~o~ of that point.

7~c~o~q/'a~o~Thé angle at which the plane of the orbit is inclined to the plane of the ecliptic.

T~e~Mo~y, Great, of 6'a<M/'M and ~M~~6?'A variation in thé orbital motions of these planets, caused by their mutual disturbing attractions. See Chapter VI.

T~e~Ma~, Parallactic, Moon's.-See Parallactic Ty~yM~~y, ~foo~'s. Inferior Planet.-A planet whose orbit lies within that of thé earth. Za~< 6'60MM<n'c, of a ~e~<M/y body.-The geocentric departure of the body from the ecliptic, measured along a great circle passing through the body and the poles of the ecliptic.

.Z< Geocentric, of a place on the gar~Thé ~~e angular distance of the place n'om the equator; or, in other words, the angle between the vertical at the place and the vertical at the nearest point ofthe equator. Latitude, (yeo~'ap/c~Thé angular distance of a place n'cm the equator, not corrected for thé oblateness of the earth's form; or, in other words, the angle between two lines supposed to be drawn to the place and to thé nearest point of the equator, from thé centre of the earth. Latitude, ~My/M'ce~n'c, of a place on /S'a~7'Thé true angular distance of a place from Saturn's equator.

Zï'~a~'o~ of the 3Yoo~An apparent oscillatory motion of thé moon, whereby we are enabled to see rather more than half the moon's surface. The moon's motion of rotation being uniform, but her orbital motion not so, two lunes ofthe moon's surface become visible to us in turn. The ends of these lunes lie on that diameter of the lunar dise which is at right angles to the direction of the moon's motion hence, their greatest breadths lie on the diameter which is in thé direction of the moon's motion. This is called the libration in longitude. Again, thé axis ofthe moon's rotation is notquite perpendicular to the plane of her orbit thus, two other lunes become visible by turns, whose extremities lie on that diameter of thé lunar dise which is in the direction ofthe moon's motion, so that their greatest breadths lie on the diameter at right angles to the former. This is called the libration in ~~MC/e. Thé spaces that become visible by thé two librations have parts in common; the fringe of thé moon's suri'ace, thus rendered visible, is

R 2


variable in breadth, being bounded hy parts of four gréât circles of thé inoon's surface.

Thé ~'M/c~ /i!<.< is a lésa important lihration, due to thé earth's rotation on her axis.

Z~e of ~Vo~6~See jVoc/e.?.

Longitude, <~eoce~<?'/c, of M Aga~e~ <!)o~Thé angular geocentric distance of the body from the first point of Aries, measured upon thé eclipdc in the order of the signs.

Zo~~M~, j~6~'oce~<7'tc, q/' et Aeaue/ &6)~Thé angular heliocentric distance of thé body irom the first point of Aries, measured upon thé ecliptic in the order of the signs.

Zo/~M~ ~eo.</?~~Azcf~, of <:< ~~c<?.–Thé angle between two planes through thé axis of the earth, one passing through the place and the other through a fixed station. Geographical longitude is measured through 180° east and west of the fixed station. The plane through the axis of' the earth and the place on the earth, intersects the earth's surface in an ellipse, winch is called the ~n'e.~n'<~ 7~e/<~ of the place.

Longitude of .P~e/i!Thé heliocentric longitude of thé perihelion of a planet's orbit. It is usually measured upon the ecliptic to the node, and thence along thé orbit forwards or backwards, as the case requires; the sum or difference, respectively, of thé arcs on the ecliptic and orbit, being taken as the longitudeof thé perihelion. Amoresatisfactorymethodwould be to assign the heliocentric longitude and latitude of the perihelion-point. ZM7ï.a~'o~Sce /S'?/M.o~'ca/ J~

Lune.-Part of the surface of a sphere intercepted between two great circles also a plane surface bounded by two circular arcs whose concavities are turned in thé same direction.

.~f<x/or axis f?/ or~See Axis q/'a/t o)'&!<.

3fea?~ c7~MC6.–Thé mean between the greatest and least distances of a planet from thé sun, or of a satellite from its primary. The mean distance is therefore equal to half thé major axis of an orbit. The extremities of thé minor axis of an orbit are at thé mean distance from thé ~bcus. It may be remarked that the true average distance of a planet or satellite from thé foeus of its orbit, is somewhat greater than the semi-major axis of thé orbit.

~6<M~, ~6~A dinused œthereal matter supposed to occupy thé inter-planetary and interstellar spaces, resisting thé motions of ail bodies, and perceptibly modiiying the motions of such bodies as cornets. The same medi-um is supposed to occupy the spaces between the atoms composing solid bodies, passing as freely through the densest solid, as thé air


through a grove oftrees.' It is in this médium orœtherthat the vibrations of ligbt, heat, and electricity, are supposed to be propagated. ~er!<M, Celestial, o f o~ace.–TIte gréât cirele of thé heavens passing througli thé zenith and the poles. Thé 7~ a/~M~e of a celestial body is its altitude when crossing the meridian, or at thé moment of ~e~< transit.

~y' yey'r6&See Longitude, Geographical.

