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 PRESENTED BY 
 
 PROF. E. G. LEWIS 
 
 FROM THE LIBRARY OF 
 
 M. W. JACOBS, JR. 
 1950 
 
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POPULAR ASTRONOMY. 
 
 BY 
 
 SIMON NEWCOMB, LL.D.,, 
 
 SUPERINTENDENT AMERICAN NAUTICAL ALMANAC, 
 
 FORMERLY PROFESSOR AT TIIE U. 8. NAVAL OBSERVATORY. 
 
 WITH ONE HUNDRED AND TWELVE ENGRAVINGS, 
 AND FIVE MAPS OF THE STARS. 
 
 FOURTH EDITION REVISED. 
 
 NE Weev 0 KE: 
 HARPER & BROTHERS, PUBLISHERS, 
 FRANKLIN SQUARE. 
 1882. 
 
Entered according to Act of Congress, in the year 1882, by 
 
 Harper & BroTuers, 
 
 In the Office of the Librarian of Congress, at Washington. 
 
=a 
 
 vid A 
 
 Pp pe. 
 
 a. 
 € uly 
 
 \ PREFACE. 
 
 To prevent a possible misapprehension in scientific quar- 
 ters, the author desires it understood that the present work 
 is not designed either to instruct the professional investi- 
 gator or to train the special student of astronomy. Its main 
 
 object is to present the general reading public with a con- 
 
 densed view of the history, methods, and results of astro- 
 nomical research, especially in those fields which are of most 
 popular and philosophic interest at the present day, couched 
 in such language as to be intelligible without mathematical 
 study. He hopes that the earlier chapters will, for the most 
 part, be readily understood by any one having clear geomet- 
 rical ideas, and that the later ones will be intelligible to all. 
 
 ; To diminish the difficulty which the reader may encounter 
 
 Pe 
 from the unavoidable occasional use of technical terms, a 
 
 _ Glossary has been added, including, it is believed, all that 
 
 ip are used in the present work, as well as a number of others 
 
 ~ which may be met with elsewhere. 
 
 C Respecting the general scope of the work, it may be said 
 
 that the historic and philosophic sides of the subject have 
 been treated with greater fulness than is- usual in works of 
 this character, while the purely technical side has been pro- 
 portionately condensed. Of the four parts into which it is 
 divided, the first two treat of the methods by which the mo- 
 
tions and the mutual relations of the heavenly bodies have 
 
 Vi PREFACE. 
 
 been investigated, and of the results of such investigation, 
 while in the last two the individual peculiarities of those 
 bodies are considered in greater detail. The subject of the 
 general structure and probable development of the universe, 
 which, in strictness, might be considered as belonging to the 
 first part, is, of necessity, treated last of all, because it re- 
 quires all the light that can be thrown upon it from every 
 available source. Matter admitting of presentation in tabular 
 form has, for the most part, been collected in the Appendix, 
 where will be found a number of brief articles for the use 
 of both the general reader and the amateur astronomer. 
 
 The author has to acknowledge the honor done him by 
 several eminent astronomers in making his work more com- 
 plete and interesting by their contributions. Owing to the 
 great interest which now attaches to the question of the con- 
 stitution of the sun, and the rapidity with which our knowl- 
 edge in this direction is advancing, it was deemed desirable 
 to present the latest views of the most distinguished investi- 
 gators of this subject from their own pens. Four of these 
 gentlemen—Rev. Father Secchi, of Rome; M. Faye, of Paris; 
 Professor Young, of Dartmouth College; and Professor Lang- 
 ley, of Allegheny Observatory—have, at the author’s request, 
 presented brief expositions of their theories, which will be 
 found in their own language in the chapter on the sun. 
 
: PREFACE 
 
 TO THE FOURTH EDITION. 
 
 Tue favor with which this work has been received by the 
 public has led the anthor and publishers to give it a fourth 
 revision, in order to include the latest results of astronomical 
 research. The subjects which were added in the third edition 
 comprised Dr. Draper’s investigations on the existence of oxy- 
 gen in the sun; Janssen’s new method of photographing the 
 sun; the conclusions from recent total eclipses; the prelimi- 
 nary results of the British observations of the late transit of 
 Venus, as well as of other methods of determining the solar 
 parallax; the discovery of the satellites of Mars; the results 
 of recent investigations into the motion of the noon, and Pro- 
 fessor Watson’s observations of supposed intramercurial plan- 
 ets. The principal additions to the present edition relate to 
 the great telescopes completed within the last three years, the 
 transit of Venus of December 6th, 1882, and recent develop- 
 ments in cometary astronomy. The intention has been to 
 bring it up to date in all important points, and it is now 
 hoped that the general reader will find in it the fullest prac- 
 ticable explanation of every branch of the subject which can 
 interest him. 
 
CONTENTS. 
 
 Jeeaudassh ak 
 
 THE SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 ER ROD TOL ION t Com paneer ett) cate yoo cbali « Wieelrdce code clbudeadedMuctece ere ee i 
 
 CHAPTER I. 
 THE ANCIENT ASTRONOMY, OR THE APPARENT Motions oF THE HEAv- 
 BoE ead) ALE Mame nate eo Mae cid «dtc cic dee Pak y onddsede ss deaeesZaccdensesnseusc ese 7 
 Rpbemee ee @ Mle Stile NCTC. cadre ct <oas -vecass<sscrastarinandecceversnssseecctes q 
 ee Cm LICR NLOELOTN). feyocecs gavin sete idencrsesceesacaaevsculecscouews fae 9 
 Sos Motioneor tie oan among: the Stars ...cecccccs.scee cs. coneversanceses 18 
 § 4. Precession of the Equinoxes.—The Solar Year.................0+6 ie) 
 Se em MeL GOTT Oe VIO ULOH, coc sa etc aieastds scpriesvaclenacs dancer oatbl Gneneeiaeess 21 
 SGasochipecs en ce; sum and, Moon .....0..sascacase opo.ccoetensdeeesvbeveesee 24 
 SME OME LOFCTISICE SVSLOMN esas dns ac vac venahece dus sce nen ts rehden es dae aie 2 «is 32 
 PEO MUG RU MONOCOTS ot secs ts cancers basins cto ue es di older tort a ewer ee iawaoheles 44 
 
 CHAPTER II. 
 
 Tue CoperRNICAN SYSTEM, OR THE TRUE Morions oF THE HEAVENLY 
 
 Bopies 
 $1 
 § 2. 
 
 § 3. 
 § 4. 
 § 5. 
 
 PTR Re eg Cais set pac se ides cou Relies was adains Dee's gets teset recess slotvekes vcesee . 51 
 Me ETL Spanos oa oh yrds oe de Sopme rahe es og cemtte edaes Ve oo ete Sees coors 5] 
 Obliquity of the Kcliptic; Seasons, etc. ; on the Copernican Sys- 
 EE Mere me eases cain veo ecaism tees aaae rs seeteeeeeeeeeseeeeeeeneerenseees Ton Oe 
 EERO OMIT RIG: oss se srcscnssst qchtaed non aetanmiee One prces cst hw aie ness agers « 66 
 Kepler.—His Laws of Planetary Motion............ccccesseeeeeeeeee 68 
 MeTORME IC CDIGE ACO. NOWLON. ccsstesccesccmete ts su sereccsinc denera dca sacecneael ra! 
 
x : CONTENTS. 
 
 CHAPTER III. ; PAGE 
 
 UMIVERSAL. GRAVITATION joie eins cone res betters penn rah -aets oe eiaae Pear aatote ere see 74 
 
 § lL. Newton.=-Discovery of Gravitation V2.5. te:. ac. .accctscressaueei canacc 74 
 
 § 2. Gravitation of Small Masses.—Density of the Earth............. 81 
 
 § 8. Figure lofethe siarihiso oc geacets eect ees orators serene s ceck cuenta tae 86 
 
 § 4. Précéeston tat the equine sess, y7. cock taste vas Panne eee eeiaae tears 88 
 
 § By’ Dn6 MVIGER PM, occ setae tet: bathe a sneee eke Mere ease ewele see een ae Soteweae 90 
 § 6. Inequalities in the Motions of the Planets produced by their 
 
 DMutial A ttrachiOn casa. scovaa cots stench. ih es ener eeeaesmeetieacantys 93 
 
 $7. relation of the: Planets. tos thes Stars 4... cs. scesens ce vekeeBes ch nce es 103 
 
 PAL Deete, 
 
 PRACTICAL ASTRONOMY. 
 
 INTRODUCTOR Yi OE MAR KS ocr colo anes concen ee rence ea eeu ae ae at eee aneetne e 105 
 
 CHAPTER I. 
 
 A HE MUBLESCOPE Mins cciscups ovo ndbean sys cabiecere Moana btcoestr een see cee babe nanan ety amet es 108 
 9 1. wDhesPiree Lleieseowes tn, 17i.5 ent cees ening sane avi entenean ce tee rer ae 108 
 $2. “The *Aichromaties Telescope tc diccnecen cone eons pee teee ae wae sneer 116 
 5 3.. The Mounting tot-they Velescope ..iisciwsss cece ceneew sn tonnes anew ea ae 120 
 § 4. The ‘Reflecting <lelescope 2.7 ves sccwesacpecavasatcees ceenteunedentieame 123 
 § 5. The Principal Great Reflecting Telescopes of Modern ‘Times... 127 
 $6) Gteat-Retracting 7 elescopes.i...,:-<s ose vccrsfeveonee enazns in hee oben re 137 
 
 § 7. 'The Magnifying Powers of the Two Classes of Telescopes..... 141 
 
 CHAPTER II. 
 
 APPLICATION OF THE TELESCOPE TO CELESTIAL MEASUREMENTS .........< 148 
 § 1. Circles of the Celestial Sphere, and their Relations to Positions 
 
 on then Barth's 57.2 :citet iasecnaceepelaeseae tas taleeeeyune Cie Use coms se cc ee 148 
 Syed he avieridinn Circle and rite Use. nis inonasemonet teaaa var hs sees Ac Bales 154 
 § 3. Determination of Terrestrial Longitudes .........-....c.cece eee eee 159 
 
 S eM GAT OPC lOCKs Ol aint: foie dns levers cts ream. Misceeee dros cae adis rasa sca 164 
 
CONTENTS. xi 
 
 CHAPTER III. PAGE 
 PEASE RING: DISTANCES IN, THE TLEAVENG, «2.005 /0s:iehecadescidasscl ee. 167 
 ppl bata se i Cancale ot. ek aed oy Tey ae soaks ae 167 
 § 2. Measures of the. Distance of the Sun........c..ecccceocesesecdsaceces 173 
 Sas ooarbarallax from Transits of Venus:.ci.:..... 7... b YC 
 § 4. Otler Methods of Determining the Sun's Distance, and their 
 Results....... Dae Ai RAEPO NET Aro enM een inemesds cack ve able ti aaanen ree 196 
 SRneMOCOULiMiar MaKe ate dicta cs! Wee Meee a et tee Se 203 
 CHAPTER IV. 
 PERE GY ROS BGT OCG: BOA 4 2 ie a RN Pe Pe 212 
 CHAPTER V. 
 PECTS Et UO BOOE bee teng Sener yn ib oks Sea see anachy cee addeshideassatenervietsaciseses 224 
 PART III. 
 THE SOLAR SYSTEM. 
 CHAPTER I. 
 CENGUAL OIRUCTUBE OF THE SOLAR: SYSTEM !....¢.scectdivastseicavsscesmsdyeces QOD 
 CHAPTER IL. 
 ELHBOOUN ys ccsescses nt Se eme at me OR erage tae. oo tira hiei Dak A ee ee he bare seNigovanaesieds 241 
 SMM TIMER DOLOSP VET Olio) coche Mecsidsle's sac scdinevess cates otse cover edinsvessea 241 
 SPE Nee SOlale SPOS ANG NOLALION. cuc-cs.cossecncaverevscs veseevdvvcsencesrs 248 
 ® 5. Periodicity of the Spots.,..........0+.. dame Per ientats eeu tees Seer ceva, sv ae 254 
 PEA ME AW AOLEIOLALLOIN Of EUG OOUT Nu chieva-< ineccdboosceedsusestsesdsensacds dies 255 
 Oe SUN SCOMTVOUTICINIS oct caida des er che cebecakeedsceecedecvtcosverioesve SOG 
 Bios Ehysical Constitution of the Sumi... ccs)..).iseesecescasseskea se dcees'ee 264 
 § 7. Views of Distinguished Students of the Sun on the Subject of | 
 
 its Physical Constitution .........cscccescsessrseneeveesrseveeceasevees 271 
 
Xl CONTENTS. 
 
 CHAPTER III. PAGE 
 
 LHS Inner ‘GROUP ORGELANET SH. cee secestass ise ea bier es Cn vecenvente ete eer ereee ek 289 
 
 § 1; The PlaneryMercury sc: srs, cers esse Ma tostee eters crave sees pevbneaa te 289 
 
 § 2. The Supposed Intra-Mercurial’ Planets ...............scesseecseseeees 292 
 
 § 3. ThenBlanebuyv emis nos etrec reeks her ckecciaet cle ontats s heetaae Reetenee 295 
 
 § 4. ‘Thetkarth ?. eras steers nceeee ee tae scien tiny oiecacst ot an meee eee 304 
 
 § 5. “BheuB1 Gon ics 5. Ss cassie: usec eat bee eareccettasieat sos ses bee ener meee 312 
 
 8 6. (heghlanet: Mare) iciyiserisvceanasy cts sae dhs ocaeven dc bach Fee eee eee 326 
 
 §-7. he rSsmall «Planets 0:2: vise sev spactes siesseeeetces ee aee nee eee 2 331 
 CHAPTER IV. 
 
 THeADDrE GROUP“OR) PLANETS 1. psccvacesncciscmeeets wits a)s sebeeede emer ane Lenn 339 
 
 S11." The Planet sd apiters..2.a0ccs-conkartecacceren au es earcennare ee eee Ae oe 339 
 
 S 2.7’ The Satellites of sd upitor. sescscances asp tan tane estes teeth see weer en ees 344 
 
 § 3. Saturn and its System, Physical Aspect, Belts, Rotation........ 346 
 
 64 The Rings Of Satntn wots. eee areaceh ee ecre cae ee ene ee ees 349 
 
 5b. Constitaion -0f the: NMP Ox sete esos rate ces lens sceeenmeeee eee 357 
 
 6. 2The- Satellites Of Satiinisc: ssc reese cnteeeek es tates eh cant cocoa 359 
 
 $4, Uranus “and “ts Satellites: sor, ec ee cntaaeene vege pete. eer ece nee 361 
 
 $8. Neptune wand ‘its Satelbiciis. cx.s«:.cdeenthan en ssen reeset oc sneer c 366 
 CHAPTER V. 
 
 CGOMETS CAND SVMETEOHS 5 cccescutersatcertssennsgulentsask epesaten etme Ea heT Sane eiecne 373 
 
 $ 1. Aspects and Worms of (comets vic cs.cete): ose nceunames tos ees 373 
 
 § 2. Motions, Origin, and Number of Comets ...........0cccccseseeseeees 377 
 
 8'3.6 Remarkable;Comets 20s: .cscciveesteresce anes tes tases eee che Bae ae 382 
 
 § 4. Encke’s Comet, and the Resisting Medium......................0008 391 
 
 ‘$5. WOther: Periodic (Comets. tise. ses seas an se ceah rx ence <eee una sue tantra ee 394 
 
 S 6.) Meteors “and ‘Shooting-stare-....-c:actsccs aseccaene tar cedonue: sphere ass 395 
 
 $7. Relations of Comets and Metéoraids 5.0, .2sss,s0sc ies on eheewbeep ees 402 
 
 § 8. The Physical Constitution of Comets............... acter iatneencsns 409 
 
 6°97 ThecZodiacal Dights icc ssars veces pew snce tecuthian« sieecenan tetseaeecres 416 
 PAR aby 
 
 THE STELLAR UNIVERSE. 
 
 INTRODUOTOR Y ERMA TERS cchccoh Gta dl ve Seater eae ea tcdecs it sje cbbere 418 
 
CONTENTS. xiii 
 
 CHAPTER I, PAGE 
 
 eet Hee AS ETC) ARI SHENG, 8c. udscyiiioussa t5or <dakei vodtcc. vedi 422 
 § 1. Number and Orders of Stars and Nebula ........................... 422 
 
 § 2. Description of the Principal Constellations. ......................... 429 
 
 Sener ayn Mlcamy ATA LG Slates a cg coal 2 ease Gadus cosy ch ode 2 em 438 
 
 S47 Doubler Starsenccs:shecs ects ais Sp Sry EER EU ME gee ORIEL ALS, 448 
 
 § 5. Clusters of Stars....... Me dieWr ates a one epe earth casts piioc Uasiuen dc Sebccont 453 
 
 i Gil RORCUTN 6 Ge see oust ARAN Aeey Coad ema Ey! An OE Oe ee 456 
 
 DETTE FONDESMLOtIDNS COE thee OtATS 2.45 vats sakns s)ycdev ile cai sdlehavceddsasaecs 464 
 
 PES PRUCTIUR Ms OF )TEMEU NEVERSIN fA0 soc pctocel bus SacdeWea ocbhen hobdideiccsoodint 472 
 $1. Views: of Astronomers before: Herschel/.....i.R ir. ccciseessceccences 473 
 § 2. Researches of Herschel and his Successors ..............c0ceeseee00 477 
 § 3. Probable Arrangement of the Visible Universe..................... 490 
 S4ee Diop ther mlatse Teall vasOrme dd OYStOID f. .ccvacte cctveceseessackives ches’ 495 
 
 CHAPTER III. 
 
 THE COSMOGONY ......+. Fee eater MMe ae Tee ea.c 64sec ox ony diate ecleziesic eeaieiteavie tae geet 503 
 Sipe Le. Moderns Nebulan EEVPOLhGSIS .5.....00.ccaeesessaseas not sseodereces: 505 
 Siowerootessive, Changesoin: our: System <s ..ascssesseesacescedesncteusenes 511 
 Seen Net SOUrChsy OF CNENOUD St HEAL: . ...0ies.csscse verecneaceeceeses te ssaede 517 
 SPleoociinty COGN gtOn. (Ge Artic. civ; «dcadceste Qu beties bo teats clbaeaees 523 
 § 5. General Conclusions respecting the Nebular Hypothesis ......... 526 
 SOMA LIOSE LUTADY! Of WOTLUOS) dix cape .0ous coxee oo taeda beaeaepengelatess ovete 528 
 
 APPENDIX. 
 
 I. List oF THE PRINCIPAL GREAT TELESCOPES OF THE WORLD...... 533 
 
 II. List oF THE MORE REMARKABLE DOUBLE STARS........cccccceeeeeees 534 
 III. List OF THE MORE INTERESTING AND REMARKAPLE NEBUL# AND 
 
 peacbes UR. (pf O0S 7S te Ree REE Reed dec: chic yee AM eg Ae ee EER RPS Ct 587 
 
 IV. Pertopic COMETS SEEN AT MORE THAN ONE RETURN .....cceesseeers 539 
 
X1V CONTENTS. 
 
 PAGE 
 V. ELEMENTS OF THE ORBITS OF THE ErGHt Masor PLANETS FoR 1850. 540 
 ELEMENTS OF THE SATELLITES OF JUPITER 1....00cccceccecccsnceseccecee DAL 
 ELEMENTS OF THE SATELLITES OF SATURN .....cccccccsscsccscevssescesse O41 
 ELEMENTS OF THE SATELLITES OF MARS ............cceeceees See haee eee L 
 ELEMENTS OF THE SATELLITES OF URANUS........cccccscescerccsssscecee DAL 
 ELEMENTS OF THE SATELLITE OF NEPTUNE......ccccccecsecocscees catteas OD SL 
 Vi. ELements oF. THE SMALL PLANETS 5.556.502. ccc. code aadtevseskccten dears DAS 
 VII. DETERMINATIONS OF STELLAR PARALLAX......cccctceccosccoscssscesscccee 549 
 VIII. Synopsis oF PAPERS ON THE SOLAR PARALLAX, 1854-77 .......... 551 
 IX. List or ASTRONOMICAL WORKS, MOST OF WHICH HAVE BEEN CON- 
 SULTED AS AUTHORITIES IN THE PREPARATION OF THE PRESENT 
 "W OB KG Bends ve satan oes adlnshvadeth van eaaan vont ian aree couse cere an aaee mmeee a ame 
 X. Guossary oF TECHNICAL TERMS OF FREQUENT OCCURRENCE IN 
 ASTRONOMICAL: WORKS s.veiclincecteclsvnecdsstccsbabedpecce et ee nen sete ereOe 
 
 | S540) Ob. CHARTERED PIOMAbe LAE A Ree PR Ribas JR aPE AMEE AEA) Oc athe Noy dee ab ek et i ER 
 
 IGXPLANATION OF ‘THE START MAPS 22.27.25 case cocusdcenre cosceease kets ar cekl serene 
 
FIG. 
 
 15. 
 
 it. 
 
 LIST OF ILLUSTRATIONS. 
 
 PAGE 
 
 THe GREAT TELESCOPE OF THE UNITED States NAVAL OBSERVATO- 
 
 LSU ASHING TON Meerut cikl ce dec cn Siacsktbaclaas teal sh oadiessJetsad! TONLLSPTECE 
 
 SECTION OF THE IMAGINARY CELESTIAL SPHERE ....00..ccccccscceccccsccece 
 Map ILLUSTRATING THE DiurNAL MOTION ROUND THE POLE........... 
 THE CELESTIAL SPHERE AND DIURNAL MOTION ...........ccceesceceeneeees 
 MoTION OF THE SUN PAST THE STAR REGULUS... ..dvsccceseccevscsescesces 
 SHOWING THE SUN TO BE FARTHER THAN THE MOON..,............000008+ . 
 ANNU A Hip OL IPS Mr OMI PEL S UN 1. orcs ckiyaspudevecsrscsad Cade dcicaaedecceesee ses 
 ARTE Sp PCLIPSE TOF FTE OL ice restee ss cctcece sel rts cenctdead syateandades ie 
 EciirpsE OF THE SUN, THE SHADOW OF THE MOON FALLING ON THE 
 Eciipse OF THE Moon, IN THE SHADOW OF THE HARTH ........ceee eee 
 SHOWING THE APPARENT ORBIT OF A PLANET ......cccccccccccceccsecsccseces 
 APPARENT ORBITS: OF J UPITHR: AND.) SATURN . ccc cedceviccussvecddcpicsevsccess 
 ARRANGEMENT OF THE SEVEN PLANETS IN THE PTOLEMAIC SYSTEM... 
 BU EW ECE RIN DES Carre ereeta ay oiate Sep PaaS Tuk. cc cto s o¥atlasid ode Rdda's Va.dcle vod et els daew Aves 
 SHOWING THE ASTROLOGICAL DIVISION OF THE SEVEN PLANETS 
 
 AMONG OPE MY Se ORM DHE VY EE Rite cJ./\5. base ddocceva Seduce ts bicebedes tee dess 
 APPARENT ANNUAL MOTION OF THE SUN EXPLAINED.......ccccccseesscees 
 SHOWING HOW THE APPARENT Epicyciic Motion OF THE PLANETS 
 
 PLAC COUN TE PUM OR Hh cates nastareed abe ate et ert nats obedes a pe cesik deaeenct 
 RELATION OF THE TERRESTRIAL AND CELESTIAL POLES AND EQUATORS. 
 CAUSES OF CHANGES OF SEASONS ON THE COPERNICAN SYSTEM....... 
 ENLARGED VIEW OF THE EARTH, SHOWING WINTER IN THE NORTH- 
 
 ERN HEMISPHERE, AND SUMMER IN THE SOUTHERN..........0..0000: Ye 
 ILLUSTRATING KeEpLer’s First Two Laws oF PLANETARY MOTION... 
 ILLUSTRATING THE FALL OF THE MOON TOWARDS THE EARTH ......... 
 Baity’s APPARATUS FOR DETERMINING THE DENSITY OF THE EARTH. 
 WRE MELO TSAT EY SteA PRAR LANDS Sa ucuuscosl dense Levdinclolad te oo Veede's debiceedanb py 
 DIAGRAM ILLUSTRATING THE ATTRACTION OF MOUNTAINS ......ccceceeeee 
 EREOEAEION Oe OLAS LOUINO XESS gieis cds 5 Tavs (odes Bids Nictseb soso thernsoe ray bebas 
 
 85 
 88 
 
59. 
 
 LIST OF ILLUSTRATIONS. 
 
 ATTRACTION OF THE MOON TENDING TO PRODUCE TIDES.........0se000 
 ARMILLARY SPHERE AS DESCRIBED BY PTOLEMY..........scccccecescssceee 
 "THE GALIGEAN pee DNSCOPD secs ctrss bobs +cckossecsenpechuend bec sney Be ee 
 FORMATION OF AN IMAGE. BY A LENS. .sseseeceecseeeereneeeteneeeseennecesens 
 GREAT TELESCOPE OF THE SEVENTEENTH CENTURY.........ccccesceveseee 
 
 . REFRACTION THROUGH A COMPOUND PRISM.....00cccccececccccscscccsses Rode 
 
 SECTION OF AN ACHROMATIC OBJECTIVE.....scecccesnccednsccevsscresscaras a 
 SECTION OF ESYE-PIECE OF A TELESCOPE, ...cecccscecccccscccesvevces Ae sSend 
 
 . Move or Mountine a TELESCOPE...... Yee bad coeres sou eee ee eee eee 
 
 SPecuLUM BrinGcinc Rays To A Since Focus By REFLECTION...... 
 PIBRECHELIAN LELESCOPES..0ccevvesetescviecctessnspbadescsioeee ep eeetree PE ae 
 HORIZONTAL SECTION OF A NEWTONIAN TELESCOPE........csccecccceeeee 
 SECTION OF THE. GREGORIAN TELESCOPE .......ccecsessdecscnevecvsebsseseuna 
 
 PLBRSCREL S. GREAT (TELESCOPE 4 6 o5 05.035 ictus beved loc ccvatncdespieeeeneennenes 
 
 Lorp Rosse’s GREAT TELESCOPE...... NE. BA ALLs cca ceseet eee Wes Pe ae 
 Mr. LAassevtyt’s Great Four-Foot REFLECTOR..... pees es oe ct ; 
 
 wT He UNEW (PARIS. REBLECTOR /...s)s.ccisesecvcdeens Sete REA event coe a 
 
 THe | GREAT MELBOURNE. REFLECTOR 6.5.60 hi cie ccd ds dese ee ensins eee Suoaee 
 CAROLS, OF THE CELESTIAL /SPRERD « 5..00sedesvecstonse deste ct ti nocsvenenee 2 
 
 SPIDER Lines IN FIELD OF ViEW OF A MERIDIAN CIRCLE..........0. 
 DIAGRAM ILLUSTRATING PARALLAX........ ed isals ese EH Metres cee tt 
 
 PEUITAGRAM ILEAISTRATING <P ARBALLAR Ass, coe derek hs doves dtu cone ete e ome renee 
 
 VARIATION. OF PARALLAX WITH THE! ALTITUDE, ...5.h.ccccccuvecssecececee 
 APPARENT PATHS OF VENUS. ACROSS THE SUN.......ccccoseccvescccsessccss 
 VENUS APPROACHING INTERNAL ConTACT ON THE FACE OF THE SUN. 
 INTERNAL Contact oF Limp OF VENUS WITH THAT OF THE SUN.... 
 Jb) BLACK, DROP, On -LiGAMRN EID. us. Ae siatin eegeethe ees vaereneeees Oe 
 METHOD OF PHOTOGRAPHING THE TRANSIT OF VENUS......cccccceveees ‘ 
 ARTIFICIAL. TRANSIT! OW. .V ERUS) cs, .enssccs dupastesdeee te Sore eee wee ee 
 Map or THE EARTH, SHOWING THE AREAS OF VISIBILITY OF THE 
 
 RANAIT) OF MLS TAcr ce thie, cele tees Tohavassancs tthe tac peets sete cee tr tan 
 Map or THE WORLD, SHOWING THE REGIONS IN WHICH THE TRAN- 
 
 SIT OF VENUS WILL BE VISIBLE ON DECEMBER 6TH, 1882....... Ne 
 EREWOM ORL STEDLAB PARATLAXS..llscct.scioessdcceleretes 
 ABERERTION OF LAGHTV coleiss teense ste csselcubansve lets 
 REVOLVING WHEEL FOR MEASURING THE VELOCITY OF LIGHT........ 
 ILLUSTRATING FoucauLt’s MretHop OF MEASURING THE VELOCITY 
 
 ahd Bites tack Ripe roy ee es eR gee by Bene Savbescateess ts ae 
 
 eeeeee tee reerereweres 
 
 CouURSE OF RAYS THROUGH A SPECTROSCOPE,. ....0.cscecscccccccccccoasecece 
 
 220 
 226 
 
FIG. 
 63. 
 64, 
 
 65. 
 