~6~or!'c ~o~M or ~c~o/Cosmical bodies which traverse thé upper régions of thé atmosphere or iall upon thé surface of thé ea)-th, commonly called ~oo~'y~ s~.ys,/<x~?~ s~s, orj~?'6-&6'. Ithas beeu noticed that on certain days in thé year, thèse meteors appear in greater numbers than on others, occasionaUy 'falling in showers on these days. For an account of thèse periodic showers the reader is referred to Humboldt's Cosmos. The theory now generally accepted in explanation of these phenomena is that suggested by Chiadni, that:-Vast numbers ofsmaU masses of solid matter are dispersed through the interplanetary spaces; they travel in irregular orhits under thé influences of their mutual attractions and thé attractions of the sun and planets; and when they approach a planet of powerfui gravitation, they are attracted towards it, and may fall upon its suriace. Thé modern science of thermo-dynamics explains tlie brilliancy of these meteoric stones, and the fact that, in general, they are dissipated into vapour in passing through the earth's atrnosphere. These effects are due to thé intense heat generated as tlie vis viva of a swiftly travelling meteoric body is destroyed by the resistance of thé air. j!~7~/ B~y.–Thé nebula of which our sun is a member it may be traced as an irregular luminous band extending completely round the heavens, aud divided into two parts through a great portion of its length, It is probably similar in form to the great spiral nebulœ. The irregular nebulte 'which lie near its borders–as thé nehula in Orion, and thé nebulœ in Argo-are, in ail probability, distant outlying wisps of the Milky Way. The Magellanic Clouds may be connected with thé Milky Wav in a dînèrent manner:The spiral nebulae n'equently exhibit amid their convolutions vast globular condensations and it is conceivable that thé Magellanic Clouds arc such star-clusters connected with thé Milky Way by starstreams too distant to be visible. Thé conformation of thé gréât nebula. in Andromeda, which is probably a spiral nebula seen from the side, seems to indicate that thé whoris of spiral nebulœ may be separated by wide intervals from the mean plane of thé spiral, a circumstance that would explain the distance at which the Magellanic Clonds are found from thé borders of thé Milky Way.

~7K)r axis of <?r&See .4x'/R o/' «~ orbit,


Month, .HO~o~zc.–Thé period of the moon's revolution from perigee to périgée of her orbit.

Month, Nodical.-The period of the moon's passage from ascending to ascending, or from descending to descending node of her orbit. Month, A$'~er6~Thé period in which the moon passes through the twelve signs of the Zodiac.

Month, 6'~?~r/c<ï/Thé common ZM~a/~bfb~ orLunation:-viz., thé period in which the moon goes through ail her phases, as from new to new, or from full to full.

J~o~'oM, Direct, of a planet.-The apparent motion of a planet in the order of the signs.

Motion, jPy'o~r, of a star.-The apparent motion of a star due to the star's real motion in space.

j~/b~'o~, Relative.-The change of position ot' one body with respect to another, when one or both are in motion.

Motion, Retrograde, of a planet.-The apparent motion of a planet contrary to the order of the signs.

~M.Thé point of the celestial sphere vertically below the observer. jV~M/a.–A collection of stars so closely congregated through effect of distance as to appear in ordinary telescopes as a cloudlike spot. ~&M~' Theory, .06~c/s.–A theory advanced by the elder Herschel, that certain classes of nebulœ consist of true nebulons matter, self-luminous, and spread in the manner of a cloud or fog through extensive regions of space.' Modem discoveries do not favour this supposition. It appears probable thàt, with sufficient teleacopic power, ail nebulœ would be resolvable into stars. Herschel considered the irresolvability of the great nebula in Orion (see ~y 1~2~) a strong argument in favour of his hypothesis. Since Herschel's time, this nebula bas been resolved by the Parsonstown renector, and by the Harvard réfracter. Herschel's hypothesis is frequently confounded with Laplace's Nebular Theory. Laplace drew an illustration of his theory, or rather of a part (probably erroneous) of his theory, from the views of Herschel but, beyond this, the two theories are in no way connected.

Nebular Theory, Laplace's.-See Note B, Appendix I.

Node.-The points of intersection of any great circle on the celestial sphère with any other, are called the nodes of the former circle upon the latter the point at which the former passes from north to south of the latter is called the ascending y:<?<~e,–its sign is 8 the opposite point is called the desrending M<its sign is ~3 and the line joining the two nodes is called the line 0/~0~.5 or the nodal line. The ecliptic is usually thé circle of reference so that, uniess the contrary is expressed, thc


~ce7!C~/ node of a planet's orbit signifies the point at which thé planet passes froin the southern Lo thé northern side of the ecliptic. Oblate j~ero!Thé solid figure generated by Hie revolution of un ellipse about its minor axis. If thé ellipse revolve about its major axis, thé figure generated is a pro~~e ~Agro~.

0&~M! of the ec/c.–Thé inclination of the plane of the ecliptic to thé plane of the equator.

OccM~o~See Eclipse.

Opposition.-T wo heavenly bodies are said to be in opposition when their longitudes differ by 180°. See C'o~MMC~'o~ similar remarks apply in thc case of opposition. The symbol expressing opposition is < <9?'&Thé path of a planet or cornet about the sun, or of a satellite about its primary.

Parallactic 7Me~M«/ J~oo~'s.–An inequality in tlie moon's motion,of sonie interest, as it has been applied to the determination of the sun's distance. If we suppose that s (fig. 5, plate X.) represents the earth, p~p;~p3P~ the moon's orbit, and Q~ thé sun, then thé investigation of p's motion about s (Q at reat) in pp. 134-140 would suffice to explain the inequality in the moon's motion known as the MMO~'s variation. Now ifQ~s be very great compared with s P2, thé ratio Q,?~ (~s is ~er~ ~e~y equal to thé ratio Q}S: QiP~, but not quite; hence arises a small inequality in the effets of the moon's variation this inequality is called the moon's parallactic inequality. It never anects the moon's longitude by more than 2', and its period is that of a lunar synodical revolution.

jPara~aa;An apparent change in the position of an object, caused by a change in the position of the observer.

.Parallel.-A term sometimes applied to small circles of the celestial sphere, or of the earth's globe. The word parallel is used in combination with another terni, as Declination, Latitude, or the like; and the small circle referred to is a circle for ail points of which the element mentioned is constant. Thus, a Declination-parallel is a circle every point of which bas thé same declination, or is equi-distant from the poles of the celestial equator. Hence the plane of a Declination-parallel is parallel to the plane of thé equator.

.P~t'o~That point in the orbit of a planet or cornet which is nearest to the sun.

Period, or Pe-riodic Time.-See Revolution.

~'6?'~a~rMï'M~Thé point in a satellite's orbit nearest to Satum. Perturbations.-Variations of the motion of a hearenly body from the elliptic path it would describe about a central body, if undisturbed hy thé attractions of the other celestial bodies.


Phase.-The appearance at any moment of a celestial body s~bject to periodie changes of appearance.

P~M6~, ~'Mo?'See Asteroids.

Planets, jPy'y'y.–Thé planets which revolve about the sun as centre. Planets, *S'eco~<r~Thé satellites which revolve about some of thé primary planets.

Pole of a ~'ea< c~'rc/e on ~Ae celestial ~Aë7'6.–Thé points in which a straight line through the centre ofthe circle, and at right angles to its plane, meets the celestial sphere.

Precession of the .E'o.re.?.–A slow rétrograde motion of the equinoctial points upon the ecliptic.

JPn'~6 Ve?'<ca~See Ver~'ca~, ~nwe.

Q?/a~ra~Mre.–Two celestial bodies are said to be in quadrature when their longitudes differ by 90°.–See Co~M~c~/t and 0/?~os~o~Thé symbol expressing Quadrature is Q.

Radius Fec~An imaginary,line supposed to be drawn from a body to its centre of motion, and to accompany the body in its revolution about that centre.

Reflecting Telescope.-A telescope in which images ofobjects, ibrmed by reflection in a polished mirror, are magnified by a lens or by a combination of lenses.

jR6/rac<~ Tele8cope.-A telescope in which images of objects, -formed by refraction through an object-glass, are magnified by a lens or by a combination of lenses.

.Refraction.-A property by which rays of light are bent in passing through transparent media, or rather, by which thé wa.ve-ironts of light are made to travel in a new direction.

~6/?'<xc< ~o~pAer/c.–Reiraction of light by the atmosphere, Atmospheric refraction bas the effect of making ail bodies appear higher above the horizon than they really are ;-near the horizon, by upwards of 33~ thence by an angle whicb at first diminishes ra.pidiy, afterwards more slowly, till at the zenith it vanishes.

JP~ro~r~~o~jR6<r~r~See ~c, and J/o~'o~.

Revolution, Time of.-The period in which a body completes the circuit cf its orbit about a centre. It is synonymous with the terms p~0~, p6r!o~c <?'7~e. For the different intervals of revolution in the case of the planets, see J.?K)~a~'c, Sidereal, ~y/?o~ca~ and ~'o~z'c< ~6~o/M<oM. To these the Noclical Revolution may be added it is the interval of passage from ascending to ascending, or from descending to descending node of the orbit; it will vary slightiy with thé node chosen as thé starting-point,


owing to the variations of planetary motions. For the lunar revolutions, see~oM~A.

Right J.sc~o~See Ascension,

7?o~o/ï.–See Axis o/'J~o~o~.

~'os.–A Chaldœan period, now known as thé cycle of ëc~'p~ It contains 228 lunations, or i-ather more than 6585 days; in wbich period there are 238-992 anomalistic, 241-029 sidereal, and 241-999 nodical months.

/S'<x<6~~e.–A moon attending on a primary planet.

~erea~ J?euo~o~Thé interval between thé successive returns of a planet to the same heliocentric position among thé fixed stars; or the period in which a planet, viewed heliocentrically, would appear to traverse the twelve signs of the Zodiac. The sidereal revolution of a planet is subject to slight variations, owing to thé perturbing attractions of thé other planets. The average value of many successive révolutions is called the sidereal revolution of the planet, and is its ~e period. q/< Zo~ïac.–Thé twelve divisions of the Zodiac. Each division contains 30°. The names and symbols of the signs are as follows:-

Spring signs. Stunmer signs. Autumn signs. Winter signs. ~t~CN T 6'aHCC?' °B Libra C'Ctp~COT'MtM. W y~r~ H Zeo ~eorpM Aquarius.. K~ 6~MMZ n Virgo T~ <S'rM~. -PMCM. X

Thé Zodiacal constellations are each removed one sign from the sign whose name they bear. Thus the constellation J.~Mar!'MS falls on the sign Pisces, the constellation Pisces on the sign ~.n'65, and so on. ~o~<!CM.–Thé points of the ecliptic which are at thé greatest distance north and south of thé equator. The former point is called the Winter Solstice, the latter the ~M7M~~r Solstice. When the sun is passing these points his daily change of declination is small, so that he appears for several days together to ibUow thé same diurnal path.

~OM~'y~Thé meridian transit of a celestial body is called thé southing of thé body, if such transit takes place on the visible southem quadrant of the celestial meridian. See 7~'6~ï'aM.