 LIST OF ILLUSTRATIONS. XVll 
 
 PAGE 
 
 240 
 
 244 
 249 
 
 IRECATIVE, DIZW. OF LOUN. AND. PLANETS.) colds yd ods cdeodepeosaceeevsansanenate 200 
 ORBITS OF THE PLANETS FROM THE EARTH OUTWARD .....cccceceeceeces 
 64a. ASPECT OF THE Sun’s SURFACE AS PHOTOGRAPHED BY JANSSEN AT 
 THE OBSERVATORY OF MEUDON......... PResatoegeScsetctean sect cmenerames 
 METHOD OF HOLDING TELESCOPE, TO SHOW SUN ON SCREEN........ he 
 SOLAR LDPOT, APTHR: OECCHI: Ayt cvcehlss das styuesr5o Moeeds dha none. Goda Shab 
 
 66. 
 67. 
 
 68. 
 
 69. 
 70. 
 
 (ee 
 72. 
 73. 
 
 74. 
 75. 
 76. 
 7% 
 78. 
 79. 
 80. 
 81. 
 2) 
 83. 
 84, 
 85. 
 
 85a. 
 
 86. 
 
 87. 
 
 88. 
 89. 
 90. 
 91. 
 92, 
 
 CHANGES IN THE ASPECT OF A SOLAR SPOT AS IT CROSSES THE Sun’s 
 ToraL Eciirse OF THE SUN, AS SEEN AT Des Mornes, Iowa, Av- 
 
 Rha (EE Lo oed ao eaa it eiesaaes acest onc ioncendss Cenk suiceeh sc dees sv Seredeaie sts ot ¢ 
 SPECIMENS OF SOLAR PROTUBERANCES, AS DRAWN BY SECCHI......... 
 Ture SUN, WITH ITS CHROMOSPHERE AND RED FLAmeEs, on JULY 
 
 DODLG Ll econeeeese Woes Rao satesscper asthe kde cebls « Seder b adadiiean Sebes tones ee 
 ILLUSTRATING SEccHI’s THEORY OF SOLAR SPOTS..........ccceeee 
 
 eosesee 
 
 SotarR Spot, AFTER LANGLEY........... Sasstesse Miah Ae reso wee tnaeas oer dees 
 Orpits oF THE Four INNER PLANETS, ILLUSTRATING HE ECCEN- 
 
 TRICITY OF THOSE OF MERCURY AND MARG...........cccccesscceccceess 
 PHASES OF VENUG..........0006 Bit hag cone WE dapat ahd fe 
 SHOWING THE THICKNESS OF THE EARTH’S CRUST...........ccces0e0e 
 DrerTRIBUTIONY OF LA URORAS cess vatenSucouasienvessideos eastes 
 VMivw ,OMUATRORA. cous Server pwn Met Saedl's coed Ghee aPeohne AE Bae 
 SPECTRUM OF Two OF THE GREAT AURORAS OF 187]1..... Ccontet eee 
 RELATIVE SIZE OF EARTH AND MOON........cccccceevceeees 
 View oF Moon NEAR THE THIRD QUARTER...... baa ea teat as dec depn iee 
 (PUMA R OC RATER | °° COPMENIOUSE seretrrclccsustesueerestvacece secs SE Ea ele We 
 Tue PLtanet Mars On JUNE 23D, 1875........... duns saere es rae: 
 MAPFOROM ARS +2 .- carcass rene few dara tte veelieccsetce te eencdes ees Bey les y 
 NORTHERN HEMISPHERE OF MARS.....cccccccsccececcecsces 
 SouTHERN HEMISPHERE OF Mars........... Mb anaste reds ee 
 APPARENT ORBITS OF THE SATELLITES OF Mars 1n 1877, AS OB- 
 
 SERVED AND LAID DOWN BY PROFESSOR HALL............ 
 JUPITER, AS SEEN WITH THE GREAT WASHINGTON TELESCOPE, MArcH 
 
 21st, 1876...... SpE saat rete ear aeericd Bsig en eC ropa 
 VIEW OF JUPITER, AS SEEN IN LorD Rosser’s GREAT TELESCOPE, 
 
 FEBRUARY 27TH, 1861....... Bache Sasso te biel ele aa Heeinendes ote RSet ke Sted wets 
 VIEW OF SATURN AND HIS RINGS...... sea eeeeh saa wed she's SAP eg ee cae 
 SPECIMENS OF DRAWINGS OF SATURN BY VARIOUS OBSERVERG....... 
 Eee! FONORIM 6) COMBTIING I SUL. cite crec.cesncuessocdcevoctedsesccessssoes 
 HEAD OF DONATI S GREAT. COMET OF 1858. .....ci.ccsccccccocsccccesevndas 
 
 PARABOLIC AND ELLipTic ORBIT OF A COMBET............ MNES ae 
 
 2 
 
 250 
 
 252 
 
 259 
 262 
 
eee 
 
 XV111 
 
 FIG. 
 93. 
 
 94, GREAT COMBT IDR Basie eras isch te dec dseresvccs 
 
 95. 
 
 Ornit. oF HALLEY 8) COMET oie csie. cn sess ceacecctscves 
 
 LIST OF ILLUSTRATIONS. 
 
 PAGK 
 
 *e@eoeseeeeeeeeeeeeeeeseeeeee 385 
 ee Tee eeeeeeeeeeeeeeeeeeeee 388 
 METEOR PATHS, ILLUSTRATING THE RADIANT POINT.........ccescecceeeee 401 
 
 96. Orsit oF NOVEMBER METEORS AND THE COMET OF 1861............. 405 
 97. ORBIT OF THE SECOND Comer oF 1862...... oc dia'e sis.e 0 893 aegresre eae eae a 
 98. MEASURE OF POSITION ANGLE OF. DOUBLE STAR........ccceseceeevseees 450 
 99. DisTANCE OF COMPONENTS OF DOUBLE STAR....... oastoppesenseenenyanre amend 
 100. DIAGRAM TO ILLUSTRATE POSITION ANGLE........sccccccceccssvsscecscccss 400 
 
 101. TRLESCGOPIG VIEW OF THE PLEIADES. ....cccocceccccccsoeevsceredececcuneeto ier 
 
 102. 
 103. 
 
 CPUS DE VORA WoO LGA IL CAe ss Sahn sca \sedieds oc orpscees scebee aioe 
 
 sdeckeverer es? si cenaatee 
 
 CLUSTER tip (COR NUATIRIA GS cvocs xcotuwtnddescosccasveccccocve biceccne bite meee amet ammaInG 
 
 104. THe Great NEBULA OF ORION......... PeoaMmCtt: ot ee oe oc andehcak echt en eta 
 TOSALL TE CANNUTA RN HBULAMING LINEA scarce toccccbcs cases ceeet senor eeteeee TEE: OU 
 
 DOGS S LEE  OMBGAS IN WB UUA <o. ap crass Bcssl vdceieabendece os viecsnemaclece shee teeese ce meeee mare nm 
 
 MOTs GN EBUIGA SEL ERSCH Wise 1 orc boos casus oes cccbeu ccboceicduace toe teup ee teene ce tae mmm 
 
 108. 
 109. 
 110. 
 111. 
 
 Tre Loorpep Neputa; HerRscHer 2941............. 
 
 WITHTHE NUL RA COPRE. aki csc- cas sch cvchcovestnae weeeeunes 
 
 HERSCHEL’S VIEW OF THE ForM OF THE UNIVERSE............ses0000. 481 
 ILLUSTRATING HERSCHEL’S ORDERS OF DISTANCE OF THE STARS.... 483 
 PROBABLE ARRANGEMENT OF THE Srars AND NEBULZ VISIBLE 
 
 o'sisee evcewen pena eran 
 
 112. DIAGRAM ILLUSTRATING ExLuipric ELEMENTS OF A PLANET........... 565 
 
 Mar 
 
 ce 
 
 66 
 
 6e 
 
 66 
 
 PLA UMAPS. 
 
 I.—Tuxr NortTHEeRN CONSTELLATIONS WITHIN 50° ) 
 OF UTHD POLES ss cree vis bbe eee tees CER 
 
 II.—SoutHERN CONSTELLATIONS VISIBLE IN AU- 
 TUMN AND SVVANTER Usp. canst. cereeatcesrocuae tes 
 
 III.—SovutHerRN CoNnsTELLATIONS VISIBLE IN WInN- 
 
 IV.—SouTHERN CONSTELLATIONS VISIBLE IN SPRING 
 
 TER AND SPRING sfsticsecscnten Fo dee Cee he ae Oe eee | 
 | 
 
 AND: UMM 2 sic vas costae Sededeveudiptudsasen ueeeee 
 V.—SouTHERN CONSTELLATIONS VISIBLE IN SuM- 
 MER AND AUTUMN. ie ss0s,cssees assess cues dvsanqueat) 
 
 At End of Book. 
 
POPULAR ASTRONOMY. 
 
 PART I.—THE SYSTEM OF THE WORLD 
 HISTORICALLY DEVELOPED. 
 
 INTRODUCTION. 
 
 Astronomy is the most ancient of the physical sciences, be- 
 ing distinguished among them by its slow and progressive 
 development from the earliest ages until the. present time. 
 In no other science has each generation which advanced it 
 been so much indebted to its predecessors for both the facts 
 and the ideas necessary to make the advance. The conception 
 of a globular and moving earth pursuing her course through 
 the celestial spaces among her sister planets, which we see as 
 stars, is one to the entire evolution of which no one mind and 
 no one age can lay claim. It was the result of a gradual 
 process of education, of which the subject was not an indi- 
 vidual, but the human race. The great astronomers of all 
 ages have built upon foundations laid by their predecessors ; 
 and when we attempt to search out the first founder, we find 
 ourselves lost in the mists of antiquity. The theory of uni- 
 versal gravitation was founded by Newton upon the laws of 
 Kepler, the observations and measurements of his French con- 
 temporaries, and the geometry of Apollonius. Kepler used 
 as his material the observations of Tycho Brahe, and built 
 upon the theory of Copernicus. When we seek the origin of | 
 the instruments used by Tycho, we soon find ourselves among 
 
Z SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 the medieval Arabs. The discovery of the true system of 
 the world by Copernicus was only possible by a careful study 
 of the laws of apparent motion of the planets as expressed in 
 the epicycles of Ptolemy and Hipparchus. Indeed, the more 
 carefully one studies the great work of Copernicus, the more 
 surprised he will be to find how completely Ptolemy furnished 
 him both ideas and material. If we seek the teachers and 
 predecessors of Hipparchus, we find only the shadowy forms 
 of Egyptian and Babylonian priests, whose names and writings 
 are all entirely lost. In the earliest historic ages, men knew 
 that the earth was round; that the sun appeared to make an 
 annual revolution among the stars; and that eclipses were 
 caused by the moon entering the shadow of the earth, or the 
 earth that of the moon. 
 
 Indeed, each of the great civilizations of the ancient world 
 seems to have had its own system of astronomy strongly 
 marked by the peculiar character of the people among whom 
 it was found. Several events recorded in the annals of China 
 show that the movements of the sun and the laws of eclipses 
 were studied in that country at a very early age. Some of 
 these events must be entirely mythical; as, for instance, the 
 despatch of astronomers to the four points of the compass for 
 the purpose of determining the equinoxes and solstices. But 
 there is another event which, even if we place it in the same 
 category, must be regarded as indicating a considerable amount 
 of astronomical knowledge among the ancient Chinese. We 
 refer to the tragic fate of Hi and Ho, astronomers royal to one 
 of the ancient emperors of that people. It was part of the 
 duty of these men to carefully study the heavenly movements, 
 and give timely warning of the approach of an eclipse or other 
 remarkable phenomenon. But, neglecting this duty, they gave 
 themselves up to drunkenness and riotous living. In conse- 
 quence, an eclipse of the sun occurred without any notice being 
 given ; the religious rites due in such a case were not performed, 
 and China was exposed to the anger of the gods. ‘To appease 
 their wrath, the unworthy astronomers were seized and sum- 
 marily executed by royal command. Some historians have 
 
INTRODUCTION. 3 
 
 gone so far as to fix the date of this occurrence, which is vari- 
 ously placed at from 2128 to 2159 years before the Christian 
 era. If this is correct, it is the earliest of which profane his- 
 tory has left us any record. 
 
 In the Hindoo astronomy we see the peculiarities of the 
 contemplative Hindoo mind strongly reflected. Here the 
 imagination revels in periods of time which, by comparison, 
 dwarf even the measures of the celestial spaces made by mod- 
 ern astronomers. In this, and in perhaps other ancient sys-— 
 tems, we find references to a supposed conjunction of all the 
 planets 8102 years before the Christian era. Although we 
 have every reason for believing that this conjunction was 
 learned, not from any actual record of it, but by calculating 
 back the position of the planets, yet the very fact that they 
 were able to make this calculation shows that the motions of 
 the planets must have been observed and recorded during 
 many generations, either by the Hindoos themselves, or some 
 other people from whom they acquired their knowledge. As 
 a matter of fact, we now know from our modern tables that 
 this conjunction was very far from being exact; but its error 
 could not be certainly detected by the rude observations of the 
 times in question. 
 
 Among a people so prone as the ancient Greeks to speculate 
 upon the origin and nature of things, while neglecting the ob- 
 servation of natural phenomena, we cannot expect to find any- 
 thing that can be considered a system of astronomy. But there 
 are some ideas attributed to Pythagoras which are so frequent- 
 ly alluded to, and so closely connected with the astronomy of 
 a subsequent age, that we may give them a passing mention. 
 He is said to have taught that the heavenly bodies were set 
 in a number of crystalline spheres, in the common centre of 
 which the earth was placed. In the outer of these spheres 
 were set the thousands of fixed stars which stud the firma- 
 ment, while each of the seven planets had its own sphere. The 
 transparency of each crystal sphere was perfect, so that the 
 bodies set in each of the outer spheres were visible through 
 all the inner ones. These spheres all rolled round on each 
 
4 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 other in a daily revolution, thus causing the rising and setting 
 of the heavenly bodies. ‘This rolling of the spheres on each 
 other made a celestial music, the “music of the spheres,” 
 which filled the firmament, but was of too elevated a char- 
 acter to be heard by the ears of mortals. 
 
 It must be admitted that the idea of the stars being set in a 
 hollow sphere of crystal, forming the vault of the firmament, 
 was a very natural one. They seemed to revolve around the 
 earth every day, for generation after generation, without the 
 slightest change in their relative positions. If there were no 
 solid connection between them, it does not seem possible that 
 a thousand bodies could move around their vast circuit for 
 such long periods of time without a single one of them vary- 
 ing its distance from one of the others. It is especially diffi- 
 cult to conceive how they could all move around the same 
 axis. But when they are all set in a solid sphere, every one is 
 made secure in its place. The planets could not be set in the 
 same sphere, because they change their positions among the 
 stars. This idea of the sphericity of the heavens held on to 
 the minds of men with remarkable tenacity. The funda- 
 mental proposition of the system, both of Ptolemy and Ooper- 
 nicus, was that the universe is spherical, the latter seeking to 
 prove the naturalness of the spherical form by the analogy 
 of a drop of water, although the theory served him no pur- 
 pose whatever. Faint traces of the idea are seen here and 
 there in Kepler, with whom it vanished from the mind of the 
 race, as the image of Santa Claus disappears from the mind of 
 the growing child. 
 
 Pythagoras is also said to have taught in his esoteric lect- 
 ures that the sun was the real centre of the celestial move- 
 ments, and that the earth and planets moved around it, and it 
 is this anticipation of the Copernican system which constitutes 
 his greatest glory. But he never thought proper to make a 
 public avowal of this doctrine, and even presented it to his 
 disciples somewhat in the form of an hypothesis. It must 
 also be admitted that the accounts of his system which have 
 reached us are so vague and so filled with metaphysical speen- 
 
An Eminent Astronomer on Sun Spots. 
 Prof. Silas Newcomb to a Washington Reporter, 
 
 “T have no opinion to express on the subject 
 of the tornado * was thereply. “Itis one that 
 requires careful study before satisfactory con- 
 clusions can be reached, and as I hav not given 
 it that study I do not care to theoriazc in the 
 matter.’ 
 
 * You will tell me whether, in your opinion, 
 Spots on the sun eause these disturbances, - ill 
 you not?” asked the reporter, 
 
 “Yes, i will say that there is not the least 
 probability of their being caused by the changes 
 On the sun. Nobody has as yet been able to show 
 any immediate connection between them.” 
 
CHAS. WOLTERS’ 
 
 oat a brewery 
 : Eleventh and Oxiord Sts. 
 
Benjamin PP) Ash- 
 méad, United States Inspector of Drugs 
 aethis port, accused. of’ selling drug, is 
 discharged from Government service 
 by, ‘Secretary MacVeagh. PAGE. 2. 
 Four men are injured in series of. trol- 
 hey accidents in widely separatea parts 
 Mf city. PAGE 2. 
 Striking carmen attack State Railroad 
 mmission as incompetent and pro. 
 s0ses that United Business Men arbi- 
 rate, PAGE 2. 
 John ©’ Donnell, former Recorder of 
 eeds, and: stancl Republican, dies 
 addenly of heart disease. PAGE 2. 
 seth Low attacks. ‘Tran: é 
 or refusal to arbitrate in car 
 
 2S jon ‘or efforts te 
 
 a 
 
 ra came a EO 
 
ENTERTAINMENTS. 
 
 Professor Langley’s Lecture on the Sun, 
 —In the Star Course last evening at the Aca- 
 demy of Music, Prof. S. P. Langley, of the 
 Allegheny Observatory, delivered a most in- 
 teresting lecture on ‘‘The Sun,’’ a subject 
 which he has studied with great success 
 since 1870. The lecture was finely illustrated 
 by photographs of the sun, and of parts of 
 the surface, showing the sun spots and the 
 changes they undergo, and also by drawings 
 made by Prof. Langley, in which were dis- 
 played theaction of the mighty forces which 
 
 | Keep up the circulation thatis the life not 
 | only of the sun but of the earth itself. 
 
 The sun-spots, as presented on the screen, 
 resembied in some respects ice crystals, cir- 
 rhus clouds, delicate lace and nodding 
 plumes, but the lecturer explained that, as 
 seen through the telescope, they were con- 
 stantly changing, and that the effect was 
 that of mighty outbursts of burning gas, 
 drawn inward, as by cyclones, to the dark 
 abysses which appear to us as spotson the 
 
 1 face of the sun. Thesize of these spots was 
 
 graphically shown by a representation of 
 the continents of North andSouth America, 
 
 | drawn to scale upon the picture of a sec- 
 | tion of ‘the sun, this great conti- 
 
 nent appearing as one of the _ least 
 conspicuous spots in the picture, . Prof, 
 Langley said thatthe relation between sun | 
 Spots and magnetic disturbances was not a | 
 mere coihcidence, but had been so often ob- 
 served that astronomers had become accus- 
 tomed to look for magnetic storms whenever 
 
 | they observed an unusual increase in the size | 
 
 or number of the spots. He did not mean to 
 say that the spots caused the magnetic dis- 
 turbances, but that they were ‘‘the outward 
 and visible signs’’ of some disturbance on 
 the sun that was reflected upon the earth, In 
 trying togive the audience some conception 
 of the relative size of the sun and its distance 
 from the earth, he used many illustrations, 
 one of them being that if the sun were a 
 hollow globe, the earth and the moon could 
 be put Inside of it and the moon could still 
 revolve about the earth at its accustomed 
 distance and have one hundred thousand 
 miles togpare, Toillustrate the great heat 
 
 of the sun, he said thatif Pennsylvania had 
 
 coal beds ten feet thick under its entire sur- 
 face, this vast supply, if used as fuel in the 
 sun to produce the heat now evolved, would 
 last only the one nine-hundredth part of a 
 second. 
 
 In discussing, by request, the cause of the 
 prolonged sunsets, Prof. Langley introduced 
 some of the studies he made in the clear at- | 
 mosphere of the Sierra Nevadas, 12,000 feet 
 above the level of thesea, where he extended 
 the study of the solar spectrum far beyond 
 anything heretofore known. He considered 
 that dust in the atmosphere was necessary | 
 to explain the prolongation of the sunset | 
 glow, and, after dismissing the meteoric dust | 
 theories as insufficient to explain the phe- | 
 nomenon, described and _ illustrated the | 
 eruption at Krakatoa last summer, and said | 
 that there was hardiy a doubt that this had | 
 given rise to the dust that enveloped the 
 earth and produced the afterglow. Itis at 
 least known, he said, that such eruptions 
 are capable of producing these results. 
 
 The lecture was delivered in simple terms, 
 and was abundantly and beautifully illus- | 
 
 } trated, 
 
IL LLL LLL LL ODP 
 
 ENTLEMAN, AN 
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 QZOARD W ANTED FOR GENTLE) 
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 YW ANTED—BY YOUNG LADY ENGAGE: 
 VY guring day. board in private familv, withir 
 
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 7 OUNG COUPLY V A. 
 board; siate terms. Address P 19, Ledive 
 Office. F571 
 
 a oral VENDOMF, BROAD) ST.. BELOW 
 & H Arch, opposite Masonic Temple, is now open 
 elegant rooms, table strictly first-cl ss:the loca 
 tion the test; all the modern improvements 
 rooms, with board, $7 to $10 per week; tabie hoard 
 5 per week. pec al! rates to families. =871 
 
 rT ANY CAN i: Op-STORY BACK. WIT! 
 5 Mt. Vernonsiteet. *210 
 
INTRODUCTION. 5 
 
 lation that it is questionable whether the frequent application 
 of his name to the modern system is not more pedantic than 
 justifiable. 
 
 The Greek astronomers of a later age not only rejected the 
 vague speculations of their ancestors, but proved themselves 
 the most careful observers of their time, and first made astron- 
 omy worthy the name of a science. From this Greek astrono- 
 my the astronomy of our own time may be considered as com- 
 ing by direct descent. Still, were it not for the absence of his- 
 toric records, we could probably trace back both their theories 
 and their system of observation to the plains of Chaldea. The 
 zodiac was mapped out and the constellations named many 
 centuries before they commenced their observations, and these 
 works marked quite an advanced stage of development. This 
 prehistoric knowledge is, however, to be treated by the histo- 
 rian rather than the astronomer. If we confine ourselves to 
 men whose names and whose labors have come down to us, 
 we must concede to Hipparchus the honor of being the father 
 of astronomy. Not only do his observations of the heavenly 
 bodies appear to have been far more accurate than those of 
 any of his predecessors, but he also determined the laws of the 
 apparent motions of the planets, and prepared tables by which 
 these motions could be calculated. Probably he was the first 
 propounder of the theory of epicyclic motions of the planets, 
 commonly called after the name of his successor, Ptolemy, who 
 lived three centuries later. 
 
 Commencing with the time of Hipparchus, the general 
 theory of the structure of the universe, or “system of the 
 world,” as it is frequently called, exhibits three great stages of 
 development, each stage being marked by a system quite dif- 
 ferent from the other two in its fundamental principles. ‘These 
 are: 
 
 1. The so-called Ptolemaic system, which, however, really 
 belongs to Hipparchus, or some more ancient astronomer. In 
 this system the motion of the earth is ignored, and the appar- 
 ent motions of the stars and planets around it are all regarded 
 as real. 
 
6 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 2. The Copernican system, in which it is shown that the sun 
 is really the centre of the planetary motions, and that the earth 
 is itself a planet, both turning. on its axis and revolving round 
 the’ sun. 
 
 3. The Newtonian system, in which all the celestial motions : 
 are explained by the one law of universal gravitation. 
 
 This natural order of development shows the order in which 
 a knowledge of the structure of the universe can be most 
 clearly presented to the mind of the general reader. We 
 shall therefore explain this structure historically, devoting a 
 separate chapter to each of the three stages of development 
 which we have described. We commence with what is well 
 known, or, at least, easily seen by every one who will look at 
 the heavens with sufficient care. We imagine the observer 
 out-of-doors on a starlit night, and show him how the heav- 
 enly bodies seem to move from hour to hour. Then, we show 
 him what changes he will see in their aspects if he contin- 
 ues his watch through months and years. By combining the 
 apparent motions thus learned, he forms for himself the an. 
 cient, or Ptolemaic, system of the world. Having this system 
 clearly in mind, the passage to that of Copernicus is but a 
 step. It consists only in showing that certain singular oscilla- 
 tions which the sun and planets seem to have in common are 
 really due to a revolution of the earth around the sun, and 
 that the apparent daily revolution of the celestial sphere arises 
 from a rotation of the earth on its own axis. The laws of 
 the true motions of the planets being perfected by Kepler, 
 they are shown by Newton to be included in the one law of 
 gravitation towards the sun. Such is the course of thought to 
 which we first invite the reader. 
 
~} 
 
 THE CELESTIAL SPHERE. 
 
 CHAPTER I. 
 
 THE ANCIENT ASTRONOMY, OR THE APPARENT MOTIONS OF THE 
 HEAVENLY BODIES. 
 
 §1. The Celestial Sphere. 
 
 Ir is a fact with which we are familiar from infancy, that 
 all the heavenly bodies—sun, moon, and stars—seem to be set 
 in an azure vault, which, rising high over our, heads, curves 
 down to the horizon on every side. Here the earth, on which 
 it seems to rest, prevents our tracing it farther. But if the 
 earth were out of the way, or were perfectly transparent, we 
 could trace the vault downwards on every side to the point 
 beneath our feet, and could see sun, moon, and stars in every 
 direction. The celestial vault above us, with the correspond- 
 ing one below us, would then form a complete sphere, in the 
 centre of which the observer would seem to be placed. This 
 has been known in all ages as the celestial sphere. The direc- 
 tions or apparent positions of the heavenly bodies, as well as 
 their apparent motions, have always been defined by their sit- 
 uation and motions on this sphere. ‘The fact that it is purely 
 imaginary does not diminish its value as enabling us to form 
 distinct ideas of the directions of the heavenly bodies from us. 
 
 It matters not how large we suppose this sphere, so long as 
 we always suppose the observer to be in the centre of it, so 
 that it shall surround him on all sides at an equal distance. 
 But in the language and reasoning of exact astronomy it is 
 always supposed to be infinite, as then the observer may con- 
 ceive of himself as transported to any other point, even to one 
 of the heavenly bodies themselves, and still be, for all practical 
 purposes, in the centre of the sphere. In this case, however, 
 the Tea bodies are not considered as attached to the cir- 
 
8 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 cumference of the infinite sphere, but only as lying on the line 
 of sight extending from the observer to some point of the 
 sphere. ‘Their relation to it may be easily understood by the 
 observer conceiving himself to be luminous, and to throw out 
 rays in every direction to the infinitely distant sphere. Then 
 the apparent positions of the various heavenly bodies will be 
 those in which their shadows strike the sphere. or instance, 
 the observer standing on the earth and looking at the moon, 
 
 Fra. 1.~Section of the imaginary celestial sphere. The observer at O, looking at the 
 stars or other bodies, marked p, q, 7, 8, t, u, v, Will imagine them situated at P, Q, R, S, 
 T, U, V, on the surface of the sphere, where they will appear projected along the 
 straight pP, qQ, etc. 
 the shadow of the latter will strike the sphere at a point on a 
 straight line drawn from the observer’s eye through the centre 
 of the moon, and continued till it meets the sphere. The point 
 of meeting will represent the position of the moon as seen by 
 the observer. Now, suppose the latter transported to the moon. 
 Then, looking back at the earth, he will see it projected on the 
 sphere in a point diametrically opposite to that in which he 
 formerly saw the moon. To whatever planet he might trans- 
 
THE DIURNAL MOTION. 9 
 
 port himself, he would see the earth and the other planets pro- 
 jected on this imaginary sphere precisely as we always seem 
 to see the heavenly bodies so projected. 
 