~p/~yo!See Oblate ~Aey'O!

~~<!0~a~ Points.-The points of a planet's apparent path on the celestial sphère, at -which progressive merges into retrograde, or rétrograde into progressive motion.

~M~erMr .P~?!e<A planet whose orbit lies outside that of thé earth. ~~o~'c~ Period, or~ë~o/M~'o~Theperiod which elapses between successive conjunctions or successive oppositions of a superior planet or between successive conjunctions of the same Idnd, of an inferior planet.


Telescopic Objects.-Objects not visible to thé naked eye.

~-a7M~See JM'e/t, Celestial, o/c6.

~'?'~M.s~ of a ~a<e~!7e.–Thé passage of a satellite across the dise of its primary. The passage of the shadow of a satellite across the dise is called a transit of ~e shadow,

~op~c~ J?euo/<o?<Thé revolution of a planet refeiTed to the nodes of the plane of its equator upon the plane of its orbit. Thus a tropical revolution of the earth is the interval between successive passages of either equinox or of either solstice. The length of a tropical revolution varies with the point from which it is supposed to commence for the precession of the equinoxes carries them forward in each sidereal year by a quantity very nearly uniform, whereas the motion cf the earth is variable in digèrent parts of its orbit. Thus, if the vernal or autumnal equinox is the commencement of a tropical year, the period bas very nearly its mean value, since the earth at the equinoxes is very nearly at its mean distance from thé sun but the period estimated from the vernal is rather greater than the period estimated from the autumnal equinox, the motion of the earth being rather more rapid near the vernal than near the autumnal equinox, so that the sidereal year is diminished by a smaller quantity in the former than in the latter case. Thé ?M6<~ ~oy/c~ revolution of the earth, or the mean tropical y MM', is equal to the sidereal year diminished by the interval in which the earth would move with her mean velocity over an arc equal to thé annual precession of thé equinoxes. An application of the same principles in the case of Saturn will be found under the explanation of Table X.

Vertical C~c~s.–Circles passing through the zenith and nadir of the celestial sphere.

Vertical, jPyw~Thé vertical circle through the east and west points of the horizon.

Vis Viva.-The vis viva of a particle is the product of its mass into the square of its velocity. The vis viva of a system is the sum of the vires of the particles composing the system. It is sometimes stated that the vis viva of a system free from external influences is constant. This is not exactly true, as will appear from a simple illustration :-Let two perfectly cold bodies be supposed to start from rest under the influence of their mutual attractions only they will approach with constantly increasing velocity and thus the system, which at first had no vis viva, gradually acquires a larger and larger amount of vis viva till the bodies impinge, when more or less of the acquired vis viva will take the form of ~6~ Since the true living' ~brce of a system (as distinguished irom the technical vis v~) can never be diminished or increased save A'om external


sonrces, it may be asked, What was the form in whieh this acquired vis viva, or ita equivalent heat, originally appeared in the system ?' Though the attraction of gravity between the two masses plainly operated to generate the vis viva acquired by the System, yet that attraction alone would not have produced such effect since, if the two bodies had been originally in contact, the attraction of gravity would have aubsisted between them, yet no vis viva would have accrued. The element of distance plainly has to be considered and the answer to the above question ia, that thé work <~o~ in removing the two bodies from contact to the given distance is thé "living force of the system.' This living force may be variously distributed in vis viva and change o/ distance or again may appear in the form of heat, which is merely the distribution of vis viva and change of ~!s~<c6 among the molecules of the two bodies but whatever forms the living force of the system may assume, it can never be diminished or increased but by the operation of extemal influences. Thé same is true of ail systems, however varied or complex the relations they may present.

Year, ~M(WM~c.–Thé period of the anomalistic revolution of the earth about the sun. See ~Tïo~s~'c Revolution.

Yeur, ~e7'6a/Thé period of the sidereal revolution of the earth about the sun. See Sidereal Ti'e~o~'o~.

year, Tropical.-The period of the tropical revolution of the earth about the sun. See Tropical Revolution.

~?M~Thé point vertically above the observer's head or, in other words, thé pole of the horizon.

Zenith Distance.-The complément of the altitude of a heavenly body or, in other words, the angular distance of a heavenly body from the zenith. Zodiac.-A belt of the heavens extending 9° on each side of thé ecliptie. Within this l~eit the sun, ail the primary planets, and by far the larger number of the asteroids perform their revolutions.

Zodiacal Light.-A light in the form of a long triangle, observed In spring above thé western horizon after sunset, and in autumn above the eastern horizon before sunrise. The light extends obliquely upwards (the base of the triangle being towards the horizon) to a distance from the sun's place varying from 40° to 100°. The breadth of this meteor at its base varies from 7° to about 40°. It probably consists of flights of small disconnected cosmical bodies travelling about thé sun, as the satellites composing Saturn's ring travel about Satum. The bodies composing the parts of this meteor nearest to thé sun must travel with tremendous velocity, and as the vis viva of the system, and especially of its interior zones,


gradually diminishes through the effects of collisions, Higbtaof these bodies, becoming entangled in the solar atmosphere, must be dissipated into vapour through the effects of intense heat, and spreading over vast areas of the solar surface generate the light and heat distributed by the sun to the worlds thut revolve around him.

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ANCIENT HISTORICAL EPOCHS.

Now in course of publication, uniform with Epocns of MoDERN HISTORY, each volume complete in itself,

EPO'CHS OF ANCIENT HISTORY: Series of Books Narrating the History of Greece and Rome and of their Relations fo other Countries at Successive Epochs.