 This is all that is left of the old crystalline spheres of Py- 
 thagoras by modern astronomy. From being a solid which 
 held all the stars, the sphere has become entirely immaterial, 
 a mere conception of the mind, to enable it to define the di- 
 rections in which the heavenly bodies are seen. By examin- 
 ing the figure it will be clear that all bodies which lie in the 
 same straight line from the observer will appear on the same 
 point of the sphere. For instance, bodies at the three points 
 marked ¢ will all be seen as if they were at 7. 
 
 § 2. The Diurnal Motion. 
 
 If we watch the heavenly bodies for a few hours we shall 
 always find them in motion, those in the east rising upwards, 
 those in the south moving towards the west, and those in the 
 west sinking below the horizon. We know that this motion 
 is only apparent, arising from the rotation of the earth on its 
 axis; but as we wish, in this chapter, only to describe things 
 as they appear, we may speak of the motion as real. A few 
 days’ watching will show that the whole celestial sphere seems 
 to revolve, as on an axis, every day. It is to this revolution, 
 carrying the sun alternately above and below the horizon, that 
 the alternations of day and night are due. The nature and 
 effects of this motion can best be studied by watching the ap- 
 parent movement of the stars at night. We should soon learn 
 from such a watch that there is one point in the heavens, or 
 on the celestial sphere, which does not move at all. In our 
 latitudes this point is situated in the north, between the zenith 
 and the horizon, and is called the pole. Around this pole, as 
 a fixed centre, all the heavenly bodies seem to revolve, each 
 one moving in a circle, the size of which depends on the dis- 
 tance of the body from the pole. There is no star situated 
 exactly at the pole, but there is one which, being situated lit- 
 tle more than a degree distant, describes so small a circle that 
 the unaided eye cannot see any change of place without mak- 
 
10 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 ing some exact and careful observation. This is therefore 
 called the pole star. The pole star can nearly always be very 
 readily found by means of the pointers, two stars of the con- 
 stellation Ursa Major, the Great Bear, or, as it is familiarly 
 called, the Dipper. By referring to the figure, the reader will 
 readily find this constellation, by the dotted line from the pole 
 and thence the pole star, which is near the centre of the map. 
 
 * 
 * ee 
 se EE ie 
 * 
 x * 
 vA * x ‘ * 
 / * aK 
 | a 
 a | 
 sg e * Rene 
 g 
 * 8 * ay is 
 ener a . f ‘ 
 Be Pole % Det 
 — if 2 
 * a ee? Ha fd 
 Ket od A 
 xo Za st 
 
 \ — # 
 
 7 % 
 * 
 ~ 9) a. fs eee Bes % 
 - a tea Sa CaO ath ae EAT Se = ee: as 5 Cerys, . “ 
 Bee A RAs NE Rh eo AR ae ea ates aap Nee 
 iss hesrw eh hl 6oe— aera an are sa nely his ews 
 ph aainaane SSS a as be 
 
 Fig. 2.—Map of the principal stars of the northern sky, showing the constellations which 
 never set in latitude 40°, but revolve round the pole star every day in the direction 
 shown by the arrows. The two lower stars of Ursa Major, on the left of the map, 
 point to the pole star in the centre. 
 
 The altitude of the pole is equal to the latitude of the place. 
 In the Middle States the latitude is generally not far from 
 forty degrees; the pole is therefore a little nearer to the hori- 
 zon than to the zenith. In Maine and Canada it is about half- 
 way between these points, while in England and Northern 
 Europe it is nearer the zenith. 
 
THE DIURNAL MOTION. ha: 
 
 Now, to see the effect of the diurnal motion near the pole, 
 let us watch any star in the north between the pole and the 
 horizon. We shall soon see that, instead of moving from east 
 to west, as we are accustomed to see the heavenly bodies move, 
 it really moves towards the east. After passing the north 
 point, it begins to curve its course upwards, until, in the north- 
 east, its motion is vertical. Then it turns gradually to the 
 west, passing as far above the pole as it did below it, and, sink- 
 ing down on the west of the pole, it again passes under it. 
 The passage above the pole is called the upper culmination, 
 and that below it the lower one. The course around the pole 
 is shown by the arrows on Fig.2. We cannot with the naked 
 eye follow it all the way round, on account of the intervention 
 of daylight; but by continuing our watch every clear night for 
 a year, we should see it in every point of its course. <A star 
 following the course we have described never sets, but may be 
 seen every clear night. If we imagine a circle drawn round 
 the pole at such a distance as just to touch the horizon, all the 
 stars situated within this circle will move in this way; this is 
 therefore called the circle of perpetual apparition. 
 
 As we go away from the pole we shall find the stars mov- 
 ing in larger circles, passing higher up over the pole, and lower 
 down below it, until we reach the circle of perpetual appari- 
 tion, when they will just graze the horizon. Outside this circle 
 every star must dip below the horizon for a greater or less 
 time, depending on its distance. If it be only a few degrees 
 outside, it will set in the north-west, or between north and 
 north-west ; and, after a few hours only, it will be seen to rise 
 again between north and north-east, having done little more 
 than graze the horizon. The possibility of a body rising so 
 soon after having set does not always occur to those who live 
 in moderate latitudes. In July, 1874, Coggia’s comet set in 
 the north-west about nine o’clock in the evening, and rose 
 again about three o’clock in the morning ; and some intelligent 
 people who then saw it east of the pole supposed it could not 
 be the same one that had set the evening before. 
 
 Passing outside the circle of perpetual apparition, we find 
 
12 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 that the stars pass south of the zenith at their upper culmina- 
 tion, that they set more quickly, and that they are a longer 
 time below the horizon. This may be seen in Fig. 3, the por- 
 tion of the sphere to which we refer being between the celes- 
 tial equator and the line ZV. When we reach the equator 
 one-half the course will be above and one-half below the hori- 
 
 x 
 iets Ait ped ah Vee oe eS 
 : * 
 
 O 
 
 HOON ON ISTS £S EES re H EM Seo tive! Rie 
 
 Fira. 3.—The celestial sphere and diurnal motion. Sis the south horizon, N the north hori- 
 zon, Z the zenith. The circle LN around the north pole contains the stars shown in 
 Fig. 2; and the observer at O, in the centre of the sphere, looking to the north, sees the 
 stars as they are depicted in that figure. The arrows show the direction of the diurnal 
 motion in the west. 
 
 zon. South of the equator the circles described by the stars 
 become smaller once more, and more than half their course is 
 below the horizon. Near the south horizon the stars only show 
 themselves above the horizon for a short time, while below it 
 there is a circle of perpetual disappearance, the stars in which, 
 to us, never rise at all. This circle is of the same magnitude 
 
MOTION OF THE SUN AMONG THE STARS. 13 
 
 with that of perpetual apparition, and the south pole is situated 
 in its centre, just as the north pole is in the centre of the other. 
 
 If we travel southward we find that the north pole gradually 
 sinks towards the horizon, while new stars come into view above 
 the south horizon ; consequently the circles of perpetual appari- 
 tion and of perpetual disappearance both grow smaller. When 
 we reach the earth’s equator the south pole has risen to the 
 south horizon, the north pole has sunk to the north hori- 
 zon; the celestial equator passes from east to west directly 
 overhead; and all the heavenly bodies in their diurnal revolu- 
 tions describe circles of which one half is above and the other 
 half below the horizon. These circles are all vertical. 
 
 South of the equator only the south pole is visible, the north 
 one, which we see, being now below the horizon». Beyond the 
 southern tropic the sun is north at noon, and, instead of mov- 
 ing from left to right, its course is from right to left. 
 
 The laws of the diurnal motion which we have described 
 may be summed up as follows: 
 
 1. The celestial sphere, with the sun, moon, and stars, seems 
 to revolve daily around an inclined axis passing through the 
 point where we may chance to stand. 
 
 2. The upper end of this axis points (in this hemisphere) to 
 the north pole; the other end passes into the earth, and points 
 to the south pole, which is diametrically opposite, and therefore 
 below the horizon. 
 
 3. All the fixed stars during this revolution move together, 
 keeping at the same distance from each other, as if the revolv- 
 ing celestial sphere were solid, and they were set in it. 
 
 4, The circle drawn round the heavens half-way between 
 the two poles being the celestial equator, all bodies north of 
 this equator perform more than half their revolution above 
 the horizon, while south of it less than half is above it. 
 
 § 3. Motion of the Sun among the Stars. 
 
 The most obvious classification of the heavenly bodies which 
 we see with the naked eye is that of sun, moon, and stars. 
 But there is also this difference among the stars, that while the 
 
14. SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 great mass of them preserve the same relative position on the 
 celestial sphere, year after year and century after century, there 
 ,are five which constantly change their positions relatively to 
 the others. Their names are Mercury, Venus, Mars, Jupiter, 
 and Saturn. These five, with the sun and moon, constitute the 
 seven planets, or wandering stars, of the ancients, the motions 
 of which are next to be described. Taking out the seven 
 planets, the remaining heavenly bodies visible to the naked 
 eye are termed the Hixed Stars, because they have no appar- 
 ent motion, except the regular diurnal revolution described in 
 the last section. But if we note the positions of the sun, 
 moon, and planets among the stars for a number of successive 
 nights, we shall find certain slow changes among them which 
 we shall now describe, beginning with the sun. In studying 
 this description, the reader must remember that we are not 
 seeking for the apparent diurnal motion, but only certain 
 much slower motions of the planets relative to the fixed stars, 
 such as would be seen if the earth did not rotate on its axis. 
 If we observe, night after night, the exact hour and minute 
 at which a star passes any point by its diurnal revolution, we 
 shall find that passage to occur some four minutes earlier 
 every evening than it did the evening before. The starry 
 sphere therefore revolves, not in 24 hours, but in 23 hours 
 56 minutes. In consequence, if we note its position at the 
 same hour night after night, we shall find it to be farther and 
 farther to the west. Let us take, for example, the brightest 
 star in the constellation Leo, represented on Map IIL, and 
 commonly known as Regulus. If we watch it on the 22d of. 
 March, we shall find that it passes the meridian at ten o’clock 
 in the evening. On April 22d it passes at eight o’clock, and 
 at ten it is two hours west of the meridian. On the same day 
 of May it passes at six, before sunset, so that it cannot be seen 
 on the meridian at all. When it first becomes visible in the 
 evening twilight, it will be an hour or more west of the me- 
 ridian. In June it will be three hours west, and by the end of 
 July it will set during twilight, and will soon be entirely lost 
 in the rays of the sun. This shows that during the months in 
 
MOTION OF THE SUN AMONG. THE STARS. 15 
 
 question the sun has been approaching the star from the west, 
 and in August has got so near it that it is no longer visible. 
 
 Carrying forward our computation, we find that on August 
 21st the star crosses the meridian at noon, and therefore at 
 nearly the same time with the sun. In September it crosses 
 at ten in the morning, while the sun is on the eastern side. 
 The sun has therefore passed from the west to the east of the 
 star, and the latter can be seen rising in the morning twilight 
 before the sun. It constantly rises earlier and earlier, and 
 therefore farther from the sun, until February, when it rises 
 at sunset and sets at sunrise; and is therefore directly opposite 
 the sun. In March the star would cross the meridian at ten 
 o’clock once more, showing that in the course of a year the 
 sun and star had resumed their first position. But, while the 
 sun has risen and set 365 times, the star has risen and set 366 
 times, the sun having lost an entire revolution by the slow 
 backward motion we have described. 
 
 If the stars were visible in the daytime (as they would be 
 but for the atmosphere), the apparent motion of the sun among 
 them could be seen in the course of a single day. For in- 
 stance, if we could have seen Regulus rise on the morning of 
 August 20th, 1876, we should have seen the sun a little south 
 
 _ and west of it, the relative position of the sun being as shown 
 
 “by the circle numbered 1 in the figure. i 
 Watching the star all day, we should find CHO 
 that at sunset it was north from the sun, oe oh | 
 as from circle No. 2. The sun would Waeco eas Eatin 
 during the day have moved nearly its own about August 26th of 
 diameter. Next morning we should have "°°" 
 seen that the sun had gone past the star into position 3, so 
 that the latter would now rise before the former. By sun- 
 set it would have advanced to position 4, and so forth. The 
 path which the sun describes among the stars in his annual 
 revolution is called the ecliptic. It is marked down on Maps 
 I]., IL, 1V.,and V., and the months in which the sun passes 
 through each portion of the ecliptic are also indicated. A 
 belt of the heavens, extending a few degrees on each side of 
 
16 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 the ecliptic, is called the zodiac. The poles of the ecliptic are 
 two opposite points, each in the centre of one of the two hemi- 
 spheres into which the ecliptic divides the celestial sphere. 
 
 The determination of the solar motion around the ecliptic 
 may be considered the birth of astronomical science. The 
 prehistoric astronomers divided the ecliptic and zodiac into 
 twelve parts, now familiarly known as the signs of the zodiac. 
 This proceeding was probably suggested by the needs of agri- 
 culture, and of the chronological reckoning of years. A very 
 little observation would show that the changes of the seasons 
 are due to the variations in the meridian altitude of the sun, 
 and in the length of the day; but it was only by a careful 
 study of the position of the ecliptic, and the motion of the sun 
 in it, that it could be learned how these variations in the daily 
 course of the sun were brought about. This study showed 
 that they were due to the fact that the ecliptic and equator 
 did not coincide, but were inclined to each other at an angle 
 of between twenty-three and twenty-four degrees. This in- 
 clination is known as the obliquity of the ecliptic. The two 
 circles, equator and ecliptic, cross each other at two opposite 
 points, the positions of which among the stars may be seen by 
 reference to Maps IJ.-V. When the sun is at either of 
 these points, it rises exactly in the east, and sets exactly in the 
 west; one-half its diurnal course is above the horizon, and the 
 other half below. The days and nights are therefore of equal 
 length, from which the two points in question are called the 
 Lquinoxes. 
 
 The vernal equinox is on the right-hand edge of Map II. 
 Leaving that equinox about March 21st, the sun crosses over 
 the region represented by the map in the course of the next 
 three months, working northward as it does so, until June 20th, 
 when it is on the left-hand edge of the map, 233° north of the 
 equator. This point of the ecliptic is called the summer solstice, 
 being that in which the snn attains its greatest northern declina- 
 tion. When near this solstice, it rises north of east, culmi- 
 nates at a high altitude (in our latitudes), and sets north of 
 west. As explained in describing the diurnal motion of an 
 
MOTION OF THE SUN AMONG THE STARS. 17 
 
 object north of the celestial equator, more than half the daily 
 course of the sun is now above our horizon, so that our days 
 are longer than our nights, while the great meridian altitude 
 of the sun produces the heats of summer. 
 
 The portion of the ecliptic represented on Map IL. com- 
 mencing at the vernal equinox, where the sun crosses the equa- 
 tor, was divided by the early astronomers into the three signs 
 of Aries, the Ram; Taurus, the Bull; and Gemini, the Twins. 
 It will be seen that these signs no longer coincide with the 
 constellations of the same name: this is owing to a change in 
 the position of the equator, which will be described presently. 
 
 Turning to Map III., we see that during the three months, 
 from June to September, the sun works downwards towards 
 the equator, reaching it about September 20th. The point of 
 crossing marks the autumnal equinox, found also on the right 
 hand of Map IV. The days and nights are now once more of 
 equal length. 
 
 During the next six months the sun is passing over the re- 
 gions represented on Maps IV. and V., and is south of the 
 equator, its greatest southern declination, or “the southern 
 solstice,’ being reached about December 21st. More than 
 half its daily course is then below the horizon, so that in our 
 latitudes the nights are longer than the days, and the low 
 noonday altitude of the sun gives rise to the colds of winter. 
 
 We have no historic record of this division of the zodiac 
 into signs, and the ideas of the authors can only be inferred 
 from collateral circumstances. It has been fancied that the 
 names were suggested by the seasons, the agricultural opera- 
 tions,and so on. Thus the spring signs (Aries, the Ram; Tan- 
 rus, the Bull; and Gemini, the Twins) are supposed to mark the 
 bringing forth of young by the flocks and herds. Cancer, the 
 Crab, marks the time when the sun, having attained its great- 
 est declination, begins to go back towards the equator; and the 
 crab having been supposed to move backwards, his name was 
 given to this sign. Leo, the Lion, symbolizes the fierce heat — 
 of summer; and Virgo, the Virgin, gleaning corn, symbolizes 
 the harvest. In Libra, the Balance, the day and night balance 
 
18 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 each other, being of equal length. Scorpius, the Scorpion, is 
 supposed to have marked the presence of venomous reptiles in 
 October; while Sagittarius, the Archer, symbolizes the season 
 of hunting. The explanation of Capricornus, the Goat, is more 
 fanciful, if possible, than that of Cancer. It was supposed that 
 this animal, ascending the hill as he feeds, in order to reach 
 the grass more easily, on reaching the top, turns back again, so 
 that his name was used to mark the sign in which the sun, 
 from going south, begins to return to the north. Aquarius, 
 the Water-bearer, symbolizes the winter rains; and Pisces, the 
 Fishes, the season of fishes. 
 
 All this is, however, mere conjecture; the only coincidences 
 at all striking being Virgo and Libra. The names of the con- 
 stellations were probably given to them several centuries, per- 
 haps even thousands of years, before the Christian era; and in 
 that case the zodiacal constellations would not have correspond- 
 ed to the seasons we have indicated. An attempt has even been 
 made to show that the names of the zodiacal constellations were 
 intended to commemorate the twelve labors of Hercules; but 
 this theory rests on no better foundation than the other. 
 
 The zodiacal constellations occupy quite unequal spaces in 
 the heavens, as may be seen by inspection of the maps. In 
 the beginning they were simply twelve houses for the sun, 
 which that luminary occupied in the course of the year. Hip- 
 parchus found this system entirely insuflicient for exact astron- 
 omy, and therefore divided the ecliptic and zodiac into twelve 
 equal parts, of 30° each, called signs of the zodiac. He gave 
 to these signs the names of the constellations most nearly cor- 
 responding to them. Commencing at the vernal equinox, the 
 first are of 30° was called the sign Aries, the second the sign 
 Taurus, and so forth. The mode of reckoning positions on 
 the ecliptic by signs was continued until the last century, but 
 is no longer in use among professional astronomers, owing to 
 its inconvenience. The whole ecliptic is now divided into 
 360°, like any other circle, the count commencing at the vernal 
 equinox, and following the direction of the sun’s motion all the 
 way round to 360°. 
 
PRECESSION OF THE EQUINOXES. 19 
 
 § 4. Precession of the Equinoxes.—The Solar Year. 
 
 By comparing his own observations with those of preceding 
 astronomers, Hipparchus found that the equinoxes were slowly 
 shifting their places among the stars, the change being at least 
 a degree in a century towards the west. His successors deter- 
 mined it with greater exactness, and it is now known to be 
 nearly a degree in seventy years. Careful study of the change 
 shows that it is due mainly to a motion of the equator, which 
 again arises from a change in the direction of the pole. The 
 position of the ecliptic among the stars varies so slowly that the 
 change can be seen only by the refined observations of modern 
 times. In the explanation of the diurnal motion, it was stated 
 that there was a certain point in the heavens around which all 
 the heavenly bodies seem to perform a daily revolution. This 
 point, the pole of the heavens, is marked on the centre of Map 
 I., and is also in the centre of Fig. 2, page 10. It is little more 
 than a degree distant from the pole star. Now, precession real- 
 ly consists in a very slow motion of this pole around the pole 
 of the ecliptic, the rate of motion being such as to carry it all 
 the way round in about 25,3800 years. The exact time has 
 never been calculated, and would not always be the same, ow- 
 ing to some small variations to which the motion is subject; 
 but it will never differ much from this. There is a very slight 
 motion to the ecliptic itself, and therefore to its pole; and this 
 fact renders the motion of the pole of the equator around it 
 ~ somewhat complicated; but the curve described by the latter 
 is very nearly a circle 46° in diameter. In the time of Hip- 
 parchus, our present pole star was 12° from the pole. The pole 
 has been approaching it steadily ever since, and will continue 
 to approach it till about the year 2100, when it will slowly 
 pass by it at the distance of less than half a degree. The 
 course of the pole during the next 12,000 years is laid down 
 on the map, and it will be seen that at the end of that time 
 it will be near the constellation Lyra. Since the equator is 
 always 90° distant from the pole, there will be a correspond- 
 ing motion to it, and hence to the point of its crossing the 
 
20 »=69SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 ecliptic. To show this, the position of the equator 2000 years 
 avo, as well as its present position, is given on Map II. 
 
 The reader will, of course, understand that the various ce- 
 lestial movements of which we have spoken in this chapter are 
 only apparent motions, and are due to the motion of the earth 
 itself, as will be explained in the chapter on the Copernican 
 system. The diurnal revolution of the celestial sphere is due 
 to the rotation of the earth on its axis, while precession is real- 
 ly a change in the direction of that axis. 
 
 One important effect of precession is that one revolution of 
 the sun among the stars does not accurately correspond to the 
 return of the same seasons. The latter depend upon the posi- 
 tion of the sun relative to the equinox, the time when the sun 
 crosses the equator towards the north always marking the sea- 
 son of spring (in the northern hemisphere), no matter where 
 the sun may be among the stars. If the equator did not move, 
 the sun would always cross it at nearly the same point among 
 the stars. But when, starting from the vernal equinox, it 
 makes the circuit of the heavens, and returns to it again, the 
 motion of the equator has been such that the sun crosses it - 
 20 minutes before it reaches the same star. In one year, this 
 difference is very small; but by its constant accumulation, at 
 the rate of 20 minutes a year, it becomes very considerable 
 after the lapse of centuries. We must, therefore, distinguish 
 between the sidereal and the tropical year, the former being 
 the period required for one revolution of the sun among the 
 stars, the latter that required for his return to the same equi- 
 nox, whence it is also called the equinoctial year. The exact 
 lengths of these respective years are: 
 
 Days. Days. Hours. Min. Sec. 
 pitkereal | VEAars «cashews smeeeeeeete cassie 365.256386 = 365 6 9 9 
 BLEODICAL VOR... \suubapetee gh seuss tokce ee 365.24220 = 865 6& 48 46 
 
 Since the recurrence of the seasons depends on the tropical 
 year, the latter is the one to be used in forming the calendar, 
 and for the purposes of civil life generally. Its true length is 
 11 minutes 14 seconds less than 8654 days. Some results of 
 this difference will be shown in explaining the calendar. 
 
THE MOON. 21 
 
 § 5. The Moon’s Motion. 
 
 Every one knows that the moon makes a revolution in the 
 celestial sphere in about a month, and that during its revolu- 
 tion it presents a number of different phases, known as “new 
 moon,” “first quarter,’ “full moon,” and so on, depending 
 on its position relative to the sun. A study of these phases 
 during a single revolution will make it clear that the moon is 
 a globular dark body, illuminated by the light of the sun, a 
 fact which has been evident to careful observers from the re- 
 motest antiquity. This may be illustrated by taking a large 
 globe to represent the moon, painting one half white, to rep- 
 resent the half on which the sun shines, and the other half 
 dark. Viewing it at a proper distance, and turning it into 
 different positions, it will be found that the visible part of the 
 white half may be made to imitate the various appearances of 
 the moon. 
 
 As the sun makes a revolution around the celestial sphere 
 in a year, so the moon makes a similar revolution among the 
 stars in a little more than 27 days. This motion can be seen 
 on any clear night between first quarter and full moon, if the 
 moon happens to be near a bright star. If the position of the 
 moon relatively to the star be noted from hour to hour, it will 
 be found that she is constantly working towards the east by a 
 distance equal to her own diameter in an hour. The follow- 
 ing night she will be found from 12° to 14° east of the star, 
 and will rise, cross the meridian, and set from half an hour to 
 an hour later than she did the preceding night. At the end 
 of 27 days 8 hours, she will be back in the same position 
 among the stars in which she was first seen. 
 
 If, however, starting from one new moon, we count forwards 
 this period, we shall find that the moon, although she has re- 
 turned to the same position among the stars, has not got back 
 to new moon again. The reason is that the sun has moved 
 forwards, in virtue of his apparent annual motion, so far that 
 it will require more than two days for the moon to overtake 
 him. So, although the moon really revolves around the earth 
 
22 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 in 274 days, the average interval between one new moon and 
 the next is 294 days. 
 
 A comparison of the phases of the moon with her direction 
 will show that the sun is many times more distant than the 
 moon. In Fig. 5, let / be the position of an observer on the 
 earth, JZ the moon, and S the sun, illuminating one half of it. 
 When the observer sees the moon in her first quarter—that is, 
 when her disk appears exactly half illuminated—the angle at 
 
 ki ee ae a ee i a Rs Pe ae pe a a ae es re ee ee 
 
 Fig. 5.—Showing the sun to be farther than the moon. 
 
 the moon, between the observer and the sun, must be a right 
 angle. If the sun were only about four times as far as the 
 moon, as in the figure, the observer, by measuring the angle 
 SEM between the sun and moon, would find it to be 75°; and 
 the nearer the sun, the smaller he would find it. But actual 
 measurement would show it to be so near 90° that the dif- 
 ference would be imperceptible with ordinary instruments. 
 Hence, the sun is really at the point where the dotted line and 
 the line ZS continued meet each other, which is many times 
 the distance /'/ to the moon. 
 
 This idea was applied by Aristarchus, who flourished in’ the 
 third century before Christ, preceding both Hipparchns and 
 Ptolemy, to determine the distance of the sun, or, more ex- 
 actly, how many times it exceeded the distance of the moon. - 
 He fonnd, by measurement, that, in the position represented 
 in the figure, the distance between the directions of the sun 
 and moon was 87°, and that the sun was therefore something 
 like twenty times as far as the moon. We now know that this 
 result was twenty times too small, the angle being really so 
 near 90° that Aristarchus could not determine the difference 
 with certainty. In principle, the method is quite correct, and 
 
THE MOON. 28 
 
 very ingenious, but it cannot be applied in practice. The one 
 insuperable difficulty of the method arises from the impossi- 
 bility of seeing when the moon is exactly half illuminated, 
 the uncertainty arising from the inequalities in the lunar sur- 
 face being greater than the whole angle to be measured. 
 
 Watching and mapping down the path of the moon among 
 the stars, it is found not to be the same with that of the sun, 
 being inclined to it about 5°. The paths cross each other in 
 two opposite points of the heavens, called the moon’s nodes. 
 The path of the moon in the middle of the year 1877 is 
 marked on star Maps Il—V. Referring to Map IIL, it will 
 be seen that the descending node of the moon is in the con- 
 stellation Leo, very near the star Regulus. Here the moon 
 passes south of or below the ecliptic, and continues below it 
 over the whole of Map IV. On Map V., it approaches the 
 ecliptic again, crossing to the north of it in the constellation 
 Aquarius, and continuing on that side till it reaches Regulus 
 once more. 
 
 Such is the moon’s path in July, 1877. But it is con- 
 stantly changing in consequence of a motion of the nodes 
 towards the west, amounting to more than a degree in every 
 revolution. In order that the line drawn on the map may 
 continue to represent the path of the moon, we must suppose 
 it to slide along the ecliptic towards the right at the rate of 
 about 20° a year, so that a slightly different path will be de- 
 scribed in every monthly revolution. The path will always 
 cross the ecliptic at the same angle, but the moon will not 
 always pass over the same stars. In August, 1877, she will 
 cross the ecliptic a little farther to the right (west), and will 
 pass a little below Regulus. The change going on from 
 month to month and from year to year, in a little less than 
 ten years the ascending node will be found in Leo; and the 
 other node, now. in Leo, will have gone back to Aquarius. 
 In a period of eighteen years and seven months, the nodes 
 will have made a complete revolution, and the path of the 
 moon will have resumed the position given on the map. 
 
24 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 § 6. Lelipses of the Sun and Moon. 
 