Edited by the Re~ GEORGE W. COX, M.A. late Scholar of Trin. Coll. Oxford; andjointly by CHARLES SANJKEY, M.A. late Scholar of Q.ueen's Coll. Oxford.

Thé special purpose for which these manuals are intended, they will we should think, a.dmir.~ly serve. Their clearness as narratives will make them acceptable to the schoolboy as well as to the teacher; and their critical acumen will commend them to the use of the more adTancod studeut who is not only getting up, but trying to understand and appreciate, his HERODOT~a and TnucYDiDBS. As for thé general plan of the séries of -which they form paît, we must confess, without vishing to draw comparisons for which 'we should be sorry to

hâve to examine a.11 the materiale, that it strikes us as decidedly eensible. For thé beginner, at ail events, the most instructive, as it is thé eaaiest and most natural, way of studying history is to study it by periods and with regard to earlier Greek and Roman history at ail events, there is no serious obstacle in the way of bis being enabled to do so, since here period and what bas corne, to be quasi technically called subject frequently coincide, and form what may ftlirly be called a.n Epoch of Ancient History.' SAT~RDAY BEViNV.

The GRACCHI, MARIUS, and SULLA. By A. H. Beesly, M.A. AssistantMaster, Marlborough CoUege. With 2 Maps. Fcp. 8ïo. price 2a. 6d.

The EARLY ROMAN EMPIRE. From the Assassination of Julius Cssar ~theAB~tioa of Domiti~. By the Rev.W.WbLFE OApES,M.A.Re.derof Ancicnt History in the University of (Mord. With 2 Coloured Maps. Fcp. 8yo. priée 2~. 6d. The ROMAN EMPIRE of the SECOND CENTURY, or the AGE of the ANTONINES By thé Rev. W. WoLFE CAPES, M.A. Render of Ancient History in thé Univer. sity of Oxford. With 2 Coloured M&pa. Fcp. 8vo. price 2~.M.

The GREEKS and the PERSIANS. By the Rev. G, W.Cox,M.A.late Scholar of Trinity CoUege, Oxford; Joint-Editor of thé Series. With 4 Colourod Maps. Fcp. 8vo. price 2~. 6<f.

The ATHENIAN EMPIRE from thé FLIGHT of XERXES to the FALL of ATHENS. By the Re-v. &. W. Cox, MJL late Scholar of Trinity College, Oxford JointEditor of the Series. WithSMape. Fcp.8yo.price2t.6ft.

The RISE of the MACEDONIAN EMPIRE. By Arthur M. Curteis, M.1. formerly Fellow of Trinity Coî!ege, Oxford, ànd late AssistMit.Maater in Sherhome School. With 8 Maps. Fcp. 8vo. price 2s. 6~.

ROME to its CAPTURE by the GAULS. By Wilhelm Ihne, Anthor of History of Rome.' With a Coloured Map. Fcp. 8TO. price 2<. 6d.

The ROMAN TRI~MVIRATES. By the Tery Rev. Charles Merivale, D.D. Dea~ofNy; Aathorof History of the Romans under the Empire.' With a Coloured Map. Fcp. 8vo. price 2<. M.

The SPARTAN and'THEBANS?PRI;MAC~S.By Charles~ M.A. Joint-Editor of the Seriez A~tant-M~ter, Marlborough College. With5Map.andFIaM. Fcp.8vo.price2t.6J.

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INDEX.


~/&t Handbook ofTelegraphy. i~ Curteis's Macedonian Empire Z)'~M3<~w~ Reformation 18 De Caisne and Le Maout's Botany 13 De y~f!j Democracy in America. 5 Dobson on the Ox. 23 Z)~~ Law of Storms 10 Dowells History of Taxes 6 Z)oy~(R.) Fairyland. 14 Z?~*«~~<?~JjewishMessiah 17 Eastlake's Hints on Household Taste i~ .Ë~M/a~t Rambles among the Dolomites 20 Nite. ic) Year in Western France 19

Elements of Botany. 13 ~<-o~Commentaryon Ephesians 17 Galatians 17

–Thessalonians 17

Elsa, a Tale of the Tyrolean Alps 2t Epochs of Ancient History. Modem History 4.

JTt/aM/ (J.) Ancient Stone Implements 13 A. J.)Bosnia 19

~M/a/~J History of Israel 18

Antiquitiesof Israël. 18 ~M~a~'j s Application of Cast and Wrought Iron to Building. 16

Farrar's Chapters on Language 8 Familles of Speech 8 /<9M'Jjudicial System 2~ Fitzwygram on Horses and Stables. 22 ~?~j'j Two Years in Fiji. 19 Frampton's (Bishop) L ife Francis's Fishing Book 22 /r~/f<M'.yIta)ianA!ps 19 Froude's English in Ireland 2 –History of England 2 –Short Studies. 7 Gairdner's Houses of Lancaster and York 4 Ganot's Elementary Physics i c –NaturalPhiIosophy i i Gardiner's Buckingham and Charles 2 Personal Government of Charles I. 2 –FirstTwoStuarts Thirty Years' War 4 G~fChurchandState 6 German Home Life. 8 <?~7~~ &~ Churchill's Dolomites 20 Girdlcstone's Bible Synonyms. 17 Goldziher's Hebrew Mythology. 17 Goodeve's Mechanics. 12 Mechanism 12 Gra~jEthicsofAristotle. 6 Graver Thoughts of a Country Parson. 8 Greville's Journal. 2 Gr~j Algebra and Trigonometry. 12 G~/A'J Behind the Veil. 18 <?n~M~y Tyrol and the Tyrolese 19