 The early inhabitants of the world were, no doubt, terrified 
 by the occasional recurrence of eclipses many ages before 
 there were astronomers to explain their causes. But the mo- 
 tions of the sun and moon could not be observed very long 
 without the causes being seen. It was evident that if the 
 moon should ever chance to pass between the earth and the 
 sun, she must cut off some or all of his light. If the two bodies 
 followed the same track in the heavens, there would be an 
 eclipse of the sun every new moon; but, owing to the ineli- 
 nation of the two orbits, the moon will generally pass above 
 or below the sun, and there will be no eclipse. If, however, 
 the sun happens to be in the neighborhood of the moon’s node 
 when the moon passes, then there will be an eclipse. For an 
 example, let us refer to Map III. We see that the sun passes 
 the moon’s descending node about August 25th, 1877, and is 
 within 20° of this node from early in August till the middle 
 of September. The moon passes the sun on August 8th and 
 September 6th of that year, which are, therefore, the dates of 
 new moon. At the first date, the moon passes so far to the 
 north that, as seen from the centre of the earth, there is no 
 eclipse at all; but in the northern part of Asia the moon 
 would be seen to cut off a small portion of the sun. 
 
 While the moon is performing another circuit, the sun has 
 moved so far past the node, that the moon passes south of it, 
 and there is only a small eclipse, and that is visible only 
 around the region of Cape Horn. Thus, there are two solar 
 eclipses while the sun is passing this node in 1877, but both 
 are very small. Indeed, every time the sun crosses a node, 
 the moon is sure to cross his path, either before he reaches 
 the node, or before he gets far enough from it to be out of 
 the way. As he crosses both nodes in the course of the year, 
 there must be at least two solar eclipses every year to some 
 points of the earth’s surface. 
 
 The cause of Innar eclipses might not have been so easy to 
 guess as was that of solar ones; but a great number could 
 
ECLIPSES OF THE SUN AND MOON. 25 
 
 not have been observed, and their times of occurrence record- 
 ed, without its being noticed that they always occurred at full 
 moon, when the earth was opposite the sun. The idea that 
 the earth cast a shadow, and that the moon passed into it, 
 could then hardly fail to suggest itself; and we find, accord- 
 ingly, that the earliest observers of the heavens were perfectly 
 acquainted with the cause of lunar eclipses. 
 
 The reason why eclipses of the moon only occur occasion- 
 ally is of the same general nature with that of the rare occur- 
 rence of solar eclipses. The centre of the earth’s shadow is 
 always, like the sun, in the ecliptic; and unless the moon hap- 
 pens to be very near the ecliptic, and therefore very near one 
 of her nodes at the time of full moon, she will fail to strike 
 the shadow, passing above or below it. Owing to the great 
 magnitude of the sun, the earth’s shadow is, at the distance of 
 the moon, much smaller than the earth itself. The result of 
 this is, that the moon must be decidedly nearer her node to 
 produce a lunar than to produce a solar eclipse. Sometimes 
 a whole year passes without there being any eclipse of the 
 moon. 
 
 The nature of an eclipse will vary with the positions and 
 apparent magnitudes of the sun and moon. Let us suppose, 
 first, that, in a solar eclipse, the centre of the moon happens 
 to pass exactly over the centre of the sun. Then, it is clear 
 that if the apparent angular diameter of the moon exceed that 
 of the sun, the latter will be entirely hidden from view. This 
 is called a total eclipse of the sun. It is evident that such an 
 eclipse can occur only when the observer is near the line join- 
 ing the centres of ‘the sun and moon. If, under the same cir- 
 cumstances, the apparent magnitude of the moon is less than 
 that of the sun, it is evident that the whole of the latter cannot 
 be covered, but a ring of light around his edge will still be visi- 
 ble. This is called an annular eclipse. If the moon does not 
 pass centrally over the sun, then it can cover only a portion of 
 the latter on one side or the other, and the eclipse is said to be 
 partial. So with the moon: if the latter is only partially im- 
 mersed in the earth’s shadow, the eclipse of the moon is called 
 
26 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 partial ; if she is totally immersed in it, so that no direct sun- 
 light can reach her, the eclipse is said to be total. An an- 
 
 os BY 
 
 Fig. 6.—Annular eclipse of the sun, Fie. 7.—Partial eclipse of the sun, 
 
 nular eclipse of the moon is impossible, because the earth’s 
 shadow always exceeds the diameter of the moon in breadth. 
 Some points respecting eclipses will be seen more clearly 
 by reference to the accompanying figures, in which S repre- 
 sents the sun, / the earth, and J/ the moon. Jeferring to the 
 first figure, it will be seen that an observer at either of the 
 points marked QO, or indeed anywhere outside the shaded por- 
 tions, will see the whole of the sun, so that to him there will 
 be no eclipse at all. Within the lightly shaded regions, marked 
 PP, the sun will be partially eclipsed, and more so as the ob- 
 server is near the centre. This region is called the penumbra. 
 
 Fia. 8.—Eclipse of the sun, the shadow of the moon falling on the earth. 
 
 Within the darkest parts between the two letters P is a region 
 where the sun is totally hidden by the moon. This is the 
 shadow, and its form is that of a cone, with its base on the 
 moon, and its point extending towards the earth. Now, it 
 happens that the diameters of the sun and moon are very 
 nearly proportional to their respective mean distances, so that 
 the point of this shadow almost exactly reaches the surface of 
 the earth. Indeed, so near is the adjustment, that the dark 
 shadow sometimes reaches the earth, and sometimes does not, 
 
ECLIPSES OF THE SUN AND MOON. lb ea 
 
 owing to the small changes in the distance of the sun and 
 moon. When the shadow reaches the earth, it is comparative- 
 ly very narrow, owing to its being so near its sharp point; but 
 if an observer-can station himself within it, he will see a total 
 eclipse of the sun during the short time the shadow is passing 
 over him. If the reader will study the figure, he will see why 
 a total eclipse of the sun is so rare at any one place on the 
 earth. The shadow, when it reaches the earth, is so near down 
 to a point that its diameter is not generally more than a hun- 
 dred miles; consequently, each total eclipse is visible only 
 along a belt which may not average more than a hundred 
 miles across. | 
 
 In most eclipses, the shadow comes to a point before it 
 reaches the earth; in this case, the apparent angular diameter 
 of the moon is less than that of the sun, and there can be no 
 total eclipse. But if an observer places himself in a line with 
 the centre of the shadow, he will see an annular eclipse, the 
 sun showing itself on all sides of the moon. 
 
 The next figure shows us the form of the earth’s shadow. 
 
 Fia. 9.—Eclipse of the moon, the latter being in the shadow of the earth. 
 
 The earth being much larger than the moon, its shadow ex- 
 tends far beyond it; and where it reaches the moon, it is al- 
 ways so much larger than the latter that she may be wholly 
 immersed in it, as shown in the figure. Now, suppose the 
 moon, in her course round the earth, to pass centrally through 
 the shadow, and not above or below it, as she commonly does; 
 then, when she entered the shaded region, marked P, which 
 is called the penumbra, an observer on her surface would see 
 a partial eclipse of the sun caused by the intervention of the 
 
28 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 earth. The time when this begins is given in the almanacs, 
 being expressed by the words, “ Moon enters penumbra.” 
 Some of the sunlight is then cut off from the moon, so that 
 the latter is not so bright as usual; but the eye does not 
 notice any loss of light until the moon almost reaches the 
 dark shadow. As she enters the shadow, a portion of her sur- 
 face seems to be cut off and to disappear entirely, and her vis- 
 ible portion continually grows smaller, until, in case of a total 
 eclipse, her whole disk is immersed in the shadow. When this 
 occurs, it is found that she is not entirely invisible, but still 
 faintly shines with a lurid copper-colored light. This light is 
 refracted into the shadow by the earth’s atmosphere, and its 
 amount may be greater or less, according to the quantity of 
 clouds and vapor in the atmosphere around that belt of the 
 earth which the sunlight must graze in order to reach the moon. 
 
 In about half of the lunar eclipses, the moon passes so far 
 above or below the centre of the shadow that part of her body 
 is in it, and part outside, at the time of greatest eclipse. This 
 is called a partial eclipse of the moon. The magnitude of a 
 partial eclipse, whether of the sun or moon, was measured by 
 the older astronomers in digits. The diameter of the solar or 
 lunar disk was divided into twelve equal parts, called digits ; 
 and the magnitude of the eclipse was said to be equal to the 
 number of digits cut off by the shadow of the earth in case of 
 a lunar eclipse, or by the moon in case of a solar eclipse. The 
 most ancient astronomers were in the habit of measuring the 
 digits by surface: when the moon was said to be eclipsed four 
 digits, it meant that one-third of her surface, and not one- 
 third her diameter, was eclipsed. 
 
 The duration of an eclipse varies between very wide limits, 
 according to whether it is nearly central or the contrary. The 
 duration of a solar eclipse depends upon the time required for 
 the moon to pass over the distance from where she first comes 
 into apparent contact with the sun’s disk, until she separates 
 from it again; and this, in the case of eclipses which are pret- 
 ty large, may range between two and three hours. In a total 
 eclipse, however, the apparent disk of the moon exceeds that 
 
- ECLIPSES OF THE SUN AND MOON. 29 
 
 of the sun by so small an amount, that it takes her but a short 
 time to pass far enough to uncover some part of the sun’s 
 disk; the time is rarely more than five or six minutes, and 
 sometimes only a few seconds. A total eclipse of the moon 
 may, however, last nearly two hours, and the partial eclipses 
 on each side of the total one may extend the whole duration 
 of the eclipse to three or four hours. 
 
 Total eclipses of the sun afford very rare and highly prized 
 opportunities for studying the operations going on around that 
 luminary. Of these we shall speak in a subsequent chapter. 
 
 Returning, now, to the apparent motions of the sun and 
 moon around the celestial sphere, we see that since the moon’s 
 orbit has two opposite nodes in which it crosses the ecliptic, 
 and the sun passes through the entire course ofthe ecliptic in 
 the course of the year, it follows that there are two periods in 
 the course of a year during which the sun is near a node, and 
 eclipses may occur. Roughly speaking, these periods are each 
 about a month in duration, and we may call them seasons of 
 eclipses. Jor instance, it will be seen on Map V. that the 
 sun passes one node of the moon’s orbit towards the end of 
 February, 1877. A season of eclipses for that year is there- 
 fore February and the first half of March. Actually, there is 
 a total eclipse of the moon on February 27th, and a very small 
 eclipse of the sun on March 14th, of that year, visible only in 
 Northern Asia.* From this time, the sun is so far from the 
 node that there can be no eclipses until he approaches the 
 other node in August. Then we have the two eclipses of the 
 sun already mentioned, and, between them, a total eclipse of 
 the moon on August 23d. Thus, in the year 1877, the first 
 season of eclipses is in February and March, and the second 
 in August and September. 
 
 We have said that the length of each eclipse season is about 
 a month. To speak with greater accuracy, the average season 
 for eclipses of the sun extends 18 days before and after the 
 
 * There is an extraordinary coincidence between this eclipse and that of Au- 
 gust 8th of the same year, both being visible from nearly the same region in Cen- 
 tral Siberia. 
 
30 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 sun’s passage through the node, while that for lunar eclipses 
 extends 113 days on each side of the node. ‘The total season 
 is, therefore, 36 days for solar, and 23 days for lunar eclipses. 
 
 Owing to the constant motion of the moon’s node already 
 described, the season of eclipses will not be the same from 
 year to year, but will occur, on the average, abont 20 days 
 earlier each year. We have seen that the sun passed the de- 
 scending node of the moon marked on Map III. on August 
 24th, 1877; but during the year following the node will have 
 moved so far to the west that the sun will again reach it on 
 August 5th, 1878. The effect of this constant shifting of the 
 nodes and seasons of eclipses is that in 1887 the August sea- 
 son will be shifted back to February, and the February season 
 to August. The reader who wishes to find the middle of the 
 eclipse seasons for twenty or thirty years can do so by starting 
 from March ist and August 24th, 1877, and subtracting 19% 
 days for each subsequent year. 
 
 There is a relation between the motions of the sun and 
 moon which materially assisted the early astronomers in the 
 prediction of eclipses. We have said that the moon makes 
 one revolution among the stars in about 274 days. Since the 
 node of the orbit is constantly moving back to meet the moon, 
 as it were, she will return to her node in a little less than this 
 period—namely, as shown by modern observations, in a mean 
 interval of 27.21222 days. The sun, after passing any node 
 of the orbit, will reach the same node again in 346.6201 days. 
 The relation between these numbers is this: 242 returns of 
 the moon to a node take very nearly the same time with 19 
 returns of the sun, the intervals being 
 
 242 returns of the moon to her node..........cecrseeees 6585.357 days ; 
 OMe ‘F.') ‘SUN tO D00N'S MOGGA.,..csreneee ths 6585.780 ‘* 
 
 Consequently, if at any time the sun and moon should start 
 out together from a node, they would, at the end of 6585 
 days, or 18 years and 11 days, be again found together very 
 near the same node. During the interval, there would have 
 been 223 new and full moons, but none so near the node as 
 
fr 
 ‘ 
 
 ECLIPSES OF THE SUN AND MOON. 81 
 
 this. The exact time required for 223 lunations is 6585.3212 
 days; so that, in the case supposed, the 223d conjunction of 
 the sun and moon would happen a little before they reached 
 the node, their distance from it being, by calculation, a little 
 less than one of their diameters, or, more exactly, 28’. If, 
 instead of being exactly at the node, they are any given dis- 
 tance from it, say 3° east or west, then, in the same period, 
 they will be again together within half a degree of the same 
 distance from the node. 
 
 The period just found was called the Saros, and may be ap- 
 plied in this way: Let us note the exact time of the middle 
 of any eclipse, either of the moon or of the sun; then let us 
 count forwards 6585 days, 7 hours, 42 minutes, and we shall 
 find another eclipse of very nearly the same kind. Reduced 
 to years, the interval will be 18 years and 10 or 11 days, ac- 
 cording to whether the 29th of February has intervened four 
 or five times during the interval. This being true of every 
 eclipse, if we record all the eclipses which occur during a 
 period of 18 years, we shall find the same series after 10 or 
 11 days to begin over again; but the new series will not gen- 
 erally be visible at the same places with the old ones, or, at 
 least, will not occur at. the same time of day, since the mid- 
 dle will be nearly eight hours later. Not till the end of three 
 periods will they recur near the same meridian; and then, 
 owing to the period not being exact, the eclipse will not be 
 precisely of the same magnitude, and, indeed, may fail entire- 
 ly. Every successive recurrence of an eclipse at the end of 
 the period being 28’ farther back relatively to the node, the 
 conjunction must, in process of time, be so far back from the 
 node as not to produce an eclipse at all. During nearly every 
 period it will be found that some eclipse fails, and that some 
 new one enters in. A new eclipse of the moon thus entering 
 will be a very small one indeed. At every successive recur- 
 rence of its period it will be larger, until, about its thirteenth 
 recurrence, it will be total. It will be total for about twenty- 
 two or twenty-three recurrences, when it will become partial 
 
 once more, but on the opposite side of the moon from that on 
 C 
 
32. SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 which it was first seen. There will then be about thirteen par- 
 tial eclipses, each smaller than the last, until they fail entirely. 
 The whole interval of time over which the recurrence of a 
 lunar eclipse thus extends will be about 48 periods, or 8654 
 years. ‘The solar eclipses, occurring farther from the node, 
 will last yet longer, namely, from 65 to 70 periods, or over 
 1200 years. 
 
 As a recent example of the Saros, we may cite some total 
 eclipses of the sun well known in recent times; for instance, 
 
 1842, July 8th, 1" 8 a.m., total eclipse, observed in Europe ; 
 
 1860, July 18th, 95 a.m., total eclipse America and Spain ; 
 
 1878, July 29th, 42 2 p.m., one visible in Colorado and on the Pacific Coast. 
 
 A yet more remarkable series of total eclipses of the sun 
 occurs in the years 1850, 1868, 1886, etc., the dates being— 
 
 1850, August 7th, 45 4 p.m., in the Pacific Ocean ; 
 
 1868, August 17th, 12" p.m., in India; 
 
 1886, August 29th, 85 a.m., in the Central Atlantic Ocean and Southern Africa; 
 1904, September 9th, noon, in South America. ; 
 
 This series is remarkable for the long duration of totality, 
 amounting to some six minutes. 
 
 It must be understood that the various numbers we have 
 given in this section are not accurate for all cases, because the 
 motions both of the sun and moon are subject to certain small 
 irregularities which may alter the times of eclipses by an hour 
 or more. We have given only mean values, which are, how- 
 ever, always quite near the truth. 
 
 § 7. The Ptolemaic System. 
 
 There is still extant a work which for fourteen centuries 
 was a sort of astronomical Bible, from which nothing was 
 taken, and to which nothing material in principle was added. 
 This is the “Almagest” of Ptolemy, composed about the mid- 
 dle of the second century of our era. Nearly all we know of 
 the ancient astronomy as a science is derived from it. Frag- 
 ments of other ancient authors have come down to us, and 
 most of the ancient writers make occasional allusions to astro- 
 nomical phenomena or theories, from which various ideas re- 
 
THE PTOLEMAIC SYSTEM. oo 
 
 specting the ancient astronomy have been gleaned; but the 
 work of Ptolemy is the only complete compendium which we 
 possess. Althongh his system is in several important points 
 erroneous, it yet represents the salient features of the apparent 
 motions of the heavenly bodies with entire accuracy. Defec- 
 tive as it is when measured by our standard, it is a marvel of 
 ingenuity and research when measured by the standard of the 
 times. 
 
 The immediate object of the present chapter is to explain 
 the apparent movements of the planets, which can be most 
 easily done on the Ptolemaic system. But, on account of its 
 historic interest, we shall begin with a brief sketch of the 
 propositions on which the system rests, giving also Ptolemy’s 
 method of proving them. His fundamental doctrines are that 
 the heavens are spherical in form, and all the heavenly mo- 
 tions spherical or in circles; that the earth is also spherical, 
 and situated in the centre of the heavens, or celestial sphere, 
 where it remains quiescent, and that it is in magnitude only a 
 point when compared with the sphere of the stars. We shall 
 give Ptolemy’s views of these propositions, and his attempts 
 to prove them, in their regular order. 
 
 Ist. The Heavenly Bodies move in Circles.—Here Ptole- 
 my refers principally to the diurnal motion, whereby every 
 heavenly body is apparently carried around the earth, or, rath- 
 er, around the pole of the heavens, in a circle every day. But 
 all the ancient and medizeval astronomers down to the time 
 of Kepler had a notion that, the circle being the most perfect 
 plane figure, all the celestial motions must take place in cir- 
 cles; and as it was found that the motions were never uni- 
 form, they supposed these circles not to be centred on the 
 earth. Where a single circle did not suffice to account for 
 the motion, they introduced a combination of circular motions 
 in a manner to be described presently. 
 
 2d. The Earth is a Sphere.—That the earth is rounded 
 from east to west Ptolemy proves by the fact that the sun, 
 moon, and stars do not rise and set at the same moment to all 
 the inhabitants of the earth. The times at which eclipses of 
 
34 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 the moon are seen in different countries being compared, it is 
 found that the farther the observer is west, the earlier is the 
 hour after sunset. As the time is really the same everywhere, 
 this shows that the sun sets later the farther we go to the west. 
 Again, if the earth were not rounded from north to south, a 
 star passing the meridian in the north or south horizon would 
 always pass in the horizon, however far to the north or south 
 the observer might travel. But it is found that when an ob- 
 server travels towards the south, the stars in the north ap- 
 proach the horizon, and the circles of their diurnal motion cut 
 below it, while new stars rise into view above the south hori- 
 zon. ‘This shows that the horizon itself changes its direction 
 as the observer moves. Finally, from whatever direction we 
 approach elevated objects from the sea, we see that their bases 
 are first hidden from view by the curvature of the water, and 
 gradually rise into view as we approach them. 
 
 3d. The Harth is in the Centre of the Celestial Sphere.— 
 If the earth were displaced from the centre, there would be 
 various irregularities in the apparent daily motion of the ce- 
 lestial sphere, the stars appearing to move faster on the side 
 towards which the earth was situated. If it were displaced 
 towards the east, we should be nearer the heavenly bodies 
 when they are rising than when they are setting, and they 
 would appear to move more rapidly in the east than in the 
 west. The forenoons would therefore be shorter than the af- 
 ternoons. Towards whatever side of the turning sphere it 
 might be moved, the heavenly bodies would seem to move 
 more rapidly on that side than on the other. No such irreg- 
 ularity being seen, but the diurnal motion taking place with 
 perfect uniformity, the earth must be in the centre of mo- 
 tion. 
 
 4th. The Earth has no Motion of Translation — Because 
 if it had it would move away from the centre towards one 
 side of the celestial sphere, and the diurnal revolution of the 
 stars would cease to be uniform in all its parts. But the uni- 
 formity of motion just described being seen from year to year, 
 the earth must preserve its position in the centre of the sphere. 
 
THE PTOLEMAIC SYSTEM. 3D 
 
 It will be interesting. to analyze these propositions of Ptole- 
 my, to see what is true and what is false. The first proposi- 
 tion — that the heavenly bodies move in circles, or, as it is 
 more literally expressed, that the heavens move spherically— 
 is quite true, so far as the apparent diurnal motion is con- 
 cerned. What Ptolemy did not know was that this motion is 
 only apparent, arising from a rotation of the earth itself on its 
 axis. ‘he second proposition is perfectly correct, and Ptole- 
 my’s proofs that the earth is round are those still found in our 
 school- books at the end of seventeen hundred years. Most 
 curious, however, is the mixture of truth and falsehood in the 
 third and fourth propositions, that the earth remains quies- 
 cent. We cannot denounce it as unqualifiedly false, because, 
 in a certain sense, and indeed in the only sense in which there 
 is any celestial sphere, the earth may be said to remain in the 
 centre of the sphere. What Ptolemy did not see is that this 
 sphere is only an ideal one, which the spectator carries with 
 him wherever he goes. His demonstration that the centre of 
 revolution of the sphere is in the earth is, in a certain sense, ' 
 correct ; but what he really proves is that the earth revolves 
 on its own axis. He did not see that if the earth could carry 
 the axis of revolution with it, his demonstration of the quies- 
 cence of the earth would fall to the ground. 
 
 Considerable insight into Ptolemy’s views is gained by his 
 answers to two objections against his system. ‘The first is the 
 vulgar and natural one, that it is paradoxical to suppose that 
 a body like the earth could remain supported on nothing, and 
 still be at rest. These objectors, he says, reason from what 
 they see happen to small bodies around them, and not from 
 what is proper to the universe at large. There is neither up 
 nor down in the celestial spaces, for we cannot conceive of it 
 in a sphere. What we call down is simply the direction of 
 our feet towards the centre of the earth, the direction in 
 which heavy bodies tend to fall. The earth itself is but a 
 point in comparison with the celestial spaces, and is kept fixed 
 by the forces exerted upon it on all sides by the universe, 
 which is infinitely larger than it, and similar in all its parts. 
 
386 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 This idea is as near an approach to that of universal gravita- 
 tion as the science of the times would admit of. 
 
 He then says there are others who, admitting this reason- 
 ing, pretend that nothing hinders us from supposing that the 
 heavens are immovable, and that the earth itself turns round 
 its own axis once a day from wesf to east. It is certainly 
 singular that one who had risen so far above the illusions of 
 sense as to demonstrate to the world that the earth was round; 
 that up and down were only relative; and that heavy bodies 
 fell towards a centre, and not in some unchangeable direction, 
 should not have seen the correctness of this view. 
 
 To refute the doctrine of the earth’s rotation, he proceeds 
 in a way the opposite of that which he took to refute those 
 who thought the earth could not rest on nothing. He said of 
 the latter that they regarded solely what was around them on 
 the earth, and did not consider what was proper to the un.- 
 verse at large. To those who maintained the earth’s rotation, 
 he says, if we consider only the movements of the stars, there 
 is nothing to oppose their doctrine, which he admits has the 
 merit of simplicity; but in view of what passes around us and 
 in the air, their doctrine is ridiculous. He then enters into a 
 disquisition on the relative motion of light and heavy bodies, 
 which is extremely obscure; but his conclusion is that if the 
 earth really rotated with the enormous velocity necessary to 
 carry it round in a day, the air would be left behind. If they 
 say that the earth carries round the air with it, he replies that 
 this could not be true of bodies floating in the air; and hence 
 concludes that the doctrine of the earth’s rotation is not tena- 
 ble. It is clear, from this argument, that if Ptolemy and his 
 contemporaries had devoted to experimental physics half the 
 careful observation, research, and reasoning which we find in 
 their astronomical studies, they could not have failed to estab- 
 lish the doctrine of the earth’s rotation. 
 
 In the Ptolemaic system, all the celestial motions are repre- 
 sented by a series of circular motions. We have already ex- 
 plained the motions of the sun and moon among the stars, the 
 first describing a complete circuit of the heavens from west to 
 
THE PTOLEMAIC SYSTEM. Si 
 
 east in a year, and the second a similar circuit in a month. 
 Though not entirely uniform, these movements are always for- 
 ward. But it is not so with the five planets— Mercury, Ve- 
 nus, Mars, Jupiter, and Saturn. These move sometimes to the 
 east and sometimes to the west, and are sometimes stationary.* 
 On the whole, however, the easterly movements predominate ; 
 and the planets really oscillate around a certain mean point 
 itself in regular motion towards the east. Let us take, for in- 
 stance, the planet Jupiter. Suppose a certain fictitious Jupi- 
 ter performing a circuit of the heavens among the stars every 
 twelve years with a regular easterly motion, just as the sun 
 performs such a circuit every year; then the real Jupiter will 
 be found to oscillate, like a pendulum, on each side of the fic- 
 titious planet, but never swinging more than 12° trom it. The 
 time of each double oscillation is about thirteen months—that 
 is, if on January Ist we find it passing the fictitious planet 
 towards the west, it will continue its westerly swing about 
 three months, when it will gradually stop, and return with a 
 somewhat slower motion to the fictitious planet again, passing 
 to the east of it the middle of July. The easterly swing will 
 continue till about the end of October, when it will return 
 towards the west. The westerly or backward motion is called 
 retrograde, and the easterly motion direct. Between the two 
 is a point at which the planet appears stationary once more. 
 The westerly motions are called retrograde because they are 
 in the opposite direction both to the motion of the sun among 
 the stars, and to the average direction in which all the planets 
 move. It was seen by Hipparchus, who lived three centuries 
 before Ptolemy, that this oscillating motion could be repre- 
 sented by supposing the real Jupiter to describe a circular or- 
 bit around the fictitious Jupiter once in a year. This orbit is 
 called the epicycle, and thus we have the celebrated epicyclic 
 theory of the planetary motions laid down in the “ Almagest.” 
 The movement of the planet on this theory can be seen by 
 
 * It may not be amiss to remind the reader once more that we here leave the 
 diurnal motion of the stars entirely out of sight, and consider only the motions of 
 the planets relative to the stars. 
 
38 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 Fig. 10. £# is the earth, around which the fictitious Jupiter 
 moves in the dotted circle, 1, 2, 38,4, etc. To form the epicycle 
 in which the real planet moves, we must suppose an arm to be 
 constantly turning ronnd the fictitious planet once a year, on 
 the end of which Jupiter is carried. This arm will then be in 
 the successive positions, 11’, 2 2’, 33’, ete., represented by the 
 light dotted lines. Drawing a line through the successive po- 
 sitions 1’, 2’, 3’, etc., of the real Jupiter, we shall have a series 
 of loops representing its apparent orbit. 
 
 Fia. 10.—Showing the apparent orbit of a planet, regarding the earth as at rest. 
 
 It will be seen that although it requires only a year for the 
 arm carrying the real Jupiter to perform a complete revolu- 
 tion and return to its primitive direction, it requires about 
 thirteen months to form a complete loop, because, owing to 
 the motion of the fictitious planet in its orbit, the arm must 
 move more than a complete revolution to finish the loop. For 
 instance, referring again to Fig. 10, comparing the positions 
 11’ and 88’, it will be seen that the arm, being in the same 
 direction, has performed a complete revolution; but, owing to 
 the curvature of the orbit, it does not reach the middle of the 
 second loop until it attains the position 9 9’. 
 