PAGE

Pastoral Epist. 17

Philippians, &c. 17

Lectures on Life of Christ 17

Information for Engineers. 16

–Life

PAGK

Grove's Corrélation of Physical Forces. n (~'CM (F. C.) The Frosty Caucasus 19 <w/ Encyclopaedia of Architecture. 15 ~x/~FaUof the Stuarts. llartley on the Air 10 //<ïy/w/~AerialWor!d. 12 Polar World 12

Sea and its Living Wonders ie Subterranean Wor!d. 13

Tropical World 12

Haughton's Animal Mechanics i ic Hayward's Biographical and Critical Essays 5 ~'<'r'~ Primeval World of Switzerland. 13 Heine's Life and Works, by Stigand Helmholtz on Tone n Helmholtz's Scientific Lectures. n .r~fTreesandShrubs 13 ~jc~jOutlinesofAstronomy. 10 ~y/yj Over the Sea and Far Away 19 ~/<?~<7M'~ Amateur Mechanic 15 ~o~c/j' Engineer's Valuing Assistant 15 -~<?M/cy/A'~ Mongols. 3 ~a~ History of Modern Music 13 Transition Period 13 .Essays y Treatise on Human Nature. 7 7~< Rome to its Capture. History of Rome 3 Indian Alps 19 7.cw'jPoems 21 y~o~'j Legends of the Saints & Martyrs 15 Legends of the Madonna. 15 Legends of the Monastic Orders 15

Legends of thé Saviour.15

y<7!fEIectricity and Magnetism. 12 y<c/jLifeof Napoleon 2 %y/o~'jGeographicalDictionary. 9 yo~.f~f (Ben) Every Man in his Humour 7 y~j Types of Genesis 18 –on Second Death 18 Kalisch's Commentary on the Bible 17 .A~j Evidence of Prophecy 17 jA~"r/ Metallurgy, by Cr~~andA'M~. 16 ~i:jAtkaHTrade l~ Animal Chemistry 14 Kirby and Spence's Entomology 12 ~i'MM'jPhiIosophy 6 ~«z/c~K/<~j~ Whispers from Fairy-Land 20

HiggIedy-PiggIedy 20

~< Prophets and Prophecy in Israël 17 Landscapes, Churches, &c. 8 Latham's English Dictionaries 8 Handbook of English Language 8

Lawrence's Early Hanoverians 4Z~~y'j History of European Mora)s. 3 Rationalism 3

Leaders of Public Opinion. 5 Z<?/j Bermudas .19 Leisure Hours in Town 8 Lessons of Middle Age 8


Lewes's Biographical History of Philosophy 3 Lewis on Authority. 7 Z.and~c/jGreek-Eng!ishLexicons 9 Lindley and Moore's Treasury of Botany 23 Lloyd's Magnetism 11 Wave-Theory of Light iï London Series ofEngIishCIassics. 7 .~M~M/t'-f (F. W.) Chess Openings. 24 Frederick the Grcat 4

–(W.) Edward. the Third. 2 Lectures on History of

Z.<'M<j Encyclopasdia. of Agriculture 16 –Gardening. 16

Lubbock's Origin of Civilisation 13 Z.M~/cM'.fAmerican War. 4. Lyra Germanica iK A~<z~/fZ/'j (Lord) Oive.by~w~ 7 –Essays i History ofEngiand i

Ji/cCM/~A'~ Dictionary of Commerce 9 .J~c/M on Musical Harmony 15 ~/ac/ Economical Philosophy. 6 Theory and Practice of Banking 24

Eléments of Banking. 24 Mademoiselle Mori. 21 J~/c/AnnalsoftheRoad 22 J~~M/j Mission ofthe Holy Spirit 18 A/cz~f Doctor Faustus, by H~r 7 ~~zyj~<7/j Physiology. 14 J~z~Ay/M~'jLifeofHaveIock 5 .<MM'.f Christian Life. 19 Hours of Thought. 19

Jl~TM~jBiographicaITreasury 23 –GeographicalTreasury 23

–Treasury ofKnowledge. 23

/z~M/c/j Theory ofHeat. 12 May's History of Democracy. 2 –History of England 2 A~f~<'jDigby Grand 21 General Bounce 21

–Gladiators 2E Good for Nothing 21

Holmby House 21

–Interpréter 21

–KateCoventry 21

Queen's Maries 21

Memorials of Charlotte H-~7/Mj- 4. ~~c~~joAM'~ Letters 5 .z/<f Fa!l of the Roman Republic 3 General History of Rome 3

A/<r//?<Arithmeticand Mensuration. 12

PAGE

German Dictionary 9

England 2

Old and New St. Paul's 15 5

–Plants. 13

Lays of Ancient Rome i~, 21

Life and Letters. 4

Miscellaneous Writings 7

–Speeches. 7

–Works i

Writings, Sélections from 7

Hymns. ï8

Historical Treasury 23

Scientific and Literary Treasury 23

Treasury of Natural History 23

Roman Triumvirates. 4. Romans under the Empire 3

PAGE

~fj on Horse's Foot and Horse Shoeing 23 on Horse's Teeth and Stables. 23 ~(T.)ontheMind. 6 issertations & Discussions. 6 Essays on Religion. 17 ––HamUtort'sPhiIosophy 6 (J. S.)Liberty 5 Political Economy 5