THE PTOLEMAIC SYSTEM. ah amer 
 
 The planets of which the radius of the epicycle makes an 
 annual revolution in this way are Mars, Jupiter, and Saturn. 
 The complete apparent orbits of the last two planets are shown 
 in the next figure, taken from Arago. By the radius of the 
 epicycle we mean the imaginary revolving arm which, turn- 
 ing round the fictitious planet, carries the real planet at its 
 
 0 
 ot 0% 
 Tryp tr 
 Oe Shoo Pe, oF 
 eal 
 
 I~ 
 Sy gs SAT RN faces 
 
 PE thd (AF 
 a ep 
 
 Fig. 11.—Apparent orbits of Jupiter and Saturn, 1708-1737, after Cassini. 
 
 end. The law of revolution of this arm is, that whenever the 
 planet is opposite the sun, the arm points towards the earth, 
 as in the positions 11’, 9 9’, in which cases the sun will be on 
 the side of the earth opposite the planet; while, whenever the 
 planet is in conjunction with the sun, the arm points from the 
 earth. This fact was well known to the ancient astronomers, 
 and their calculations of the motions of the planets were all 
 
40 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 founded upon it; but they do not seem to have noticed the 
 very important corollary from it, that the direction of the 
 radius of the epicycle of Mars, Jupiter, and Saturn is always 
 the same with that of the sun from the earth. Had they 
 done so, they could hardly have failed to see that the epicycles 
 could be abolished entirely by supposing that it was the earth 
 which moved round the sun, and not the sun round the earth. 
 The peculiarity of the planets Mereury and Venus is that 
 the fictitious centres around which they oscillate are always in 
 the direction of the sun, or, as we now know, the sun himself 
 is the centre of their motions. They are never seen more than 
 a limited distance from that luminary, Venus oscillating about 
 45° on each side of the sun, and Mercury from 16° to 29°. It 
 is said that the ancient Egyptians really did make the sun the 
 centre of the motion of these two planets; and it is difficult to 
 see how any one could have failed to do so after learning the 
 laws of their oscillation. Yet Ptolemy rejected this system, 
 placing their orbits between the earth and sun without assign- 
 ing any good reason for the course. | 
 The arrangement of the planets on the Ptolemaic system is 
 shown in Fig. 12. The nearest planet is the moon, of which 
 the ancient astronomers actually succeeded in roughly meas- 
 uring the distance. The remaining planets are arranged in 
 the same order with their real distance from the sun, except 
 that the latter takes the place assigned to the earth in the 
 modern system. Thus we have the following order : 
 The Moon, 
 Mercury, 
 Venus, 
 The Sun, 
 Mars, 
 Jupiter, 
 Saturn. 
 Outside of Saturn was the sphere of the fixed stars. 
 This order of the planets must have been a matter of opin- 
 ion rather than of demonstration, it being correctly judged 
 by the ancient astronomers that those which seemed to move © 
 
Rly De 
 eC 
 
 Fe 
 
 I 
 
 THE PTOLEMAIC SYSTEM. Al 
 
 Saturn 
 
 Fig. 12.—Arrangement of the seven planets in the Ptolemaic system. The orbits, as 
 marked, are those of the fictitious planets, the real planets being supposed to describe 
 a series of loops. 
 
 more slowly were the more distant. This system made it 
 quite certain that the moon was the nearest planet, and Mars, 
 Jupiter, and Saturn, in their order, the most distant ones. But 
 the relative positions of the Sun, Mercury, and Venus were 
 more in doubt, since they all performed a revolution round 
 the celestial sphere in a year. So, while Ptolemy, as we have 
 just said, placed Mercury and Venus between the earth and 
 the sun, Plato placed them beyond the sun, the order being, 
 Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn. 
 Hipparchus and Ptolemy made a series of investigations re- 
 specting the times of revolution of the planets, and the inequal- 
 ities of their motions, of which it is worth while to give a brief 
 
42 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 summary. The former was no doubt‘an abler astronomer than 
 Ptolemy; but as he was, so far as we know, the first accurate 
 observer of the celestial motions, he could not make a suf- 
 ficiently long series of observations to determine all the peri- 
 ods of the planets. Ptolemy had the advantage of being able 
 to combine his own observations with those of Hipparchus, 
 three centuries earlier. 
 
 Imperfect though their means of observation were, these 
 observers found that the easterly movements of the planets 
 among the stars were none of them uniform. This held true 
 not only of the sun and moon, but of the fictitious planets 
 ele already described. Hence they 
 
 invented the eccentric, and sup- 
 posed the motions to be really cir- 
 cular and uniform, but in circles 
 not centred in the earth. In Fig. 
 
 = 13, let #’ be the earth, and C’ the 
 centre around which the planet 
 really revolves. Then, when the 
 
 planet is passing the point P, 
 which is nearest the earth, its an- 
 gular motion would seem more 
 Se rapid than the average, because 
 Fie. 13.—The eccentric. Shows how . al eet l Alde 
 the ancients represented the unequal in genera the angular ve ocity 
 apparent velocities of the planets of g moving body is greater the 
 when their real motion was supposed = A 7 
 uniform, by placing the earth away Nearer the observer is to it, while 
 pOuLAne Contry Of me Oe eae when passing A it will seem to be 
 more slow than the average. The angular velocity being 
 always greatest in one point of the orbit, and least in a point 
 directly opposite, changing regularly from the maximum to 
 the minimum, the general features of the movement are cor- 
 rectly represented by the eccentric. By comparing the angu- 
 lar velocities in different points of the orbit, Hipparchus and 
 Ptolemy were able to determine the supposed distance of the 
 earth from the centre, or rather the proportion of this distance 
 to the distance of the planet. The distance thus determined 
 
 is double its true amount. The point P is called the Perigee, 
 
THE PTOLEMAIC SYSTEM. 43 
 
 and A the Apogee. The distance C#' from the earth to the 
 centre of motion is the eccentricity. As there was no way of 
 determining the absolute dimensions of the orbit, it was neces- 
 sary to take the ratio of C/ to the radius of the orbit CP or 
 CE for the eccentricity.* 
 
 In determining the motions of the moon, TACO and 
 Ptolemy Bonended almost entirely on ate oa tiote of lunar 
 eclipses. The first of these, it is said, was observed at Babylon 
 in the first year of Mardocempad, between the 29th and 30th 
 days of the Egyptian month Thoth. It commenced a little 
 more than an hour after the moon rose, and was total. The 
 date, in our reckoning, was B.c. 720, March 19th. The series 
 of eclipses extended from this date to that of Ptolemy him- 
 self, who lived between eight and nine centuries'iater. If the 
 observations of these eclipses had been a little more precise, 
 they would still be of great value to us in fixing the mean 
 motion of the moon. As it is, we can now calculate the cir- 
 cumstances of an ancient eclipse from our modern tables of 
 the sun and moon almost as accurately as any of the ancient 
 astronomers could observe it. 
 
 Notwithstanding the extremely imperfect character of the 
 observations, both Hipparchus and Ptolemy made discoveries 
 respecting the peculiarities of the moon’s motions which show 
 a most surprising depth of research. By comparing the inter- 
 vals between eclipses, they found that her motion was not uni- 
 form, but that, like the sun, she moved faster in some parts of 
 her orbit than in others. To account for this, they supposed 
 her orbit eccentric, like that of the sun; that is, the earth, in- 
 stead of being in the centre of the circular orbit of the moon, 
 was supposed to be displaced by about a tenth part the whole 
 distance of that body. So far the orbit of the moon was like 
 that of the sun and the fictitious planets, except that its eccen- 
 tricity was greater. But a long series of observations showed 
 
 * Compared with the modern theory of the elliptic motion, approximately treat- 
 ed, the distance C‘ is double the eccentricity of the ellipse. One-half the appar- 
 ent inequality is really caused by the orbit being at various distances from the 
 earth or sun, but the other half is real. 
 
44. SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 that the perigee and apogee did not, as in the case of the sun 
 and planets, remain in the same points of the orbit, but moved 
 forwards at such a rate as to carry them round the heavens in 
 nine years; that is, supposing Fig. 13 to represent the orbit of 
 the moon, the centre of the circle C revolved round the earth 
 in nine years, and the orbit changed its position accordingly. 
 
 It was also found by Ptolemy, by measuring the apparent 
 angle between the moon and sun in various points of the 
 orbit of the former, that there was yet another inequality in 
 her motion. This has received the name of the evection. In 
 consequence of this inequality, the moon oscillates more than 
 a degree on each side of her position as calculated from the 
 eccentric, in a period not differing much from her revolution 
 round the earth. To represent this motion, Ptolemy had to 
 introduce a small additional epicycle, as in the case of the 
 planets, only the radius was so small that there was no looping 
 of the orbit. In consequence, his theory of the moon’s motion 
 was quite complicated; yet he managed to represent this mo- 
 tion, within the limits of the errors of his observations, by a 
 combination of circular motions, and thus saved the favorite 
 theory of the times, that all the celestial motions were circular 
 and uniform. 
 
 § 8. The Calendar. 
 
 One of the earliest purposes of the study of the celestial 
 motions was that of finding a convenient measurement of 
 time. This application of astronomy, being of great antiquity, 
 having been transmitted to us without any fundamental altera- 
 tion, and depending on the apparent motions of the sun and 
 moon, which we have studied in this chapter, is naturally con- 
 sidered in connection with the ancient astronomy. 
 
 The astronomical divisions of time are the day, the month, 
 and the year. The week is not such a division, because it does 
 not correspond to any astronomical cycle, although, as we shall 
 presently see, a certain astronomical signification was said to 
 have been given to it by the ancient astrologers. Of these 
 divisions the day is the most well-marked and striking through 
 
THE CALENDAR. AD 
 
 out the habitable portion of the globe. Had a people lived at 
 or near the poles, it would have been less striking than the year. 
 But wherever man existed, there was a regular alternation of 
 day and night, with a corresponding alternation in his physical 
 condition, both occurring with such regularity and uniformity 
 as to furnish in all ages the most definite unit of time. For 
 merely chronological purposes the day would have been the 
 only unit of time theoretically necessary; for if mankind had 
 begun at some early age to number every day by counting 
 from 1 forwards without limit, and had every historical event 
 been recorded in connection with the number of the day on 
 which it happened, there would have been far less uncertain- 
 ty about dates than now exists. But keeping count of such 
 large numbers as would have accumulated in the:lapse of cen- 
 turies would have been very inconvenient, and a simple count 
 of time by days has never been used for the purposes of civil 
 life through any greater period than a single month. 
 
 Next to the day, the most definite and striking division of 
 time is the year. The natural year is that measured by the 
 return of the seasons. All the operations of agriculture are 
 so intimately dependent on this recurrence, that man must 
 have begun to make use of it for measuring time long before 
 he had fully studied the astronomical cause on which it de- 
 pends. The years in the lifetime of any one generation not 
 being too numerous to be easily reckoned, the year was found 
 to answer every purpose of measuring long intervals of time. 
 
 The number of days in the year is, however, too great to 
 be conveniently kept count of; an intermediate measure was 
 therefore necessary. This was suggested by the motion and 
 phases of the moon. The “new moon” being seen to emerge 
 from the sun’s rays at intervals of about 30 days, a measure 
 of very convenient length was found, to which a permanent 
 interest was attacheé by the religious rites connected with the 
 reappearance of the moon. 
 
 The week is a division of time entirely disconnected with 
 the month and year, the employment of which dates from the 
 Mosaic dispensation. The old astrologers divided the seven 
 
46 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 days of the week among the seven planets, not in the order of 
 their distance from the sun, but in one shown by the follow- 
 ing figure. If we go round the circle in the direction of the 
 hands of a watch, we shall find the names of the seven plan- 
 ets of the ancient astronomy, in the order of their supposed 
 distances ;* while, if we follow the lines drawn in the circle 
 from side to side, we shall have the days of the week in their 
 order. . 
 
 Fic. 14.—Showing the astrological division of the seven planets among the days of the 
 week. 
 
 If the lunar month had been an exact number of days, say 
 30, and the year an exact number of months, as 12, there | 
 would have been no difficulty in the use of these cycles for 
 the measurement of time. But the former is several hours 
 less than 30 days, while the latter is nearly 125 lunar months. 
 In the attempt to combine these measures, the ancient calen- 
 
 * See pages 40, 41. 
 
THE CALENDAR. 47 
 
 dars were thrown into a confusion which made them very per- 
 plexing, and which we see to this day in the irregular. lengths 
 of our months. ‘To describe all the devices which we know to 
 have been used for remedying these difficulties would be very 
 tedious; we shall therefore confine ourselves to their general 
 nature. 
 
 The lunar month, or the mean interval between successive 
 new moons, is very nearly 293 days. In counting months by 
 the moon, it was therefore common to make their length 29 
 and 30 days, alternately. But the period of 293 days is really 
 about three-quarters of an hour too short. In the course of 
 three years the count will therefore be a day in error, and it 
 will be necessary to add a day to one of the months. When 
 lunar months were used, the year, comprising 12‘such months, 
 would consist of only 354 days, and would therefore be 11 
 days too short. Nevertheless, such a year was used both by 
 the Greeks and Romans, and is still used by the Mahome- 
 tans; the Romans, however, in the calendar of Numa, adding 
 22 or 28 days to every alternate year by inserting the inter- 
 calary month Jlercedonius between the 23d and 24th of Feb- 
 ruary. , 
 
 The irregularity and inconvenience of reckoning by lunar 
 months caused them to be very generally abandoned, the only 
 reason for their retention being religions observances due at 
 the time of new moon, which, among the Jews and other an- 
 cient nations, were regarded as of the highest importance. Ac- 
 cordingly, we find the Egyptians counting by months of 30 
 days each, and making every year consist’of 12 such months 
 and five additional days, making 365 days in all. As the true 
 length of the year was known to be about six hours greater 
 than this, the equinox would occur six hours later every year, 
 and a month later after the lapse of 120 years. After the lapse 
 of 1460 years, according to the calculations of the time, each 
 season would have made a complete course through the twelve 
 months, and would then have returned once more at the same 
 time of year as in the beginning. This was termed the Sothze 
 
 Period; but the error of each year being estimated a little 
 5 
 
48 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 too great, as we now know, the true length of the period 
 would have been about 1500 years. 
 
 The confusion in the Greek year was partly remedied 
 through the discovery by Meton of the cycle which has since 
 borne his name. ‘This cycle consists of 19 solar years, during 
 which the moon changes 235 times. The error of this cycle 
 is very small, as may be seen from the following periods, com- 
 puted from modern data: 
 
 Days. Hours. Min. 
 
 235 lunations require in the MEAN..........ccececseccsrseves G9389 16) 181 
 19 tre solar years (tropical )..cs-s-csec.caese mene eree eee 69390 "14 7 227 
 PO onian years'of B65) Uays, ac <sesssnrepeensspseutonsnses 6959" | 18 0 
 
 Hence, if we take 235 lunar months, and divide them up as 
 nearly evenly as is convenient into 19 years, the mean length 
 of these years will be near enough right for all the purposes 
 of civil reckoning. The years of each cycle were numbered 
 from 1 to 19, and the number of the year was called the Gold- 
 en Number, from its having been ordered to be inscribed on 
 the monuments in letters of gold. 
 
 This is the only religious festival which, in Christian coun- 
 tries, depends directly on the motion of the moon. The rule 
 for determining Easter is that it is the Sunday following the 
 first full moon which occurs on or after the 21st of March. 
 The dates of the full moon correspond to the Metonic Cycle ; 
 that is, after the lapse of 19 years they recur on or about the 
 ‘same day of the year. Consequently, if we make a list of the 
 dates on which the Paschal full moon occurs, we shall find 
 no two dates to bé the same for nineteen successive years; 
 but the twentieth will occur on the same day with the first, 
 or, at most, only one day different, and then the whole series 
 will be repeated. Consequently, the Golden Number for the 
 year shows, with sufficient exactness for ecclesiastical purposes, 
 on what day, or how many days after the equinox, the Paschal 
 full moon occurs. The church calculations of Easter Sunday 
 are, however, founded upon very old tables of the moon, so 
 that if we fed it by the actual moon, we should often find 
 the calendar feast a week in error. 
 
THE CALENDAR. 49 
 
 The basis of the calendars now employed throughout Chris 
 tendom was laid by Julius Cesar. Previous to his time, the 
 Roman calendar was in a state of great confusion, the nomi- 
 nal length of the year depending very largely on the caprice 
 of the ruler for the time being. It was, however, very well 
 known that the real length of the solar year was about 3654 
 days; and, in order that the calendar year might have the same 
 mean length, it was prescribed that the ordinary year should 
 consist of 3865 days, but that one day should be added to every 
 fourth year. The lengths of the months, as we now have them, 
 were finally arranged by the immediate successors of Czesar. 
 
 The Julian calendar continued unaltered for about sixteen 
 centuries; and if the true length of the tropical year had been 
 3654 days, it would have been in use still. But, as we have 
 seen, this period is about 114 minutes longer than the solar 
 year, a quantity which, repeated every year, amounts to an en- 
 tire day in 128 years. Consequently, in the sixteenth century, 
 the equinoxes occurred 11 or 12 days sooner than they should 
 have occurred according to the calendar, or on the 10th in- 
 stead of the 21st of March. To restore them to their original 
 position in the year, or, more exactly, to their position at the 
 time of the Council of Nice, was the object of the Gregorian 
 reformation of the calendar, so called after Pope Gregory 
 XIIL, by whom it was directed. The change consisted of 
 two parts: 
 
 1. The 5th of October, 1582, aceording to the Julian calen- 
 dar, was called the 15th, the count ae thus advanced 10 
 days, and the equinoxes made once more to occur about March 
 21st and September 21st. 
 
 2. The closing year of each century, 1600, 1700, ete., in- 
 stead of being each a leap-year, as in the Julian calendar, 
 should be such only when the number of the century was di- 
 visible by 4. While 1600, 2000, 2400, etc., were to be leap- 
 years, as before, 1700, 1800, 1900, 2100, etc., were to be re- 
 duced to 365 days each. | 
 
 This change 1 in the calendar was soon adopted by the Catho- 
 lic countries, and, more slowly, by Protestant ones—England, 
 
50 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 among the latter, holding out for more than a century, but 
 finally entering into the change in 1752. In Russia it was 
 never adopted at all, the Julian calendar being still continucd 
 in that country. Consequently, the Russian reckoning is now 
 12 days behind ours, the 10 days’ difference during the six- 
 teenth and seventeenth centuries being increased by the days 
 dropped from the years 1700 and 1800 in the new reckoning. 
 
 The length of the mean Gregorian year is 3654 5 49™ 19s; 
 while that of the tropical year, according to the best astronom- 
 ical determination, is 3654 55 48™ 46s. The former is, there- 
 fore, still 26 seconds too long, an error which will not amount 
 to an entire day for more than 3000 years. If there were 
 any object in having the calendar and the astronomical years 
 in exact coincidence, the Gregorian year would be accurate 
 enough for all practical purposes during many centuries. In 
 fact, however, it is difficult to show what practical object is to 
 be attained by seeking for any such coincidence. It is im- 
 portant that summer and winter, seed-time and harvest, shall 
 occur at the same time of the year through several successive 
 generations; but it is not of the slightest importance that 
 they should occur at the same time now that they did 5000 
 years ago, nor would it cause any difficulty to our descendants 
 of 5000 years hence if the equinox should occur in the middle 
 of February, as would be the case. should the Julian calendar 
 have been continued. 
 
 The change of calendar met with much popular opposition, 
 and it may hereafter be conceded that in this instance the 
 common sense of the people was more nearly right than the 
 wisdom of the learned. An additional complication was in- 
 troduced into the reckoning of time without any other real 
 object than that of making Easter come at the right time. 
 As the end of the century approaches, the question of making 
 1900 a leap-year, as usual, will no doubt be discussed, and it is 
 possible that some concerted action may be taken on the part of 
 leading nations looking to a return to the old mode of reckoning. 
 
COPERNICUS. 51 
 
 CHARTER: IT. 
 
 THE COPERNICAN SYSTEM, OR THE TRUE MOTIONS OF THE HEAV- 
 ENLY BODIES. 
 
 § 1. Copernicus. 
 
 In the first section of the preceding chapter we described 
 the apparent diurnal motion of the heavens, whereby all the 
 heavenly bodies appear to be carried round in circles, thus 
 performing a revolution every day. Any observer of this mo- 
 tion who should suppose the earth to be flat, and the direction 
 we call downward everywhere the same, would necessarily re- 
 gard it as real. A very little knowledge of geometry would, 
 however, show him that the appearance might be accounted 
 for by supposing the earth to revolve. The seemingly fatal 
 objection against this view would be that, if such were the 
 case, the surface of the earth could not remain level, and ev- 
 ery thing would slide away from its position. But it was im- 
 possible for men to navigate the ocean without perceiving the 
 rotundity of its surface, and we have no record of a time when 
 it was not known that the earth was round. We have seen 
 that Ptolemy not only was acquainted with the true figure of 
 the earth, but knew that in magnitude it was so much smaller 
 than the celestial spaces, or sphere of the heavens, as to be only 
 a point in comparison. He had, therefore, all the knowledge 
 necessary to enable him to see that the moving body was much 
 more likely to be the earth than to be the sphere of the heav- 
 ens. Nevertheless, he rejected the theory on obscure physical 
 grounds, as shown in the last chapter, the untenability of which 
 would have been proved him by a few very simple physical ex- 
 periments. And although it is known that the doctrine of the 
 earth’s motion was sustained by others in his age, notably by 
 Timocharis, yet the weight of his authority was so great as 
 
 LIBRARY 
 UNIVERSITY OF ILLINOIS 
 
52 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. | 
 
 not only to override all their arguments, but to carry his views 
 through fourteen centuries of the intellectual history of man. 
 
 The history of astronomy during these centuries offers hard- 
 ly anything of interest to the general reader. There was no 
 telescope to explore the heavens, and no genius arose of sufli- 
 cient force to unravel the maze of their mechanism. It was 
 mainly through the Arabs that any systematic knowledge of 
 the science was preserved for the use of posterity. The as- 
 tronomers of this people invented improved methods of ob- 
 serving the positions of the heavenly bodies, and were thus 
 able to make improved tables of their motions. They meas- 
 ured the obliquity of the*ecliptic, and calculated eclipses of 
 the sun and moon with greater precision than the ancient 
 Greeks could do. The predictions of the science thus gradu- 
 ally increased in accuracy, but no positive step was taken in 
 the direction of discovering the true nature of the apparent 
 movements of the heavens. 
 
 The honor of first proving to the world what the true theory 
 of the celestial motions is belongs almost exclusively to Coper- 
 nicus. It is true that we have some reason to believe that 
 Pythagoras taught that the sun, and not the earth, was the 
 centre of motion, and that he was, therefore, the first to solve 
 the great problem. but he did not teach this doctrine public- 
 ly, and the very vague statements of his private teachings on 
 this point which have been handed down to us are so mixed 
 up with the speculations which the Greek philosophers com- 
 bined with their views of nature, that it is hard to say with 
 precision whether Pythagoras had or had not fully seized the 
 truth. It is certain that no modern would receive the credit 
 of any discovery without giving more convincing proofs of the 
 correctness of his views than we have any reason to suppose 
 that Pythagoras gave to his disciples. 
 
 The great merit of Copernicus, and the basis of his claim to 
 the discovery in question, is that he was not satisfied with a 
 mere statement of his views, but devoted a large part of the 
 labor of a life to their demonstration, and thus placed them in 
 such a light as to render their ultimate acceptance inevitable. 
 
COPERNICUS. 53 
 
 Apart from all questions of the truth or falsity of his theory, 
 the great work in which it was developed, “De Revolutionibus 
 Orbium Celestium” would deservedly rank as the most im- 
 portant compendium of astronomy which had appeared since 
 Ptolemy. Few books have been more completely the labor of 
 a lifetime than this. Copernicus was born at Thorn, in Prus- 
 sia, in 1473, twenty years before the discovery of America, 
 but studied at the University of Cracow. He became an ec- 
 clesiastical dignitary, holding the rank of canon during a large 
 portion of his life, and finding ample leisure in this position 
 to pursue his favorite studies. He is said to have conceived of 
 the true system of the world as early as 1507. He devoted the 
 years of his middle life to the observations and computations 
 necessary to the perfection of his system, and communicated 
 his views to a few friends, but long refused to publish them, 
 fearing the popular prejudice which might thus be excited. 
 In 1540, a brief statement of them was published by his friend 
 _ Rheticus ; and, as this was favorably received, he soon con- 
 sented to the publication of his great work. The first printed 
 copy was placed in his hands only a few hours before his 
 death, which occurred in May, 1543. 
 
 The fundamental principles of the Copernican system are 
 embodied in two distinct propositions, which have to be proved 
 separately, and one of which might have been true without 
 the other being so. They are as follows: 
 
 1. The diurnal revolution of the heavens is only an appar- 
 ent motion, caused by a diurnal revolution of the earth on an 
 axis passing through its centre. 
 
 2. The earth is one of the planets, all of which revolve 
 round the sun as the centre of motion. The true centre of 
 the celestial motions is therefore not the earth, but the sun. 
 For this reason the Copernican system is frequently spoken of 
 in historical discussions as the “ heliocentric theory.” 
 
 The first proposition is the one with the proof of which Co- 
 pernicus begins. He explains how an apparent motion may 
 result from a real motion of the person seeing, as well as from 
 a motion of the object seen, and thus shows that the diurnal 
 
D4 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 motion may be accounted for just as well by a revolution of 
 the earth as by one of the heavens. To sailors on a ship sail- 
 ing on a smooth sea, the ship, and every thing in it, seems to be 
 at rest and the shore to be in motion. Which, then, is more 
 likely to be in motion, the earth or the whole universe outside 
 of it? In whatever proportion the heavens are greater than 
 the earth, in the same proportion must their motion be more 
 rapid to carry them round in twenty-four hours. Ptolemy 
 himself shows that the heavens were so immense that the 
 earth was but a point in comparison, and, for any thing that 
 is known, they may extend into infinity. Then we should re- 
 quire an infinite velocity of revolution. Therefore, it is far 
 more likely that it is this comparative point that turns, and 
 that the universe is fixed, than the reverse. 
 
 The second principle of the Copernican system—that the 
 apparent annual motion of the sun among the stars, described 
 in § 3 of the preceding chapter, is really due to an annual revo- 
 lution of the earth around the sun—rests upon a very beautiful 
 result of the laws of relative motion. This movement of the 
 earth explains not only this apparent revolution of the sun, 
 but the apparent epicyclic motion of the planets described in 
 treating of the Ptolemaic system. 
 
 In Fig. 15, let S represent the sun, A &CVD the orbit of the 
 earth around it, and the figures 1, 2, 3,4, 5,6, six successive 
 positions of the earth. These positions would be about two 
 weeks apart. Also, let “’/’G// represent the apparent sphere 
 of the fixed stars. Then, an observer at 1, viewing the sun in 
 the direction 1S, will see him as if he were in the celestial 
 sphere at the point 1’, because, having no conception of the 
 actual distance, the sun will appear to him as if actually among 
 the stars at 1’ which he in the same straight line with him. 
 When the earth, with the observer on it, reaches 2, he will see 
 the sun in the direction 282’, that is, as if among the stars in 
 2’. That is, during the two weeks’ interval, the sun will ap- 
 parently have moved among the stars by an angle equal to the 
 actual angular motion of the earth around the sun. So, as the 
 earth passes through the’ successive positions 3, 4, 5, 6, the sun 
 
—— 
 
 COPERNICUS. 55 
 
 will appear in the positions 3’, 4’, 5’, 6’, and the motion of the 
 earth continuing all the way round its orbit, the sun will ap- 
 pear to move through the entire circle HYGH. Thus we 
 have, as a result of the annual motion of the earth around the 
 sun, the annual motion of the sun around the celestial sphere 
 already described in the third section of the preceding chapter. 
 
 Fig. 15.—Apparent annual motion of the sun explained. 
 
 Let us now see how this same motion abolishes the compli- 
 cated system of epicycles by which the ancient astronomers 
 represented the planetary motions. A theorem on which this 
 explanation rests is this: /f an observer in unconscious mo- 
 tion sees an object at rest, that object will seem to him to be 
 moving in a direction opposite to his own, and with an equal 
 
 velocity. A familiar instance of this is the apparent motion 
 D 
 
56 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 of objects on shore to passengers on a steamer. In Fig. 16, 
 let us suppose an observer on the earth carried around the 
 
 sun Sin the orbit ABCDEF, 
 
 jc Lore a me bt Pe 
 
 ig atts but imagining himself at rest 
 a \ in the centre of motion S. Sup- 
 of 
 ; ‘, pose that he observes the ap- 
 
 parent motion of the planet P, 
 which is really at rest. How 
 will the planet appear to move ? 
 To show this, we represent ap- 
 parent directions and motions 
 by dotted lines. Let us begin 
 with the observer at A, from 
 which position he really sees 
 the planet in the direction and 
 distance AP. But, imagining 
 himself at S, he thinks he sees 
 the planet at the point a, the 
 distance and direction of which 
 Sa is the same with AP. As 
 he passes unconsciously from A 
 to BL, the planet seems to him to 
 move past from @ to 0 in the op- 
 posite direction; and, still think- 
 ing himself at rest in S, he sees 
 the planet in 6, the line SO be- 
 Fr 14 Song now the spwrent ot ing equal and parallel to BP. 
 
 for by the motion of the earth round the As he recedes from the plan- 
 
 ao. et through the are BCD, the 
 planet seems to recede from him through décd. While he 
 moves from left to right through D/, the planet seems to 
 move from right to left throngh de. Finally, as he approaches 
 the planet through the are #/’A, the planet will seem to ap- 
 proach him through efa, and when he gets back to A he 
 will locate the planet at a, as in the beginning. Thus, in 
 consequence of the motion of the observer around the circle 
 ABCDEF, the planet, though really at rest, will seem to him 
 
COPERNICUS. 57 
 
 to move through a corresponding circle, abcdef. If there are 
 a number of planets, they will all seem to describe correspond- 
 ing circles of the same magnitude. 
 
 If the planet P, instead of being at rest, is in motion, the 
 apparent circular motion will be combined with the forward 
 motion of the planet, and the latter will now describe a circle 
 _ around a centre which is in motion. Thus we have the appar- 
 ent motion of the planets around a moving centre, as already 
 described in the Ptolemaic system. We have said, in § 7 of 
 the preceding chapter, that by this system the motions of the 
 planets are represented by supposing a fictitious planet to re- 
 volve around the heavens with a regular motion, while the 
 real planet revolves around this fictitious one as a centre once 
 ayear. Here, the progressive motion of the fictitious planet 
 is (an the case of the outer planets Mars, Jupiter, and Sat- 
 urn) the motion of the real planet around the sun, while the 
 circle which the real planet describes around this moving cen- 
 tre is only an apparent motion due to the observer being car- 
 reed around the sun on the earth. If the reader will com- 
 pare the epicyclic motion of Ptolemy, represented in Figs. 10 
 and 11 with the motion explained in Fig. 16, he will find that 
 they correspond in every particular. In the case of the inner 
 planets, Mercury and Venus, which never recede far from the 
 sun, the epicyclic motion by which they seem to vibrate from 
 one side of the sun to the other is due to their orbital motion 
 around the sun, while the progressive motion with which they 
 follow the sun is due to the revolution of the earth around 
 the sun. 
 
 We may now see clearly how the retrograde motion and 
 stationary phases of the planets are explained on the Coper- 
 nican system. The earth and all the planets are really mov- 
 ing round the sun in a direction which we call east on the 
 celestial sphere. When the earth and an outer planet are 
 on the same side of the sun, they are moving in the same 
 direction; but the earth is moving faster than the planet. 
 Hence, to an observer on the earth, the planet seems to be 
 moving west, though its real motion is east. As the earth 
 
58 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 passes to the opposite side of the sun from the planet, it 
 changes its motion to a direction the opposite of that of the 
 planet, and thus the westerly motion of the latter appears to 
 be increased by the whole motion of the earth.* Between 
 these two motions there is a point at which the planet does 
 not seem to move at all, This is called the stationary point. 
 If the planet we consider is not an outer, but an inner one, 
 Mercury or Venus, and we view it when between us and the 
 sun, its motion to us is reversed, because we see it from the 
 side opposite the sun. Hence it seems to move west to us, 
 and it is retrograde. The earth is indeed moving in the same 
 real direction; but since the planet moves faster than the 
 earth, its retrograde motion seems to predominate. As the 
 planet passes round in its orbit, it first appears stationary, 
 and then, passing to the opposite side of the sun, it seems 
 direct. 
 
 Let us now dwell for a moment on some considerations 
 which will enable us to do justice to the Ptolemaic system, as 
 it is called, by seeing how necessary a step it was in the evo- 
 lution of the true theory of the universe. The great merit of 
 that system consisted in the analysis of the seemingly compli- 
 cated motions of the planets into a combination of two circular 
 motions, the one that of a fictitious planet around the celestial 
 sphere, the other that of the real planet around the fictitious 
 one. Without that separation, the constant oscillations of the 
 planets back and forth could not have suggested any idea 
 whatever, except that of a motion too complicated to be ex- 
 plained on mechanical principles. But when, leaving out of . 
 sight the regular forward motion of the mean or fictitious 
 planet, the attention was directed to the epicyclic motion 
 alone, one could not fail to see the remarkable correspondence 
 between this latter motion and the apparent annual motion 
 of the sun. Seeing this, it took a very small step to see that 
 
 * It must not be forgotten that the direction east in the heavens is a curved di- 
 rection, as it were, and is opposite on opposite sides of the sun or celestial sphere. 
 For instance, the motions of the stars as they rise and as they set are opposite, 
 but both are considered west. 
 
Ta 
 
 COPERNICUS. 59 
 
 the sun, and not the earth, was the centre of planetary motion. 
 Then nothing but the illusions of sense remained to prevent 
 the acceptance of the theory that the earth was itself a planet 
 moving round the sun, and that both the annual motion of the 
 sun and the epicyclic motion of the planets were not real, but 
 apparent motions, due to the motion of the earth itself; and 
 in no other way than this could the heliocentric theory have 
 been developed. 
 
 The Copernican system affords the means of determining 
 the proportions of the solar system, or the relative distances of 
 the several planets, with great accuracy. That is, if we take 
 as our measuring-rod the distance of the earth from the sun, 
 we can determine how many lengths of this rod, or what frac- 
 tional parts of its length, will give the distance ot each planet, 
 although the length of the rod itself may remain unknown. 
 This determination rests on the principle that the apparent 
 circle or epicycle described by the planet in Fig. 16 is of the 
 same magnitude with the actual orbit described by the earth 
 around the sun. Hence, the nearer the observer is to this cir- 
 cle, the larger it will appear. The apparent epicycle described 
 by Neptune is rather less than two degrees in radius; that is, 
 the true planet Neptune is seen to swing a little less than two 
 degrees on each side of its mean position in consequence of 
 the annual motion of the earth round the sun. This shows 
 that the orbit of the earth, as seen from Neptune, subtends an 
 angle of only two degrees. On the other hand, the planet 
 Mars generally swings more than 40° on each side; sometimes, 
 indeed, more than 45°. From this a trigonometrical calcula- 
 tion shows that its mean distance is only about half as much 
 again as that of the earth; and the fact that the apparent 
 swing is variable shows the distance to be different at different 
 times. 
 
 As it will be of interest to see how nearly Copernicus was 
 able to determine the distances of the planets, we present his 
 results in the following table, together with what we now 
 know to be the trne numbers. The numbers given are deci- 
 mal fractions, expressing the least and greatest distance of 
 
60 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 each planet from the sun, the distance of the earth being taken 
 as unity.* 
 
 Least DISTANOE. GREATEST DISTANOE. 
 Planets, 
 
 Copernicus, Modern. Copernicus. Modern. 
 
 0.326 0.308 0.405 0.467 
 0.709 0.718 0.730 0.728 
 1.373 1.382 1.666 1.666 
 Jupiter 4.980 4.952 5.453 5.454 
 Saturn 8.66 9.00 9.76 10.07 — 
 
 Considering the extremely imperfect means of observation 
 which the times afforded, these results of Copernicus come 
 very near the truth. The greatest proportional deviation is in 
 the case of Mercury, the most difficult of all the planets to 
 observe, even to the present day. It is said that Copernicus 
 died without ever seeing this planet. 
 
 The eccentricities of the orbits were represented by Coper- 
 nicus in a way which agrees exactly with the modern formule 
 when only a rough approximation is sought for. Like Ptole- 
 my, he supposed ‘the orbits of the blatest not to be centred on 
 the sun, but to be displaced by a small quantity termed the 
 eccentricity. But it had long been known that the theory of 
 uniform motion in an eccentric circle, though it might make 
 the irregularities in the planet’s angular motion ‘come out all 
 right, would make the changes of distance double their true 
 value. He therefore took for the eccentricity a mean between 
 that which would satisfy the motion in longitude, and that 
 which would give the changes of distance, and added a small 
 epicycle of one-third this eccentricity ; and, by supposing the 
 planet to make two revolutions in this epicycle for every 
 revolution around the sun, he represented both irregulari- 
 ties.t 
 
 * T have deduced these numbers from the tables given in Book V. of ‘*De 
 Reyolutionibus Orbium Ceelestium.” They are probably the most accurate that 
 Copernicus was able to obtain. 
 
 + The mathematical form of this theory of Copernicus is as follows: Putting 
 
OBLIQUITY OF THE ECLIPTIC. 61 
 
 The work of Copernicus was the greatest step ever taken in 
 astronomy. But he still took little more than the single step 
 
 of showing what apparent motions in the heavens were real, 
 
 and what were due to the motion of the observer. Not only 
 was his work in other respects founded on that of Ptolemy, 
 but he had many of the notions of the ancient philosophy re- 
 specting the fitness of things. Like Ptolemy, he thought the 
 heavens as well as the earth to be spherical, and all the celes- 
 tial motions to be circular, or composed of circles. He argues 
 against Ptolemy’s objections to the theory of the earth’s mo- 
 tion, that that philosopher treats of it as if it were an enforced 
 or violent motion, entirely forgetting that if it exists it must 
 be a natural motion, the laws of which are altogether different 
 from those of violent motion. Thus, part of his argument was 
 really without scientific foundation, though his conclusion was 
 correct. Still, Copernicus did about all that could have been 
 done under the circumstances. His hypothesis of a small epi- 
 cycle one-third the eccentricity represented the motions of the 
 planets around the sun with all the exactness that observation 
 then admitted of, while, in the absence of any knowledge of 
 the laws of motion, it was impossible to frame any dynamical 
 basis for the motions of the planets. 
 
 $ 2. Obliquity of the Ecliptic ; Seasons, etc. » on the Coper- 
 nican System. 
 
 We have next to explain the relations of the ecliptic and 
 equator on the new system. Since, on this system, the ce- 
 lestial sphere does not revolve at all, what is the significance 
 of the pole and axis around which it seems to revolve? The 
 
 e for his eccentricity, and g for the mean anomaly of the planet, he represented its 
 rectangular coordinates in the form 
 x =a (cos. g—e+4e cos. 2g), 
 y =a (sin. g + de sin, 29); 
 while the approximate modern formule of the elliptic motion are— 
 x =a (cos. g — Ze + ge cos. 29), 
 y =a (sin. g + $e sin. 29), 
 which agree exactly when we put e = 3e. 
 
62 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 answer is, that the celestial poles are the points among the stars 
 towards which the axis of the earth is directed. Here the 
 stars are supposed to be infinitely distant, and the axis of the © 
 earth to be continued in an infinite straight line to meet them. 
 Since this point appears to the ‘unassisted sight to be the same 
 during the entire year, it follows that as the earth moves round 
 the sun, its axis keeps pointing in the same absolute direction, 
 as will be shown in Fig. 18. But in the preceding chapter we 
 showed that there is a slow but constant change in the position 
 of the pole among the stars, called precession, which the an- 
 cient astronomers discovered by studying observations extend- 
 
 | 
 ' 
 I 
 i 
 ' 
 ! 
 | 
 t 
 ' 
 ' 
 | 
 1 
 ' 
 { 
 ‘ 
 ‘ 
 ' 
 ' 
 i] 
 | 
 ‘ 
 ! 
 ‘ 
 ‘ 
 1 
 
 ‘\ 
 ‘ 
 
 te re en ee 
 
 ES Ss oe an ae ed el ws Sv is |S aps ae 
 
 Fig. 17.—Relation of the terrestrial and celestial poles and equators. 
 
 ing through several centuries, and this shows that on the Co- 
 pernican system the direction of the earth’s axis is slowly 
 changing. 
 
 To conceive of the celestial equator on the Copernican sys- 
 tem, we must imagine the globular earth to be divided into 
 two hemispheres by a plane intersecting the earth around its 
 equator, and continued out on all sides till it reaches the ce- 
 lestial sphere. This may, perhaps, be better understood by 
 referring to Fig. 17, representing the earth in the centre of the 
 
OBLIQUITY OF THE ECLIPTIC. 63 
 
 imaginary celestial sphere. The dotted lines passing from the 
 poles of the earth to the points P and S mark the poles of that 
 sphere. It is evident that as the earth turns on this axis, the 
 celestial sphere, no matter how great it may seem to be, will 
 appear to turn on the same axis in the opposite direction. 
 Again, ep being the earth’s equator, dividing it into two equal 
 parts, we have only to imagine it to be extended to # and Q, 
 all round the celestial sphere, to cut the latter into two equal 
 parts. 
 
 Let us next examine more closely the relation of the earth 
 to the sun. We have already shown that as the earth moves 
 around the sun, the latter seems to move around the celestial 
 sphere, and the circle in which he seems to move is called the 
 ecliptic. But the ecliptic and the celestial ‘equator are in- 
 clined to each other by an angle of about 284°. This shows 
 that the axis of the earth is not perpendicular to its orbit, but 
 
 Fig. 18.—Causes of changes of seasons on the Copernican system. 
 
 is inclined 234° to that perpendicular, as shown in Fig. 18, 
 which represents the annual course of the earth round the 
 sun. It is of necessity drawn on a very incongruous scale, 
 because the distance of the sun from the earth being near- 
 ly 12,000 diameters of the latter and 110 that of the sun, both 
 bodies would be almost invisible if they were not greatly mag- 
 nified in the figure. A difficulty which may suggest itself is, 
 that the present figure represents the earth as moving away 
 
64 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 from its position in the centre of the sphere. There are two 
 ways of avoiding this difficulty. One is to suppose that the 
 observer carries the imaginary celestial sphere with him as he 
 is carried around the sun; the other is to consider the sphere 
 as nearly infinite in diameter. The latter is probably the 
 easiest mode of conception for the general reader. He must, 
 therefore, in the last figure suppose the sphere to extend out 
 to the fixed stars, which are so distant that the whole orbit of 
 the earth is but a point In comparison; and the different points 
 of the sphere towards which the poles and the equator of the 
 earth point, as the latter moves round the sun, are so far as to 
 appear always the same. It now requires but an elementary 
 idea of the geometry of the sphere to see that these two great 
 circles of the celestial sphere—the ecliptic, around which the 
 sun seems to move, and the equator, which is everywhere 
 equally distant from the points in which the earth’s axis in- 
 tersects the sphere—will appear inclined to each other by the 
 same angle by which the earth’s axis deviates from the per- 
 pendicular to the ecliptic. 
 
 Next, we have to see how the changes of the seasons, the 
 equinoxes, etc., are explained on the Copernican theory. In 
 the last figure the earth is represented in four different posi- 
 tions of its annual orbit around the sun. In the position <A, 
 the south pole is inclined 234° towards the sun, while the 
 north pole, and the whole region within the arctic circle, is 
 enveloped in darkness. Hence, in this position, the sun nei- 
 ther rises to the inhabitants of the arctic zone, nor sets to 
 those of the antarctic zone. Outside of these zones, he rises 
 and sets, and the relative lengths of day and night at any 
 place can be estimated by studying the circles around which 
 that place is carried by the diurnal turning of the earth on its 
 axis. ‘To facilitate this, we present on the following page a 
 magnified picture of the earth at A, showing more fully the 
 hemisphere in which it is day and that in which it is night. 
 The seven nearly horizontal lines on the globe are examples 
 of the circles in question. We see that a point on the arctic 
 circle just grazes the dividing-line between light and darkness 
 
THE SEASONS. 65 
 
 once in its revolution, or once a day; that is, the sun just 
 shows himself in the horizon once a day. Of the next circle 
 towards the south about two- 
 
 thirds is in the dark, and one- li inane 
 third in the light hemisphere. lh 
 This shows that the nights are i \ 
 about twice as long as the Qeae, In l 
 days. This circle is near that | i Nin 
 around which London is carried WT 
 
 by the diurnal revolution of the it 
 earth on its axis. As we go on Mit 
 
 south, we see that the propor- “ety P| Mh 
 
 tion of light on the diurnal cir- Se [lls 
 
 cles constantly increases while Fie. 19. — Enlarged view of the earth in 
 - Pregame ’ the position A of the preceding figure, 
 that of darkness diminishes, un- showing winter in the northern hemi- 
 til we reach the equator, where sphere, and summer in the southern. 
 they are equal. When we pass into the southern hemisphere, 
 we see the light covering more than half of each circle, the 
 proportion of light to darkness constantly increasing, at the 
 sane rate that the opposite proportion would increase in going 
 to the north. When we reach the antarctic circle, the whole 
 circle is in the light hemisphere, the observer just grazing the 
 dividing-line at midnight. Inside of that circle the observer 
 is in sunlight all the time, so that the sun does not set at all. 
 We see, then, that at the equator the days and nights are al- 
 ; ) y 
 ways of the same length, and that the inequality increases as 
 we approach either pole. 
 
 We now go on three months to the position 6, which the 
 earth occupies in March. Here the plane of the terrestrial 
 equator being continued, passes directly through the sun; the 
 latter, therefore, seems to be in the celestial equator. All the 
 
 ; | 
 diurnal circles are here one-half in the illuminated, and one- 
 y 
 half in the unilluminated hemisphere, the latter being invisi- 
 ble in the figure, through its being behind the earth. The 
 days and nights are, therefore, of equal length all over the 
 globe, if we eall it night whenever the sun is geometrically 
 below the horizon. In the position C, which the earth takes 
 
66 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 in June, everything is the same as in position A, except that 
 effects are reversed in the two hemispheres. The northern 
 hemisphere now has the longest days, and the southern one 
 the longest nights. At J, which the earth reaches in Sep- 
 tember, the days and nights are equal once more, for the same 
 reason as in 4. Thus, all the seemingly complicated phenom- 
 ena which we have described in the preceding chapter are 
 completely explained in the simplest way on the new system. 
 We have next to see how the details of the system were filled 
 in by the immediate successors of Copernicus. 
 
 § 3. Tycho Brahe. 
 
 We have said that no great advance could be made upon 
 the Copernican system, without either a better knowledge of 
 the laws of motion or more exact observations of the positions 
 of the heavenly bodies. It was in the latter direction that 
 the advance was first made. The leader was Tycho Brahe, 
 who was born in 1546, three years after the death of Coperni- 
 cus. His attention was first directed to the study of astron- 
 omy by an eclipse of the sun on August 21st, 1560, which was 
 total in some parts of Europe. Astonished that such a phe- 
 nomenon could be predicted, he devoted himself to a study of 
 the methods of observation and calculation by which the pre- 
 diction was made. In 1576 the King of Denmark founded 
 the celebrated Observatory of Uraniberg, at which Tycho 
 spent twenty years, assiduously engaged in observations of the 
 positions of the heavenly bodies with the best instruments that 
 could then be made. This was just before the invention of 
 the telescope, so that the astronomer could not avail himself 
 of that powerful instrument. Consequently, his observations 
 were superseded by the improved ones of the centuries fol- 
 lowing, and their celebrity and importance are principally due 
 to their having afforded Kepler the means of discovering his 
 celebrated laws of planetary motion. 
 
 As a theoretical astronomer, Tycho was unfortunate. He 
 rejected the Copernican system, for a reason which, in his day, 
 had some force, namely, the incredible distance at which it 
 
TYCHO BRAHE. 67 
 
 was necessary to suppose the fixed stars to be situated if that 
 system were accepted. We have shown how, on the Coperni- 
 can system, the outer planets seem to describe an annual revo- 
 lution in an epicycle, in consequence of the annual revolution 
 of the earth around the sun. The fixed stars, which are sit- 
 uated outside the solar system, must appear to move in the 
 same way, if the system be correct. But no observations, 
 whether of Tycho or his predecessors, had shown any such 
 motion. ‘To this the friends of Copernicus could only reply 
 that the distance of the fixed stars must be so great that the 
 motion could not be seen. Since a vibration of three or four 
 minutes of arc might have been detected by Tycho, it would 
 be necessary to suppose the stellar sphere at least a thousand 
 times the distance of the sun, and a hundred times that of Sat- 
 urn, then the outermost known planet. ‘That a space so vast 
 should intervene between the orbit of Saturn and the fixed 
 stars seemed entirely incredible: to the philosophers of the 
 day it was an axiom that nature would not permit the waste of 
 space here implied. At the same time, the proofs given by 
 Copernicus that the sun was the centre of the planetary mo- 
 tions were too strong to be overthrown. ‘Tycho, therefore, 
 adopted a system which was a compound of the Ptolemaic 
 and the Copernican; he supposed the five planets to move 
 around the sun as the centre of their motions, while the sun 
 was itself in motion, describing an annual orbit around the 
 earth, which remained at rest in the centre of the universe. 
 
 Perhaps it is fortunate for the reception of the Copernican 
 system that the astronomical instruments of Tycho were not 
 equal to those of the beginning of the present century. Had 
 he found that there was no annual parallax among the stars 
 amounting to a second of arc, and therefore that, if Coperni- 
 cus was right, the stars must be at least’ 200,000 times the dis- 
 tance of the sun, the astronomical world might have stood 
 aghast at the idea, and concluded that, after all, Ptolemy must 
 be right, and Copernicus wrong. 
 
 Tycho never elaborated his system, and it is hard to say 
 how he would have answered the numerous objections to it. 
 
68 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 He never had any disciples of eminence, except among the 
 ecclesiastics ; in fact, the invention of the telescope did away 
 with the last remaining doubts of the correctness of the Co- 
 pernican system before a new one would have had time to 
 gain a foothold. 
 
 § 4. Kepler.—His Laws of Planetary Motion. 
 
 Kepler was born in 1571, in Wurtemberg. He was for a 
 while the assistant of Tycho Brahe in his calculations, but was 
 too clear-sighted to adopt the curious system of his master. 
 Seeing the truth of the Copernican system, he set himself to 
 determine the true laws of the motion of the planets around 
 the sun. We have seen that even Copernicus had adopted the 
 ancient theory, that all the celestial motions are compounded 
 of uniform circular motions, and had thus been obliged to in- 
 troduce a small epicycle to account for the irregularities of 
 the motion. The observations of Tycho were so much more 
 accurate than those of his predecessors, that they showed Kep- 
 ler the insufficiency of this theory to represent the true mo- 
 tions of the planets around the sun. The planet most favora- 
 ble for this investigation was Mars, being at the same time 
 one of the nearest to the earth, and one of which the orbit 
 was most eccentric. The only way in which Kepler could 
 proceed in his investigation was to make various hypotheses 
 respecting the orbit in which the planet moved, and its velocity 
 in various points of its orbit, and from these hypotheses to cal- 
 culate the positions and motions of the planet as seen from 
 the earth, and then compare with observations, to see whether 
 the observed and calculated positions agreed. As our modern 
 tables of logarithms by which such calculations are immensely 
 abridged were not then in existence, each trial of an hypothe- 
 sis cost Kepler an immense amount of labor. Finding that 
 the form of the orbit was certainly not circular, but elliptical, 
 he was led to try the effect of placing the sun in the focus of 
 the ellipse. Then, the motion of the planet would be satisfied 
 if its velocity were made variable, being greater the nearer 
 it was to the sun. Thus he was at length led to the first two 
 
KEPLER. 69 
 
 of his three celebrated laws of planetary motion, which are as 
 follows: 
 
 1. The orbit of each planet rs an ellipse, having the sun in 
 one focus. 
 
 2. As the planet moves round the sun, its radius-vector (or 
 the line joining it to the sun) passes over equal areas in 
 equal tumes. 
 
 To explain these laws, let PA (Fig. 20) be the ellipse in 
 which the planet moves. Then the sun will not be in the cen- 
 
 Fie. 20.—Illustrating Kepler’s first two laws of planetary motion. 
 
 tre of the ellipse, but in one focus, say at S, the other focus 
 being empty. When the planet is at P,it is at the point near- 
 est the sun; this point is therefore called the perzhelion. As 
 it passes round to the other side of the sun, it continues to re- 
 cede from him till it reaches the point A, when it attains its 
 greatest distance. This point is the aphelzon. Then it begins 
 to approach the sun again, and continues to do so till it reaches 
 P once more, when it again begins to repeat the same orbit. 
 It thus describes the same ellipse over and over. 
 
 Now, suppose that, starting from P, we mark the position 
 of the planet in its orbit at the end of any equal intervals of 
 time, say 80 days, 60 days, 90 days, 120 days, and so on. Let 
 a, b,c, d@ be the first four of these positions between each of 
 which the planet has required 30 days to move. Draw lines 
 from each of the five positions of the planet, beginning at P, 
 
70 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 to the sun at S. We shall thus have four triangular spaces, 
 over each of which the radius-vector of the planet has swept 
 in 80 days. The first of Kepler’s laws means that the areas 
 of all of these spaces will be equal. 
 
 The old theory that the motions of the heavenly bodies net 
 be circular and uniform, or, at least, composed of circular and 
 uniform motions, was thus done away with forever. The el- 
 lipse took the place of the circle, and a variable motion the 
 place of a uniform one. 
 
 Another law of planetary motion, not less important than 
 these two, was afterwards discovered by Kepler. Copernicus 
 knew, what had been surmised by the ancient astronomers, 
 that the more distant the planet, the longer it took it to per- 
 form its course around the sun, and this not merely because it 
 had farther to go, but because its motion was really slower. 
 For instance, Saturn is about 94 times as far as the earth, and 
 if it moved as fast as the earth, it would perform its revolu- 
 tion in 9$ years; but it actually requires between 29 and 30 
 years. It does not, therefore, move one-third so fast as the 
 earth, although it has nine times as far to go. Copernicus, 
 however, never detected any relation between the distances 
 and the periods of revolution. Kepler found it to be as fol- 
 lows: 
 
 Third law of planetary motion. The square of the time 
 of revolution of each planet ts proportional to the cube of 
 its mean distance from the sun. 
 
 This law is shown in the following table, which gives (1) 
 the mean distance of each planet known to Kepler, expressed 
 in astronomical units, each unit being the mean distance of 
 
 (1) (2) (3) (4) 
 
 Planets, Distance Oe ae mm oe 
 I RHOTITY, 5. ok 2 cass seks boosters 0.387 0.058 0.241 0.058 
 WH eat 526s doce as acsakceeee 0.723 0.378 0.615 0.378 
 Ue ee eee eee oe 1.000 1.000 1.000 1.001 
 WHATS sta ttedesccsestehees suse 1.524 3.540 1.881 3.538 
 oD WPIGGE eee oo oals s chtwlen seca apes 5.203 140.8 11.86 140.66 
 SabUrith cers caciisiss scene aes 9.539 868.0 29.46 867.9 
 
 —— 
 
FROM KEPLER TO NEWTON. "bl 
 
 the earth from the sun; (2) the cube of this quantity; (3) the 
 time of revolution in years; and (4) the square of this time. 
 
 The remarkable agreement between the second and fourth 
 columns will be noticed. 
 
 § 5. Krom Kepler to Newton. 
 
 So far as the determination of the laws of planetary motion 
 from observation was concerned, we might almost say that 
 Kepler left nothing to be done. Given the position and 
 magnitude of the elliptic orbit in which any planet moved, 
 and the point of the orbit in which it was found at any 
 date, and it became possible to calculate the position of the 
 planet in all future time. More than that science could not 
 do. It is true that the places of the planet thus predicted 
 were not found to agree exactly with observation; and had 
 Kepler had at his command observations as accurate as those 
 of the present day, he would have found that his laws could 
 not be made to perfectly represent the motion of the planets. 
 Not only would the elliptic orbit have been found to vary its 
 position from century to century, but the planets would have 
 been found to deviate from it, first in one direction and then 
 in the other, while the areas described by the radius-vector 
 would have been sometimes larger and sometimes smaller. 
 Why should a planet move in an elliptic orbit? Why should 
 its radius- vector describe areas proportional to the time? 
 Why should there be that exact relation between their dis- 
 tances and times of revolutions? Until these questions were 
 answered, it would have been impossible to say why the plan- 
 ets deviated from Kepler’s laws; and they were questions 
 which it was impossible to answer until the general laws of 
 motion, unknown in Kepler’s time, were fully understood. 
 