Representative Government 5

System ofLogic 6 –UnsettIedQuestions 5 Utiiita-rianism 5 Autobiography. 5 ~<j Elements of Chemistry 14. Inorganic Chemistry. 12 ~7< Manual of Assaying 16 ~c/j'Lycidas,by~M 21 Paradise Regained, by ~<xw 7 Modern Novelist's Library 21 Monsell's Spiritual Songs. 18 .<~w~f Irish Mélodies, Illustrated Edition 14 –LaDa Rookh, Illustrated Edition.. i~ ~b.r<j Mental Philosophy 6 ~/c~'<c/< on Horsebreaking 22 7!~?~<?~'jLife,by A~ 4 .j Chips from a German Workshop. 8 Science of Language 8 Science of Religion 3

.A~fM on the Moon. 10 JV~j' Horses and Riding 22 NewTestament, Illustrated Edition. 15 ~V/<rc~'j Puzzle of Life 13 A~jLathcs&Turning 15 O'Conor'sCommentary on Hebrews 18 -Romans 18

–St. John 18

O~c~'f Islam. 3 Owen's Evenings wirh the Skeptics. 7 (Prof.) Comparative Anatomy and Physio]ogyofVertebrateAnima!s 12

y~c~'j Guide to the Pyrenees 20 ~j Origines Romanne 21 Reges et Heroes. 21 ~jc~'j Casaubon. 5 ~<jlndustrial Chemistry. 15 ~~w~jComprehensiveSpeciner 24 7-<r<fChess Problems 24. j~Gameof Whist. 23 7-'<?~<j Select Poems.by~c/ 7 Powell'.f Early Engfand 20 & ~M/TeIegraphy. 12 Present-Day Thoughts. 8 ~c/jAstroaomicatEssays 10 Moon. 10

–OrbsaroundUs 10

Other Worlds than Ours 10

–Saturn 10

Scientinc Essays (Two Séries) 12 Sun 10

Transits of Venus 10 T\vo Star Atiases. 10 Universe 10

~'c/û'jDeMontfort 2 Public Schools Atlas of Ancient Geography 9 Atlas of Modem Geography 9


.~M/K~y Parthia. g –Sassanians g Recreations of a Country Parson. 8 ~?M~<M~rDictionaryofArtists i~ Reeve's Residence in Vienna and Berlin 19 ~~7~'jMapof Mont Blanc 20 –Monte Rosa. 20

Memojrs ~~tz~~fo~'jDowntheRoad 22 ~jDictionaryofAntiquities 9 .MWf' Rose Amateur's Guide. 13 .~Wf'j Eclipse of Faith. 17 Defence of Eclipse of Faith 17 Essays. ~?<y~'j Thesaurus of English Words and Phrases 8 ~MZaf'-f Fly-Fisher's Entomology 22 Roscoe's Outlines of Civil Procedure. 6 ~t'c~~z'j' Israelites 18 Rowley's Rise of the People 20 Settlement of thé Constitution 20 ~~<z~'jjustinian's Institutes 6 ~cM~SpartaandThebes 4 Savile on Apparitions. 8 -on Primitive Faith 17 Schellen's Spectrum Analysis 10 &ro~y Lectures on the Fine Arts i.). –Poems j.). Seaside Musing. 8 <S'~<?~t'.y Oxford Reformers of 1:~8. 3 Protestant Revolution ~'<w<Historyof France. 2 Passing Thoughts on Religion 18 Preparation for Communion 18 Questions of the Day 18 SeIf-Examination for Confirmation 18 -Stories and Tales 21 –Thoughts for the Age 18 Shelley's Workshop Appliances 12 Short's Church History 3 .?~M7A'.r (~) Essays 7 Wit and Wisdom 7

-(Dr.R.A.)AirandRaiti 10 '(R. B.) Rome and Carthage 4 ~OM~<:y'~ s Poetical Works. 21 ~a~/cy'~ HistoryofBritish Birds 13 .S'j Ecclesiastical Biography. ~M~<M~ on theDog. 22 'ontheGreyhound 23 Stoney on Strains. 16 Stubbs's Early Plantagenets 4 Empire under thé House of

Hohenstaufen Sunday Afternoons, by A. K. H.B. 8 Supematural Religion 18 Swinbourne's Picture Logic 6 7~ England during the Wars,

1778-1820 20 T~Zcr'~HistoryofIndîa. 2 –Ancient and Modern History 4 .(y<?~) Works, edited by-&~ 18 Text-Bobksof Science. 12

PAGE

fAGE L' t' "i

7%<?~j Botany 12 j T~cwj~'jLawsofThought. 7 Thorpe's Quantitative Analysis 12 .1 ?~~ and A~~r'j Qua.Uta.tive Analysis 12 T~M'jChemical Philosophy 12, 14 Todd on Parliamentary Government. 2 TV~j Realities of Irish Life 8 Trollope's Barchester Towers. 21 -Wajden 21 Twiss's Law of Nations 6 7~o!jAmerican Lectures on Light JT –Diamagnetism. jt i

–Fragments of Science. M –Heat a Mode of Motion n Lectures on Electricity jt

–Lectures on Light. it Lectures on Sound. ji

–Lessonsin Electricity ji –Moleculaj Physics. 11

Unawares aj: ~r Machine Design 12 6~-t'y Dictionary of Arts, Manufactures, and Mines 16~f Trident, Crescent, and Cross. iS ~z/~ron Whist 23 H-~z~/ë'~Historyof England i

P~j Edward thé Third <).

t~~fc~Geometry. jz vVatts's Dictionary of Chemistry i~. t'j Objects for Common Telescopes xo M~z'y Experimental Physics. ~i Wellington's Life, by C' 5 M~a~jEngIish Synonymes 8 –Logic 6

–Rhetoric 6

M~j Four Gospels in Greek. i& and ~j Latin Dictionaries 9 M~~Mw/AMeasunng Machine (The) 15 PP~j'jSea-Fisherman 22 M~7/MMf'jAristot!e'sEthics. 6 P!jPopu!arTabIes 24 P!~?~'j(J. G.) Bible Animas J2 –Homes withoutHands 12

Insects at Home ir2

-InsectsAbroad. 12

–OutofDoors 12

–StrangeDwellings 12

–(J.T.)Ephesus 19 Woodward's Geology 13 vVyatt's History of Prussia 2 yi?~<Engush-GreeJ<Lexicons p Horace. sr Youatt on the Dog 22 on the Horse 22 Zellers Plato. 3 –Socrates 3 Stoics, Epicureans, and Sceptics. 3 Z~M~jLessing Schopenhauer


MODERN HISTORICAL EPOCHS. In co~se q/ j3~c~ each ~o~~ 8vo. co~Ze~ ~~Z/' EPOCHS 0F MODERN HISTORY A SERIES OF BOOKS NARBATING THE

HISTORY of ENGLAND and EUROPE

At SUCCESSIVE EPOCHS SUBSEQUENT to thé CHRISTIAN ERA. BMTEDBY

E. E. MORRIS, M.A. Lincoln Coll. Oxford.

J. S. PHILLPOTTS, B.C.L. New Coll. Oxford' ~d C. COLBECK, M.A. Fellow of Trin. Coll. Cambridge.

'This striking collection of little volumes is a valuable contribution to the literature of the day, -whether for youthful or more mature readers. As an abridgmeat of several important phases of modern history it haa great merit, and some of its parts display powers and qualitiesof a high order. Sueh writers, indeed, as Professor STUBBS. césars, WARBURTON, GAIRDNEB,

CREiGHTON, and others, could not fail to g.ve us excellent work. The style of thé séries is, as a gênera! rute, correct and pure, m the case of. Mr. STUDIiS it moro than once rises into genuine, simple, and manly éloquence and thé composition of soma of the volumes displays no ordmaryhistoriealskm.TheSeriesis and deserves to bo popular.' THE TtMEs

'l'he BEGINNING of the MIDDLE AGES Charles the Great an d Alfred

"E~ that of Europe in the Ninth Century, By the Very

Bey. R. W. Cn1T.RCH, M.A. &c. Dean of St. Paul's. With 8 Coloured Maps. l}ricc 2s. Gd.

late Scholarof Trinity

College, Oxford; Author of the' 1 Aryan -Mythology' &c. With a Coloured Map. puice 2$. Gd.

CR~1G$TON, M.A. late

Fellow and Tutor of Merton College, Oxford. With /) ~ana anrl d f:lM~_I_

Notwithstanding the severe compression re- quired, m. CREiGHTON ha succeeded in present. m? a fer from unreadabje bock, which will be of great assistance to the student. Althongh pro. minence is given to the history of England, the contemporaneous history of Europe haa not been neglected, and the Author bas shewn, wherever was possible, the connexion of events passing in different conntries. An impartial view is taken of the causes which led to the rise and progress of the Reformation in Europe, duo

.u ~eneatogicfU TaM&s. ~<. 6d. as

well ns to the religious element shewing how by

the course of events tbat grootinovitabIe change

S ~?~' 'i~ all that been written Mont the reign of EuzABMn.Mr. CtŒfcHMN ?~&

epitome which is valuable, not only to the stu-

degree interested

in the history of that poriod.1

acAnnacy.

The HOUSES of LANCASTER and YORK; with the CONQUEST and

LOSS of FRANCE. By JAMES &~mD\BR of ~~Pn~ L.(JNQUEST and

LOSS of FRANCE. By JAMES G."mDXER, of the Public Record Office; Editor of' The~Paston

Letters' &c. With 5 Coloured M~ Si~ The~P~ton

~S~&S!°~ ~S~ chiefly required in ~ithmour contributions to school literature ~S~ book is the art of leaving out.

within our knowledge. The division of our na- Selections must be made of the persans to be de-

tional history into portions is an assistance to sS~d~~ P~~°s to be and

ita acquiaition as a whole; aad Mch Mrcian ~<~ °~ narrated, and

lts acquisition and each portion ~S~i~~ ~owledge brides a d~

forms a definite amount of work adapted to a criminatiug judgment. kir. (IAIftnNFR says the

definite portion of the school year. The chief ac~h~n ~ER its close merit of these little volumes, however, is to be one of the most obscure in English history. But found in their authorship It is-to borrow se a

their title-an epocll in the history of school '1']le invasion of France by HE!iRY V. and the

~rs F~ s~

their Authors a few eminent historiai)s. The n. dnimatie interest, and stand ont so promi.

writer of the volume on the Wars of the Roses i8 nently, thnt the social condition of the people i8

distingriished by his resesrches into the close of lost sight of. This Epoch is published oppor-

the period of which it treats, and by his publica- tunely, as the subject is, in part nt least, pre.

tion of Papersillwtrative'oftbe