 The first important step in the discovery of these laws was 
 taken by Galileo, the great contemporary of Kepler, one of 
 the inventors of the telescope, and the first who ever pointed 
 that instrument at the heavens. From a scientific point of 
 view, as inventor of the telescope, founder of the science of 
 dynamics, teacher and upholder of the Copernican system, and 
 
72 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 sufferer at the hands of the Inquisition, for promulgating what 
 he knew to be the truth, Galileo is perhaps the most interest- 
 ing character of his time. If any serious doubt could remain 
 of the correctness of the Copernican system, it was removed 
 by the discoveries made by the telescope. The phases of 
 Venus showed that she was a dark globular body, like the 
 earth, and that she really revolved around the sun. In Jupi- 
 ter and his satellites, the solar system, as described by Coperni- 
 cus, was repeated on a small scale with a fidelity which could 
 not fail to strike the thinking observer. ‘There was no longer 
 any opposition to the new doctrines from any source entitled 
 to respect. The Inquisition forbade their promulgation as 
 absolute truths, but were perfectly willing that they should be 
 used as hypotheses, and rather encouraged men of science in 
 the idea of investigating the interesting mathematical prob- 
 lems to which the explanation of the celestial motions by the 
 Copernican system might give rise. The only restriction was 
 that they must stop short of asserting or arguing the hypothe- 
 ses to be a reality. As this assertion was implicitly contained 
 in several places in the great work of Copernicus, they con- 
 demned this work in its original form, and ordered its revi- 
 sion.* Probably the decree of the Inquisition was entirely 
 without effect in stopping the reception of the Copernican 
 system outside of Italy and Spain. 
 
 It will be seen, from what has been said, that the next step 
 to be taken in the direction of explaining the celestial motions 
 must be the discovery of some general cause of those motions, 
 or, at least, their reduction to some general law. The first 
 attempt to do this was made by Descartes in his celebrated 
 theory of vortices, which for some time disputed the field with 
 Newton’s theory of gravitation. This philosopher supposed 
 the sun to be immersed in a vast mass of fluid, extending in- 
 definitely in every direction. The sun, by its rotation, set the 
 
 * The order for this revision was made at the time of condemning Galileo’s 
 work, but I am not aware that it was ever executed. An edition of Copernicus, 
 revised to satisfy the Inquisition, would certainly be an interesting work to the 
 astronomical bibliopole at the present time. 
 
FROM KEPLER TO NEWTON. 73 
 
 parts of the fluid next to it in rotation; these communicated 
 their motions to the parts still farther out, and so on, until 
 the whole mass was set in rotation like a whirlpool. The 
 planets were carried around in this ethereal whirlpool. The 
 more distant planets moved more slowly because the ether 
 was less affected by the rotation of the sun the more distant 
 it was from him. In the great vortex of the solar system 
 were smaller ones, each planet being the centre of one; and 
 thus the satellites, floating in the ether, were carried round 
 their primaries. Had Descartes been able to show that the 
 parts of his vortex must move in ellipses having the sun in 
 one focus, that they must describe equal areas in equal times, 
 and that the velocity must diminish as we recede from the 
 sun, according to Kepler’s third law, his theory would so far 
 have been satisfactory. Failing in this, it cannot be regarded 
 as an advance in science, but rather as a step backwards. Yet, 
 the great eminence of the philosopher and the number of his 
 disciples secured a wide currency for his theory, and we find 
 it supported by no less an authority than John Bernoulli. 
 After Galileo, the man who, perhaps, did most to prepare 
 the way for gravitation was Huyghens. As a mathematician, 
 a mechanician, and an observer, he stood in the first rank. 
 He discovered the laws of centrifugal force, and if he had 
 simply applied these laws to the solar system, he would have 
 been led to the result that the planets are held in their orbits 
 by a force varying as the inverse square of their distance from 
 the sun. Having found this, the road to the theory of gravita- 
 tion could hardly have been missed. But the great discovery 
 seemed to require a mind freshly formed for the occasion. 
 
74 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 CHAPTER III. 
 UNIVERSAL GRAVITATION. 
 
 § 1. Newton.—Discovery of Gravitation. 
 
 Tue real significance of Newton’s great discovery of univer- 
 sal gravitation is fully appreciated by but few. Gravitation 
 is generally thought of as a mysterious force, acting only be- 
 tween the heavenly bodies, and first discovered by Newton. 
 Had gravitation itself been discovered by Newton as some 
 new principle to account for the motions of the planets, it 
 would not have been so admirable a discovery as that which 
 he actually made. Gravitation, in a somewhat limited sphere, 
 is known to all men. It is simply the force which causes 
 all heavy bodies to fall, or to tend towards the centre of the 
 earth. Every one who had ever seen a stone fall, or felt it to 
 be heavy, knew of the existence of gravitation. What New- 
 ton did was to show that the motions of the planets were 
 determined by a universal force, of which the force which 
 caused the apple to fall was one of the manifestations, and 
 thus to deprive the celestial motions of all the mystery in 
 which they had formerly been enshrouded. To his predeces- 
 sors, the continuous motion of the planets in circles or ellipses 
 was something so completely unlike any motion seen on the 
 surface of the earth, that they could not imagine it to be gov- 
 erned by the same laws; and, knowing of no law to limit the 
 planetary motions, the idea of the heavenly bodies moving in 
 a manner which set all the laws of terrestrial motion at “de- 
 fiance was to them in no way incredible. 
 
 The idea of a cosmical force emanating from the sun or the 
 earth, and causing the celestial motions, did not originate with 
 Newton. We have seen that even Ptolemy had an idea of a 
 force which, always directed towards the centre of the earth, 
 
 i a EE 
 
NEWTON.—DISCOVERY OF GRAVITATION. 75 
 
 or, which was to him the same thing, towards the centre of 
 the universe, not only caused heavy bodies to fall, but bound 
 the whole universe together. Kepler also maintained that the 
 force which moved the planets resided in, and emanated from, 
 the sun. But neither Ptolemy nor Kepler could give any ade- 
 quate explanation of the force on the basis of laws seen in ac- 
 tion around us; nor was it possible to form any conception of its 
 true nature withont a knowledge of the general laws of motion 
 and force, to which neither of these philosophers ever attained. 
 
 The great misapprehension which possessed the minds of 
 nearly all mankind till the time of Galileo was, that the con- 
 tinuous action of some force was necessary to keep a moving 
 body in motion. That Kepler himself was fully possessed of 
 this notion is shown by the fact that he conceived a force act- 
 ing only in the direction of the sun to be insufficient for keep- 
 ing up the planetary motions, and to require to be supplement- 
 ed by some force which should constantly push the planet 
 ahead. The latter force, he conceived, might arise from the 
 rotation of the sun on his axis. It is hard to say who was the 
 first clearly to see and announce that this notion was entirely 
 incorrect, and that a body once set in motion, and acted on by 
 no force, would move forwards forever —so gradually did the 
 great truth dawn on the minds of men. It must have been 
 obvious to Leonardo da Vinci; it was implicitly contained in 
 Galileo’s law of falling bodies, and in Huyghens’s theory of 
 central forces; yet neither of these philosophers seems to have 
 clearly and completely expressed it. We can hardly be far 
 wrong in saying that Newton was the first who clearly laid 
 down this law in connection with the correlated laws which 
 cluster around it. The basis of Newton’s discovery were these 
 three laws of motion: 
 
 First law. A body once set in motion and acted on by no force 
 will“move forwards in a straight line and with a uniform velocity 
 
 forever. 
 Second law. Jf a moving body be acted on by any force, its de- 
 viation from the motion defined in the first law will be in the direc- 
 tion of the force, and proportional to i. 
 
76 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 Third law. Action and reaction are equal, and in opposite dt- 
 rections ; that ws, whenever any one body exerts a force on a second 
 one, the latter exerts a simular force on the first, only in the opposite 
 direction. 
 
 The first of these laws is the fundamental one. The cir- 
 cumstance which impeded its discovery, and set man astray 
 for many centuries, was that there was no body on the earth’s 
 surface acted on by no force, and therefore no example of a 
 body moving in a continuous straight line. Every body on 
 which an experiment could be made was at least acted on by 
 the gravitation of the earth—that is, by its own weight—and, 
 in consequence, soon fell to the earth. Other forces which im- 
 peded its motion were friction and the resistance of the air. 
 It needed research of a different kind from what the prede- 
 cessors of Galileo had given to physical problems to show that, 
 but for these forces, the body would move in a straight line 
 without hinderance. 
 
 We are now prepared to understand the very straightfor- 
 ward and simple way in which Newton ascended from what 
 he saw on the earth to the great principle with which his 
 name is associated. We see that there is a force acting all 
 over the earth by which all bodies are drawn towards the 
 earth’s centre. This force extends without sensible diminu- 
 tion, not only to the tops of the highest buildings, but of the 
 highest mountains. How much higher does it extend? Why 
 should it not extend to the moon? If it does, the moon would 
 tend to drop to the earth, just as a stone thrown from the 
 hand does. Such being the case, why should not this simple 
 force of gravity be the force which keeps the moon in her 
 orbit, and prevents her from flying off in a straight line under 
 the first law of motion? ‘To answer this question, it was nec- 
 essary to calculate what force was requisite to retain the moon 
 in her orbit, and to compare it with gravity. It was at that 
 time well known to astronomers that the distance of the moon 
 was sixty semidiameters of the earth. Newton at first sup- 
 posed the earth to be less than 7000 miles in diameter, and 
 consequently his calculations failed to lead him to the right 
 
 ee 
 
NEWTON.—DISCOVERY OF GRAVITATION. 77 
 
 result. This was in 1665, when he was only twenty - three 
 years of age. He laid aside his calculations for nearly twenty 
 years, when, learning that the measures of Picard, in France, 
 showed the earth to be one-sixth larger than he had supposed, 
 he again took up the subject. He now found that the deflec- 
 tion of the orbit of the moon from a straight line was such as 
 to amount to a fall of sixteen feet in one minute, the same dis- 
 tance which a body falls at the surface of the earth in one 
 second. The distance fallen being as the square of the time, 
 it followed that the force of gravity at the surface of the earth 
 was 3600 times as great as the force which held the moon in 
 her orbit. This number was the square of 60, which expresses 
 the number of times the moon is more distant than we are 
 from the centre of the earth. Hence, the force which holds the 
 moon in her orbit ts the same as that which makes a stone fall, only 
 diminished in the inverse square of the distance from the centre of 
 the earth. 
 
 To the mathematician the passage from the gravitation of an 
 apple to that of the moon is quite simple; but the non-mathe- 
 matical reader may not, at first sight, see how the moon can be 
 constantly falling towards the earth without ever becoming any 
 nearer. The following illustration will make the matter clear: 
 any one can understand the law of falling bodies, by which a 
 body falls sixteen feet the first second, three times that distance 
 the next, five times the third,and so on. If, in place of falling, 
 the body be projected horizontally, like a cannon-ball, for ex- 
 ample, it will fall sixteen feet out of the straight line in which 
 it is projected during the first second, three times that distance 
 the next, and so on, the same as if dropped from a state of 
 rest. In the annexed figure, let AB represent a portion of 
 the curved surface of the earth, and AD a straight line hori- 
 zontal at A, or the line along which an observer at A would 
 sight if he set a small telescope in a horizontal position. 
 Then, owing to the curvature of the earth, the surface will 
 fall away from this line of sight at the rate of about eight 
 inches in the first mile, twenty-four inches more in the second 
 mile, and so on. In five miles the fall will amount to sixteen 
 
78 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 feet. In ten miles, in addition to this sixteen feet, three times 
 that amount will be added, and so on, the law being the same 
 
 ° ASSSSSLLEEZEZZ a 
 
 Fie. 21.—Illustrating the fall of the moon towards the earth. 
 
 with that of.a falling body. Now, let AC be a high steep 
 mountain, from the summit of which a cannon-ball is fired in 
 the horizontal direction CH. The greater the velocity with 
 which the shot is fired, the farther it will go before it reaches 
 the ground. Suppose, at length, that we should fire it with 
 a velocity of five miles a second, and that it should meet with 
 no resistance from the air. Suppose e to be the point on the 
 line five miles from C. Since it would reach this point in one 
 second, it follows, from the law of falling bodies just cited, 
 that it will have dropped sixteen feet below e. But we have 
 just seen that the earth itself curves away sixteen feet at this 
 distance. Hence, the shot is no nearer the earth than when it 
 was fired. During the next second, while the ball would go to 
 #, it would fall forty-eight feet more, or sixty-four feet in all. 
 But here, again, the earth has still been rounding off, so the 
 distance DB is sixty-four feet. Hence, the ball is still no near- 
 er the earth than when it was fired, although it has been drop- 
 ping away from the line in which it was fired exactly like a 
 falling body. Moreover, meeting with no resistance, it is still 
 going on with undiminished velocity; and, just as it has been 
 falling for two seconds without getting any nearer the earth, 
 so it can get no nearer in the third second, nor in the fourth, 
 nor in any subsequent second; but the earth will constantly 
 curve away as fast as the ball can drop. Thus the latter will 
 pass clear round the earth, and come back to the first point C, 
 
 SO eee 
 
NEWTON.—DISCOVERY OF GRAVITATION. 79 
 
 from which it started, in the direction of the arrow, without 
 any loss of velocity. The time of revolution will be about an 
 hour and twenty-four minutes, and the ball will thus keep on 
 revolving round the earth in this space of time. In other 
 words, the ball will be a satellite of the earth, just like the 
 moon, only much nearer, and revolving much faster. 
 
 Our next step is to extend gravitation to other bodies than 
 the earth. The planets move around the sun as the moon 
 does around the earth, and must, therefore, be acted on by a 
 force directed towards the sun. This force can be no other 
 than the gravitation of the sun itself. A very simple calcula- 
 tion from Kepler’s third law shows that the force with which 
 each planet thus gravitates towards the sun is inversely as the 
 square of the mean distance of the planet. 
 
 Only one more step is necessary. What sort of an orbit 
 will a planet describe if acted on by a force directed towards 
 the sun, and inversely as the square of the distance? <A very 
 simple demonstration will show that, no matter what the law 
 of force, if it be constantly directed towards the sun, the radi- 
 us-vector of the planet will sweep over equal areas in equal 
 times. And, conversely, it cannot sweep over equal areas in 
 equal times if the force acts in any other direction than that 
 of the sun. Hence it follows, from Kepler’s second law, that 
 the force is directed towards the sun itself. 
 
 The problem of determining what form of orbit would be 
 described was one with which very few mathematicians of 
 that day were able to.grapple. Newton, succeeded in proving, 
 by a rigorous demonstration, that the orbit would be an el- 
 lipse, a parabola, or a hyperbola, according to circumstances, 
 having the sun in one of its foci, which, in the case of the 
 ellipse, was Kepler’s first law. Thus, all mystery disappeared 
 from the celestial motions, and the planets were shown to be 
 simply heavy bodies moving according to the same laws we 
 see acting all around us, only under entirely different circum- 
 stances. All three of Kepler’s laws were expressed in the sin- 
 gle law of gravitation towards the sun, with a force acting in- 
 versely as the square of the distance. 
 
 rf 
 
80 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 Very beautiful is the explanation which gravity gives of 
 Kepler’s third law. We have seen that if we take the cubes 
 of the mean distances of the several planets, and divide them 
 by the square of the times of revolution, the quotient will be 
 the same for each planet of the system. If we proceed in the 
 same way with the satellites of Jupiter, cubing the distance 
 of each satellite from Jupiter, and dividing the cube by the 
 square of the time of revolution, the quotient will be the same 
 for each satellite, but will not be the same as for the planets. 
 This quotient, in fact, is proportional to the mass or weight of 
 the central body. In the case of the planets it is 1050 times 
 as great as in the case of the satellites of Jupiter. This shows 
 that the sun is 1050 times as heavy as Jupiter. We thus have 
 a very convenient way of “weighing” such of the planets as 
 have satellites, by measuring the orbits of the satellites, and 
 determining the times of their revolution. But the weight is 
 not thus expressed in tons, but only in fractions of the mass 
 of the sun. 
 
 The law, however, is not yet complete. The attraction be- 
 tween the sun and planets must, by the third law of motion, 
 be mutual. If the earth attracts the moon, she must, if the 
 law be a general one, attract the planets also, and the planets 
 must attract each other, and thus alter their motions around 
 the sun. Now, it is known from observation that the planets 
 do not move in exact accordance with Kepler’s laws. The 
 final question, then, arises whether the attraction of the plan- 
 ets on each other fully, and exactly accounts for the deviations. 
 This question Newton could answer only in an imperfect way, 
 the problem being too intricate for his mathematics. He was 
 able to show that the attraction of the sun would cause ine- 
 qualities in the motion of the moon of the same nature as 
 those observed, but he could not calculate their exact amount. 
 Still, the general correspondence of his theory with the mo- 
 tions of the heavens was so striking that there ought not to 
 be any doubt of its truth. Very remarkable, therefore, is it 
 to see the French Academy of Sciences, as late as 1732—more 
 than forty years later—awarding a prize to John Bernoulli, the 
 
GRAVITATION OF SMALL MASSES. 81 
 
 celebrated mathematician, for a paper in which the motions 
 of the planets were explained on the theory of vortices. It 
 should not be inferred from this that that justly celebrated 
 body still considered that theory to be correct; but we may 
 infer that they still considered it an open question whether 
 the theory of gravitation was correct. 
 
 To express Newton’s theory with completeness, it is not suf- 
 ficient to say simply that the sun, earth, and planets attract 
 each other. Divide matter as finely as we may, we find it 
 still possessing the power of attraction, because it has weight. 
 Since the earth attracts the smallest particles, they must, by 
 the third law of motion, attract the earth with equal force. 
 Hence we conclude that the power of attraction resides, not 
 in the earth as a whole, but in each individual particle of the 
 matter composing it; that is, the attraction of the earth upon 
 a stone is simply the sum total of the attractions between the 
 stone and all the particles composing the earth. 
 
 There is no known limit to the distance to which the at- 
 traction of gravitation extends. The attraction of the sun 
 upon the most distant known planets, Uranus and Neptune, 
 shows not the slightest variation from the law of Newton. 
 But, owing to the rapid diminution with the distance to which 
 the law of the inverse square gives rise when we take distances 
 so immense as those which separate us from the fixed stars, 
 the gravitation even of the sun is so small that a million 
 years would be required for it to produce any important ef-. 
 fect. We are thus led to the law of uniyersal gravitation, ex- 
 pressed as follows: 
 
 Every particle of matter in the unwerse attracts every other par- 
 ticle with a force directly as their masses, and inversely as the 
 square of the distance which separates them. 
 
 § 2. Gravitation of Small Masses.—Density of the Earth. 
 
 To make perfect the proof that gravity does really reside 
 in each particle of matter, it was desirable to show, by actual 
 experiment, that isolated masses did really attract each other, 
 as required by Newton’s law. This experiment has been 
 
82 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 made in various ways with entire success, the object, howev- 
 er, being not to prove the existence of the attraction, but to 
 measure the mean density of the earth, which adinits of be- 
 ing thus determined. The attraction of a sphere upon a point 
 at its surface is shown, mathematically, to be the same as if 
 the entire mass of the sphere were concentrated in its centre. 
 It is, therefore, directly as the total amount of matter in the 
 sphere, that is, its weight, and inversely as the square of its 
 radius. Let us, then, compare the attraction of two spheres of 
 the same material, of which the diameter of the one is double 
 that of the other. The larger will have eight times the bulk, 
 and therefore eight times the mass, of the smaller. But 
 against this is the disadvantage that a particle on its surface 
 is twice as far from its centre as in the case of the smaller 
 sphere, which causes a diminution of one-fourth. Conse- 
 quently, it will attract such a particle with double the force 
 that the smaller sphere will; that is, the attractions are direct- 
 ly as the diameters of the spheres, if the densities are equal. 
 If the densities are not equal, the attraction is proportional to 
 the product of the density into the diameter. 
 
 The diameter of the earth is,in round numbers, forty millions 
 of feet. Consequently, the attraction of a sphere of the same 
 mean density as the earth, but one foot in diameter, will be 
 so-otuor part the attraction of the earth; that is, -3a24.-a09 
 the weight of the body attracted. Consequently, if we should 
 _measure the attraction of such a sphere of lead, and find that 
 it was just g>-ad0-v0 that of the weight of the body attracted, 
 we would conclude that the mean density of the earth was 
 equal to that of lead. But the attraction is actually found 
 to be nearly twice as great as this; consequently, a leaden 
 sphere is nearly twice as dense as the average of the mat- 
 ter composing the earth. Such a determination of the density 
 of the earth is known as the Cavendish experiment, from the 
 name of the physicist who first executed it. 
 
 The method in which a task seemingly so hopeless as meas- 
 uring a minute force like this is accomplished is shown in the 
 following figures. It consists primarily of a torsion balance ; 
 
 | 
 . 
 
GRAVITATION OF SMALL MASSES. 83 
 
 that is, a very light rod, e, with a weight at each end, suspend- 
 ed horizontally by a fine fibre of silk. In order to protect it 
 against currents of air, it must be completely enclosed in a 
 case. In Fig. 22, the balance ed is suspended from the end 
 
 ne === 
 K lI 
 
 =| ‘iN = 
 La 
 
 ———— il i 
 
 SS ill Ntt Al —a 
 
 ; = = 3 
 
 Fig. 22,—Baily’s apparatus for determining the density of the earth by the Cavendish ex 
 periment. The left-hand ball b is hidden behind the weight W. 
 
 of the arm AF’ by the fine fibre of silk, “#. The weights to 
 be attracted are at the two ends, 0b. When thus suspend- 
 ed, the balance will swing round in a horizontal direction, 
 twisting the silk fibre, by a very small force. The attracting 
 masses consist of a pair of leaden balls, WW, as large as the 
 experimenter can procure and manage, which are supported 
 on the turn-table, 7. In Fig. 23, a view of the apparatus from 
 above is given, showing the relative positions of the leaden 
 balls, and the suspended weights which they are to attract. 
 It will be seen that in the position in which the weights are 
 represented in the figure their attraction tends to make the 
 torsion balance turn in the direction opposite that of the hands 
 ofa watch. The effect of placing the leaden balls in this posi- 
 tion is, that the balance begins to turn as described, and, being 
 carried by its momentum beyond the position of equilibrium, 
 at length comes to rest by the twisting of the silk thread by 
 which it is suspended, and then is carried part of the way 
 
84 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 back to its original position. It makes several vibrations, 
 each requiring some minutes, and at length comes to rest in a 
 position different from its original one. The attracting balls 
 are then placed in the reverse position, corresponding to the 
 
 Fie, 23.—View of Baily’s apparatus from above. 
 
 dotted lines, so that they tend to make the balance swing in 
 the opposite direction, and the motions of the balance are 
 again determined. These motions are noted by a small mi- 
 croscope, viewed through the enclosure in which the whole 
 apparatus is placed, and from these motions the attractions of 
 the balls can be computed. 
 
 Since this experiment was first made by Cavendish, it has 
 been repeated by several other physicists; first by Professor 
 Reich, of Freiberg, in 1838, and again by Francis Baily, Esq., 
 of London. The latter repetition forms one of the most elab- 
 orate and exhaustive series of experiments ever made; we 
 have therefore chosen Baily’s apparatus for the purpose of 
 illustration. The results for the mean density of the earth 
 obtained by these several experiments are : | 
 
 Cavendish: (hfs: owl Tesalt).\...sseees+ncrvsceeedl  ndeermertanenecarcnseviess 5.48 
 pe (Hutton’s revision NAVs alilevtismtse eee ered saoees 5.32 
 
 Lorie ee) eet eee Se yee Ma LST CERES oy eee Sc dapat re tT eee ee 
 
 EXGLY a ietae cdotiein 625 8 deocinse tae ou tomt te ohds CS abkanie eater Memes geet Sele einn dn. © 5.66* 
 
 * Memoirs of the Royal Astronomical Society, vol. xix. 
 
DENSITY OF THE EARTH. 85 
 
 The same problem has been attacked by attempting to de- 
 termine the attraction of mountains, or portions of the crust 
 of the earth. In fact, the first attempt 
 of the sort ever made was by Maske- 
 lyne, Astronomer Royal of England 
 from 1766 to 1811, who determined 
 the attraction of the mountain Sche- 
 hallien, in Scotland, by observing its 
 effect on the plumb-line. The princi- 
 ple of this is very clear: on whichever 
 side of a steep isolated mountain we 
 hang a plumb-line, the attraction of 
 the mountain will cause it to incline towards it, the direction 
 of gravity, or the apparent vertical, being changed from AB 
 (Fig. 24) to AZ, and from CD to CG. The density of the 
 earth thus obtained was 4.71, a quantity much smaller than 
 that afterwards given by the leaden balls. But this method 
 is necessarily extremely uncertain, owing to the fact that the 
 earth immediately beneath the mountain will probably not be 
 of the same density as at a distance from it, and it is impos- 
 sible to determine and allow for this difference. 
 
 A third method is to find the change in the force of gravity 
 as we descend into the earth. We have said that the attrac- 
 tion of the earth upon a point outside of it is the same as if 
 the whole mass of the earth were concentrated in its centre. 
 Hence, as we rise above the surface of the earth, thus reced- 
 ing from the centre, the force of gravity diminishes. If this 
 force all resided in the centre of the earth, it would continue 
 to increase as we went below the surface, varying as the in- 
 verse square of our distance from the centre. But such is not 
 the case; because, once inside the earth, we have matter around 
 and above us, the attraction of which lessens the gravity to- 
 wards the centre. At the centre the attraction is nothing, be- 
 cause a point is there equally attracted in every direction. If 
 the density of the earth were uniform, gravity would diminish 
 with perfect uniformity from the surface to the centre. But 
 in fact the density of the interior is so much greater than that 
 
86 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 of the surface, that the force is found to increase as we go be- 
 low, instead of diminishing. Professor Airy, in 1855, made 
 an elaborate series of experiments at the Harton Colliery, in 
 Wales, in order to observe the rate of increase. He found 
 that a pendulum at the bottom of the mine went faster than 
 at the top by about 2.3 seconds per day. [rom this he con- 
 cluded that the mean density of the earth was 6.56. 
 
 § 3. Kigure of the Karth. 
 
 If the earth did not revolve, the mutual attraction of all its 
 parts would tend to make it assume a spherical form. If the 
 cohesion of the solid parts prevented the spherical form from 
 being accurately assumed, nevertheless the surface of the 
 ocean, or of any fluid covering the earth, would assume that 
 form. If, now, we set such a spherical earth in rotation 
 around an axis, a centrifugal force will be generated towards 
 the equatorial regions, which will cause the ocean to move 
 from the poles towards the equator, so that the surface will 
 tend to assume the form of an oblate spheroid, the longest di- 
 ameter passing through the equator, and the shortest through 
 the poles. A computation of the centrifugal force at the 
 equator shows it to be zy the force of gravity itself. Conse- 
 quently, the oblateness ought to be easily measurable in geo- 
 detic operations. Yet another result was that, in consequence 
 of the centrifugal force at the equator, bodies would be light- 
 er, and a clock regulated to northern latitudes would lose 
 time when taken thither. 
 
 This last result accorded with the experience of Richer, 
 sent by the French Academy to Cayenne, in 1672, to make ob- 
 servations on Mars. After that, to deny the oblate figure of 
 the earth was not so much to deny Newton’s theory of gravity 
 
 * The general law which regulates the force of gravity within the earth is this: 
 The total attraction of the shell of earth, which-is outside the attracted point ex- 
 tending all around the globe, is nothing, while the remainder of the globe, being 
 a sphere with the point on its surface, attracts as if it were all concentrated at 
 the centre. But this presupposes that the whole earth is composed of spherical 
 layers, each of uniform density, which is not strictly the case. 
 
 ~ 
 
FIGURE OF THE EARTH. 8 
 
 as to deny that mechanical forces produced their natural effect 
 in changing the form of the surface of the ocean. Neverthe- 
 less, the French astronomers long refused their assent, because 
 the geodetic operations they had undertaken in France seemed 
 to indicate that the earth was elongated rather than flattened 
 in the direction of the poles. The real cause of this result 
 was, that the distance measured in France was so short that _ 
 the effect of the earth’s ellipticity was entirely masked by the 
 ‘ unavoidable errors of the measures, yet it long delayed the en- 
 tire acceptance of the Newtonian theory by the French astron- 
 omers. We must, however, give the latter, or, speaking of 
 them individually, their successors of the next generation, the 
 credit of taking the most thorough measures to settle the ques- 
 tion. Their government sent one expedition to Peru, to meas- 
 ure the length of a degree of latitude at the equator, and an- 
 other to Lapland, to measure one as near as possible to the 
 pole. The result was entirely in accord with the theory of 
 Newton, and gave it a confirmation which had in the mean 
 time become entirely unnecessary. ) 
 
 Newton was unable to determine the exact figure which the 
 earth ought to assume under the influence of its own attrac- 
 tion and the centrifugal force of rotation, though he could see 
 that its meridian lines would be curves not very different from 
 an ellipse. The complication of the problem arises from the 
 fact that, as the earth changes its form in consequence of the 
 rotation, the direction and force of attraction at the various 
 points of its surface change also; and this, in its turn, leads 
 to a different figure. It was not until the middle of the last 
 century that the problem of the form of a rotating fluid mass 
 was solved, and the answer found to be an ellipsoid. 
 
 The figure of the earth is, however, not an exact ellipsoid, 
 there being two causes of deviation. (When we speak of the 
 figure or dimensions of the earth, we mean those of the ocean 
 as they would be if the ocean covered the entire earth.) One 
 cause of deviation is that the density of the earth increases 
 as we approach its centre. The other cause is that there are 
 great irregularities in the density of its superficial portions. 
 
88 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 In consequence of this, the real figure of the water-line is full 
 of small deviations, which are rendered very evident by the 
 refined determinations of modern times, and which are very 
 troublesome to all who are engaged in exact geodetic opera- 
 tions. 
 
 § 4. Precession of the Equinoxes. 
 
 Yet another mysterious phenomenon which gravity com- 
 pletely explained was that of the precession of the equinoxes. 
 We have already described this as a slow change in the posi- 
 tion of the pole of the celestial sphere among the stars, lead- 
 ing to a corresponding change in the position of the celestial 
 equator. But the Copernican theory shows the celestial pole 
 to be purely fictitious, because the heavens do not revolve at 
 all, but the earth. The pole of the celestial sphere is only 
 that point of the heavens towards which the axis of the earth 
 points. Hence, when we come to the Copernican system, we 
 see that precession must be in the earth, and not in the heay- 
 ens, and must consist simply in a change in the direction of 
 the earth’s axis, in virtue of which it describes a circle in the 
 heavens in about 25,800 years. This effect was traced by 
 Newton to the attraction of the sun and moon on the protu- 
 berance produced, as just described, by the centrifugal force 
 at the earth’s equator. In the present case the effect is much 
 the same as if the earth, being itself spherical, were enveloped 
 by a huge ring extending round its equator. In Fig. 25 let 
 
 Fig. 25. 
 
 AB represent this ring revolving around the sun, 8; the cen- 
 trifugal force of the earth, due to its motion around the sun, 
 will then balance the mean attraction of the sun upon it.. But 
 the point A being near the sun, the attraction of the latter upon 
 
 - a 
 
 | 
 | 
 : 
 ; 
 f 
 
PRECESSION OF THE EQUINOXES. 89 
 
 it will be more powerful than upon C,and consequently great- 
 er than the centrifugal force. So there will be a surplus force 
 drawing A towards the sun. At B the attractive force of the 
 sun is less than the mean, so that there is a surplus force tend- 
 ing to draw & from the sun. The ring being oblique towards 
 the sun, the effect of these surplus forces would be to make 
 the ring turn round on ¢ until the line AB pointed towards the 
 sun. The spherical earth being fastened in the ring, as just 
 supposed, would very slowly be turned round with the ring, so 
 that its equator would be directed towards the sun. but this 
 effect is prevented by the earth’s rotation on its axis, which 
 makes it act like a gyroscope, or like a spinning-top. Instead 
 of being brought down towards the sun, a very slow motion, at 
 right angles to this direction, is produced, and thus we have 
 the motion of precession. The nature of this motion may be 
 best seen by Fig. 18, where the north pole of the earth is rep- 
 resented as constantly inclined to the right of the observer as 
 the earth moves round the sun, so that the solstices are at A 
 and C, and the equinoxes at Band D. The effect of the at- 
 traction of the sun and moon on the protuberance at the 
 equator is, that in 6500 years the axis of the earth will incline 
 towards the observer of the picture, with nearly the inclina- 
 tion of 23°; so that the solstices will be at Band D, and the 
 equinoxes at A and C. In 6500 years more the north pole 
 will be pointed towards the left instead of the right, as in the 
 figure; in 6500 more it will be directed from the observer ; 
 and, finally, at the end of a fourth period it will be once more 
 near its present position. 
 
 The effects we have described would not occur if the plane 
 of the ring, AB, passed through the sun, because then the 
 forces which draw A towards the sun and B from it, would act 
 directly against each other, and so destroy each other’s effect. 
 Now, this is the case twice a year, namely, when the sun is on 
 the equator. Therefore, the motion of precession is not uni- 
 form, but is much greater than the average in June and De- 
 cember, when the sun’s declination is greatest; and is less in 
 March and September, when the sun is on the plane of the 
 
90 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 equator. Moreover, in December the earth is nearer the sun 
 than in June, and the force greater, so that we have still an- 
 other inequality from this cause. 
 
 Precession is not produced by the sun alone. The moon is 
 a yet more powerful agent in producing it, its smaller mass 
 being more than compensated by its greater proximity to us.* 
 The same causes which make the action of the sun variable 
 make that of the moon variable also, and we have the addi- 
 tional cause that, owing to the revolution of the moon’s node, 
 the inclination of the moon’s orbit to the plane of the earth’s 
 equator is subject to an oscillation having a period of 18.6 
 years, producing an inequality of this same period in the pre- 
 cession. The several inequalities in the precession which we 
 have described are known as nutation of the earth's axis, and 
 are all accurately computed and laid down in astronomical 
 tables. | 
 
 § 5. The Tides. 
 
 It has been known to seafaring nations from a remote an- 
 tiquity that there was a singular connection between the ebb 
 and flow of the tides, and the diurnal motion of the moon. 
 Ceesar’s description of his passages across the English Channel 
 shows that he was acquainted with the law. In describing 
 the motion of the moon, it was shown that, owing to her revo- 
 lution in a monthly orbit, she rises, passes the meridian, and 
 sets about fifty minutes later every day. ‘The tides ebb and 
 flow twice a day, but the corresponding tide is always later 
 than the day before, by the same amount, on the average, that 
 the moon is later. Hence, at any one place, the tides always 
 oceur when the moon is near the same point of her apparent 
 diurnal course. 
 
 * This may need some explanation, as the attractive force of the sun upon the 
 earth is more than a hundred times that of the moon. ‘The force which produces 
 precession is proportional to the difference of the attractions on the two sides of 
 the earth, or on A and B& in Fig. 25, and this difference is greater in the case of 
 the moon’s attraction. In fact, it varies inversely as the cube of the distance of 
 the attracting body. 
 
THE TIDES. 91 
 
 The cause of this ebb and flow of the sea, and its relation 
 to the moon, was a mystery until gravitation showed it to be 
 due to the attraction of the moon on the waters of the ocean. 
 The reason why there are two tides a day will appear by 
 studying the case of the moon’s revolution around the earth. 
 Let JZ be the moon, # the earth, and #7 the line joining their 
 centres. Now, strictly speaking, the moon does not revolve 
 around the earth, any more than the earth around the moon; 
 but by the principle of action and reaction the centre of each 
 body moves around the common centre of gravity of the two 
 bodies. The earth being eighty times as heavy as the moon, 
 this centre is situated within the former, about three-quarters 
 of the way from its centre to its surface, at the point G in the 
 
 Fie. 26.—Attraction of the moon tending to produce tides. 
 
 figure. The body of the earth itself being solid, every part of 
 ‘it, in consequence of the moon’s attraction, may be considered 
 as describing a circle once in a month, having a radius equal 
 to HG. The centrifugal force caused by this rotation is just 
 balanced by the mean attraction of the moon upon the earth. 
 If this attraction were the same on every part of the earth, 
 there would be everywhere an exact balance between it and 
 the centrifugal force. But as we pass from # to D the at- 
 traction of the moon diminishes, owing to the increased dis- 
 tance. Hence at ) the centrifugal force predominates, and 
 the water therefore tends to move away from the centre £. 
 As we pass from #’ towards C’ the attraction of the moon in- 
 creases, and therefore exceeds the centrifugal force. Conse- 
 quently, at C there is a tendency to draw the water towards 
 the moon, but still away from the centre #. At A and SL the 
 attraction of the moon increases the gravity of the water, ow- 
 
92 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 ing to the convergence of the lines BIZ and AW, along which 
 it acts; hence the action of the moon tends to make the waters 
 rise at D and C, and to fall at A and B, there are therefore 
 two tides to each apparent diurnal revolution of the moon. 
 
 If the waters everywhere yielded immediately to the at- 
 tractive force of the moon, it would always be high-water 
 when the moon was on the meridian, low-water when she was 
 rising or setting, and high-water again when she was in the 
 middle of that portion of her course which is under the hori- 
 zon. But, owing to the inertia of the water, some time is 
 necessary for so slight a force to set it in motion, and, once in 
 motion, it continues so after the force has ceased, and until it 
 has acted some time in the opposite direction. Therefore, if 
 the motion of the water were unimpeded, it would not be 
 high-water until some hours after the moon had passed the 
 meridian. Yet another circumstance interferes with the free 
 motion of the water—namely, the islands and continents. 
 These deflect the tidal wave from its course in such a way that 
 it may, in some cases, be many hours behind its time, or even 
 a whole day. Sometimes two waves may meet each other, 
 and raise an extraordinarily high tide. At other times the 
 tides may have to run up a long bay, where the motion of a 
 long mass of water will cause an enormous tide to be raised. 
 In the Bay of Fundy both of these causes are combined. A 
 tidal wave coming up the Atlantic coast meets the ocean 
 wave from the east, and, entering the bay with their com- 
 bined force, the water at the head of it is forced up to the 
 height of sixty or seventy feet, on the principle seen in the 
 hydraulic ram. 
 
 The sun produces a tide as well as the moon, the force 
 which it exerts on the two sides of the earth being the same, 
 which, acting on the equatorial protuberance of the earth, 
 produces precession. The tide-producing force of the sun is 
 about 34, of that of the moon. At new and full moon the two 
 bodies unite their forces, and the result is that the ebb and 
 flow are greater than the average, and we have the “spring- 
 tides.” When the moon is in her first or third quarter, the 
 
 ea —— 
 
INEQUALITIES IN THE MOTIONS OF THE PLANETS. 93 
 
 two forces act against each other; the tide-producing force is 
 the difference of the two, the ebb and flow are less than the 
 average, and we have the “ neap-tides.” 
 
 § 6. Inequalities in the Motions of the Planets produced by their 
 Mutual Attraction. 
 
 The profoundest question growing out of the theory of 
 gravitation is whether all the inequalities in the motion of the 
 moon and planets admit of being calculated from their mut- 
 ual attraction. This question can be completely answered 
 only by actually making the calculation, and seeing whether 
 the resulting motion of each planet agrees exactly with that 
 observed. The problem of computing the motion of each 
 planet under the influence of the attraction of all the others 
 is, however, one of such complexity that no complete and per- 
 fect solution has ever been found. Stated in its most general 
 form, it is as follows: Any number of planets of which the 
 masses are known are projected into space, their positions, ve- 
 locities, and directions of motion all being given at some one 
 moment. They are then left to their mutual attractions, ac- 
 cording to the law of gravitation. It is required to find gen- 
 eral algebraic formulz by which their position at any time 
 whatever shall be determined. In this general form, no ap- 
 proximation to an entire solution has ever been found. But 
 the orbits described by the planets around the sun, and by the 
 satellites around their primaries, are nearly circular; and this 
 circumstance affords the means of computing the theoretical 
 place of the planet as accurately as we please, provided the 
 necessary labor can be bestowed upon the work. 
 
 What makes the problem so complex is that the forces 
 which act upon the planets are dependent on their motions, 
 and these again are determined by the forces which act on 
 them. If the planets did not attract each other at all, the 
 problem could be perfectly solved, because they would then 
 all move in ellipses, in exact accordance with Kepler’s laws. 
 Supposing them to move in ellipses, their positions and dis- 
 tances at any time could be expressed in algebraic formule, 
 
94 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 and their attractions on each other could be expressed in the 
 same way. But, owing to these very attractions, they do not 
 move in ellipses, and therefore the formule thus found will 
 not be strictly correct. To put the difficulty into a nut-shell, 
 the geometer cannot strictly determine the motion of the plan- 
 et until he knows the attractions of all the other planets on it, 
 and he cannot determine these without first knowing the posi- 
 tion of the planet, that is, without having solved his problem. 
 
 The question how to surmount these difficulties has, to a 
 greater or less extent, occupied the attention of all great math- 
 ematicians from the time of Newton till now; and although 
 complete success has not attended their efforts, yet the mar- 
 vellous accuracy with which sun, moon, and planets move in 
 their prescribed orbits, and the certainty with which the laws 
 of variation of those orbits through countless ages past and to 
 come have been laid down, show that their labor has not been 
 in vain. Newton could attack the problem only in a geomet- 
 rical way; he laid down diagrams, and showed in what way 
 the forces acted in various parts of the orbits of the two plan- 
 ets, or in various positions of the sun and moon. He was thus 
 enabled to show how the attraction of the sun upon the moon 
 changes the orbit of the latter around the earth, and causes its 
 nodes to revolve from east to west, as observations had shown 
 them to do, and to calculate roughly one or two of the inequal- 
 ities in the motion of the moon in her orbit. 
 
 When the Continental mathematicians were fully convinced 
 of the correctness of Newton’s theory, they immediately at- 
 tacked the problem of planetary motion with an energy and 
 talent which placed them ahead of the rest of the world. 
 They saw. the entire insufficiency of Newton’s geometrical 
 method, and the necessity of having the forces which moved 
 the planets expressed by the algebraic method, and, by adopt- 
 ing this system, were enabled to go far ahead both of New- 
 
 ton and his countrymen. The last half of the last century — 
 
 was the Golden Age of mathematical astronomy. Five il- 
 lustrions names of this period outshine all others: Clairaut, 
 D’Alembert, Euler, Lagrange, and Laplace, all, except Euler, 
 
 a) ee 
 
 SS ee eee 
 
INEQUALITIES IN THE MOTIONS OF THE PLANETS. 95 
 
 French by birth or adoption. The great works which closed 
 it were the “ Mécanique Céleste” of Laplace, and the “ Mé- 
 canique Analytique” of Lagrange, which embody the sub- 
 stance of all that was then known of the subject, and form the 
 basis of nearly everything that has since been achieved. We 
 shall briefly mention some of the results of these works, and 
 those of their successors which may interest the non-mathe- 
 matical reader. 
 
 Perhaps the most striking of these results is that of the sec- 
 ular variations of the planetary orbits. Copernicus and Kep- 
 ler had found, by comparing the planetary orbits as observed 
 by themselves with those of Ptolemy, that the forms and posi- 
 tions.of those orbits were subject to a slow change from cen- 
 tury to century. The immediate successors of Newton were 
 able to trace this change to the mutual action of the planets, 
 and thus arose the important question, Will it continue for- 
 ever? For,should it do so, it would end in the ultimate sub- 
 version of the solar system, and the destruction of all life on 
 our globe. The orbit of the earth, as well as of the other plan- 
 ets, would become so eccentric that, approaching near the sun at 
 one time, and receding far from it at another, the vicissitudes 
 of temperature would be insupportable. Lagrange, however, 
 was enabled to show by a mathematical demonstration that 
 these changes were due to a regular system of oscillations ex- 
 tending throughout the whole planetary system, the periods of 
 which were so immensely long that only a progressive motion 
 could be perceived during all the time that men had observed 
 the planets. The number of these combined oscillations is 
 equal to that of the planets, and their periods range from 
 50,000 years all the way up to 2,000,000—“ Great clocks of 
 eternity, which beat ages as ours beat seconds.” In conse- 
 quence of these oscillations, the perihelia of the planets will 
 turn in every direction, and the orbits will vary in eccentricity, 
 but will never become so eccentric as to disturb the regularity 
 of the system. About 18,000 years ago, the eccentricity of the 
 earth’s orbit was about .019; it has been diminishing ever 
 
 since, and will continue to diminish for 25,000 years to come, 
 3 ; 
 
96 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 when it will be more nearly a circle than any orbit of our sys- 
 tem now is. 
 
 Some of the questions growing out of the moon’s motion 
 are not completely settled yet. Early in the last century it 
 was found by Halley, from a comparison of ancient eclipses 
 with modern observations of the moon, that our satellite was 
 accelerating her motion around the earth. She was, in fact, 
 about a degree ahead of where she ought to have been had 
 her motion been uniform from the time of Hipparchus and 
 Ptolemy. The existence of this acceleration was fully estab- 
 lished in the time of Lagrange and Laplace, and was to them 
 a source of great perplexity, because they had conceived them- 
 selves to have shown mathematically that the mutual attrac- 
 tions of the planets or satellites conld never accelerate or re- 
 tard their mean motions in their orbits, and thus the motion 
 of the moon seemed to be affected by some other force than 
 gravitation. After several vain attempts to account for the 
 motion, it was found by Laplace that, in consequence of the 
 secular diminution of the eccentricity of the earth’s orbit, the 
 action of the sun on the moon was progressively changing in 
 such a manner as to accelerate its motion. Computing the 
 amount of the acceleration, he found it to be about 10 see- 
 onds in a century, and its action on the moon being like that 
 of gravity on a falling body, the total effect would increase as 
 the square of the time; that is, while in one century the moon 
 would be 10 seconds ahead, in two centuries she would be 40 
 seconds ahead, in three centuries 90 seconds, and so on. 
 
 This result agreed so well with the observed acceleration, 
 as determined by a comparison of ancient eclipses with mod- 
 ern data, that no one doubted its correctness till long after the 
 time of Laplace. But, in 1853, Mr. J. C. Adams, of England, 
 celebrated as one of the two mathematicians who had calcu- 
 lated the position of Neptune from the motions of Uranus, un- 
 dertook to recompute the effect of the variation of the earth’s 
 eccentricity on the mean motion of the moon. He was sur- 
 prised to find that, carrying his process farther than Laplace 
 had done, the effect in question was reduced from 10 seconds, 
 
 a 
 
INEQUALITIES IN THE MOTION OF THE MOON. 97 
 
 the result of Laplace, to 6 seconds. On the other hand, the 
 further examination of ancient and modern observations 
 seerned to show that the acceleration as given by them was 
 even greater than that found by Laplace, being more nearly 
 12 seconds than 10 seconds; that is, it was twice as great as 
 that computed by Mr. Adams from the theory of gravitation. 
 
 The announcement of this result by Mr. Adams was at first 
 received with surprise and incredulity, and led to one of the 
 most remarkable of scientific discussions. Three of the great 
 astronomical mathematicians of the day—Hansen, Plana, and 
 De Pontécoulant — disputed the correctness of Mr. Adams’s 
 result, and maintained that that of Laplace was not affected 
 with any such error as Mr. Adams had found. In fact, Hansen, 
 by a method entirely different from that of his predecessors, 
 had found a result of 12 seconds, which was yet larger than 
 that of Laplace. On the other hand, Delaunay, of Paris, by a 
 new and ingenious method of his own, found a result agreeing 
 exactly with Mr. Adams’s. Thus, the five leading experts of 
 the day were divided into two parties on a purely mathemat- 
 _ ical question, and several years were required to settle the dis- 
 pute. The majority had on their side not only the facts of 
 observation, so far as they went, but the authority of Laplace; 
 and, if the question could have been settled either by observa- 
 tion or by authority, they must have carried the day. But the 
 problem was altogether one of pure mathematics, depending 
 on the computation of the effect which the gravitation of the 
 sun ought to produce on the motion of the moon. Both par- 
 ties were agreed as to the data, and bnt one correct result was 
 possible, so that an ultimate decision could be reached only by 
 calculation. 
 
 The decision of such a question could not long be delayed. 
 There was really no agreement among the majority as to what 
 the supposed error of Mr. Adams consisted in, or what the ex- 
 act mathematical expression for the moon’s acceleration was. 
 On the other hand, Mr. Adams showed conclusively that the 
 methods of De Pontécoulant and Plana were fallacious; and the 
 more profoundly the question was examined, the more evident 
 
98 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 it became that he was right. Mr. Cayley made a computation 
 of the result by a new method, and Delaunay by yet another 
 method, and both agreed with Mr. Adams’s. Although their 
 antagonists never formally surrendered, they tacitly abandon- 
 ed the field, leaving Delaunay and Adams in its undisturbed 
 possession.* 
 
 It was thus conclusively settled that the true value of the 
 acceleration was about 6”, the last value found by Delaunay 
 being 6.18. This result was only about half of that which 
 had been derived from the observations of ancient eclipses, so 
 that there appeared to be a discrepancy between the observed 
 and the theoretical acceleration, the cause of which was to 
 be investigated. A possible cause happened to be already 
 known: the friction of the tidal wave must constantly retard 
 the diurnal motion of the earth on its axis, though it is impos- 
 sible to say how much this retardation may amount to. The 
 consequence would be that the day would gradually, but un- 
 ceasingly, increase in length, and our count of time, depend- 
 ing on the day, would be always getting too slow. The moon 
 would, therefore, appear to be going faster, when really it was 
 only the earth which was moving more slowly. So long as 
 theory had agreed with the observed acceleration of the moon, 
 there had been no need to invoke this cause; but, now that 
 there was a difference, it afforded the most plausible explana- 
 tion. 
 
 Thus the theory of the subject is that there is an undoubted 
 real acceleration of 6.18, and an additional apparent accel- 
 eration of a few seconds, due to the tidal retardation of the 
 earth’s rotation, the amount of which can be found only by 
 comparing the motions of the moon in different centuries. 
 The absence of precise observations in ancient times renders 
 this determination difficult and uncertain. The ancient rec- 
 ords which have been most relied on are the narratives of sup- 
 
 * The writer has reason to believe it an historical fact that Hansen, on revising 
 his own calculations, and including terms he at first supposed to be insensible, 
 found that he would be led substantially to the result of Adams, although he 
 never made any formal publication of this fact. 
 
INEQUALITIES IN THE MOTION OF THE MOON. 99 
 
 posed total eclipses of the sun, which have been handed down 
 to us by the Greek and Roman classical writers. The most 
 ancient and celebrated of these eclipses is associated with the 
 name of Thales, the Ionian philosopher, our knowledge of 
 which is derived from the following account by Herodotus: 
 
 “Now after this (for Alyattes did not by any means sur- 
 render the Scythians at the demand of Cyaxares) there was 
 war between the Lydians and the Medes for the space of five 
 years, in which [period] the Medes often conquered the Lydi- 
 ans, and the Lydians, in turn, the Medes. And, in this time, 
 they also had a night engagement; for as they were protract- 
 ing the war with equal success on each side, in a battle that 
 occurred in the sixth year, it happened, as the armies en- 
 gaged, that the day was suddenly turned into night. Now 
 this change of the day [into night] Thales, the Milesian, had 
 predicted to the lonians, placing as the limit of the period 
 [within which it would take place] this very year in which 
 it did actually occur. Now, both the Lydians and the Medes, 
 when they saw night coming on instead of day, ceased from 
 battle, and both parties were more eager to make peace with 
 each other.” | 
 
 If, in this case, we knew when and where the battle was 
 fought, and if we knew that the darkness referred to was 
 really that of a total eclipse of the sun, it would be easy to 
 compute very nearly what must have been the course of the 
 moon in order that the dark shadow might have passed over 
 the field of battle. But, to the reader who reflects upon the 
 uncritical character of Herodotus, the vagueness of his descrip- 
 tion of the occurrence will suggest some suspicions whether 
 we have really a total eclipse to deal with. Besides, the time 
 when the battle was fought is doubtful by twenty years or 
 more, and the only way in which it has been fixed is by cal- 
 culating from the tables of the sun and moon all the total 
 eclipses which passed over the region in which the battle took 
 place between the admissible limits of time. Thus, it is found 
 that the only date which will fulfil the conditions is May 28th, 
 B.c. 584, when there must have been a total eclipse in Asia 
 
100 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 Minor or its neighborhood... But, unless we suppose that it 
 was really a total eclipse which caused the battle to cease, 
 nothing can be concluded respecting it; and as this point 
 seems uncertain, it is not likely that astronomers will lay 
 much stress upon it. 
 
 Another celebrated eclipse of the sun is known as the 
 eclipse of Agathocles. The fleet of this commander, being 
 blockaded in the port of Syracuse by the Carthaginians, was 
 enabled to escape to sea at a moment when the attention of 
 the enemy was diverted by a provision convoy, and sailed to 
 make a descent upon Carthage. “The next day there was 
 such an eclipse of the sun that the day wholly put on the 
 appearance of night, stars being seen everywhere.” There is 
 no reasonable doubt that this was a total eclipse of the sun, 
 and the date is well established, being August 14th, B.c. 309. 
 But, unfortunately, it is not known whether Agathocles went 
 to the north or the south of Sicily in his passage to Car- 
 thage, and hence we cannot obtain any certain result from 
 this eclipse. 
 
 These historical accounts of total eclipses being uncertain, 
 an attempt has been made to derive the moon’s acceleration 
 from the eclipses of the moon recorded by Ptolemy in the 
 Almagest, and from the observations of the Arabian astrono- 
 mers in the ninth and tenth centuries. These observations 
 agree as fairly as could be expected in assigning to the moon 
 a secular acceleration of about 8.4, a little more than 2” 
 greater than that computed from gravitation. On the other 
 hand, if we accept the eclipse of Thales as total where the 
 battle was fought, the total acceleration will be about 12”, so 
 that the two results are entirely incompatible. The question 
 which is correct must be decided by future investigation; but 
 the author believes the smaller value to be founded on the 
 more trustworthy data. | 
 
 The secular acceleration is not the only variation in the 
 moon’s mean motion which has perplexed the mathematicians. 
 About the close of the last century, it was found by Laplace 
 that the moon had, for a number of years, been falling behind 
 
INEQUALITIES IN THE MOTION OF THE MOON. 101 
 
 her calculated place, a result which seemed to show that there 
 was some oscillation of long period which had been overlooked. 
 Ile made two conjectural explanations of this inequality, but 
 both were disproved by subsequent investigators. The ques- 
 tion, therefore, remained without any satisfactory solution till 
 1846, when Hansen announced that the attraction of Venus 
 produced two inequalities of long period in the moon’s mo- 
 tion, which had been previously overlooked, and that these 
 fully accounted for the observed deviations of the moon’s po- 
 sition. These terms were recomputed by Delaunay, and he 
 found for one of them a result agreeing very well with Han- 
 sen’s. But the second came out so small that it could never be 
 detected from observations, so that here was another mathe- 
 matical discrepancy. There was not room, however, for much 
 discussion this time. Hansen himself admitted that he had 
 been unable to determine the amount of this inequality in a 
 satisfactory manner from the theory of gravitation, and had 
 therefore made it agree with observation, an empirical process 
 which a mathematician would never adopt if he could avoid 
 it. Even if observations were thus satisfied, doubt would still 
 remain. But it has lately been found that this empirical 
 term of Hansen’s no longer agrees with observation, and that 
 it does not satisfactorily agree with observations before 1700. 
 In consequence, there are still slow changes in the motion of 
 our satellite which gravitation has not yet accounted for. We 
 are, apparently, forced to the conclusion either that the motion 
 of the moon is influenced by some other cause than the gravi- 
 tation of the other heavenly bodies, or that these inequalities 
 are only apparent, being really due to small changes in the 
 earth’s axial rotation, and in the consequent length of the day. 
 If we admit the latter explanation, it will follow that the 
 earth’s rotation is influenced by some other cause than the 
 tidal friction; and that, instead of decreasing uniformly, it va- 
 ries from time to time in an irregular manner. The observed © 
 inequalities in the motion of the moon may be fully accounted 
 for by changes in the earth’s rotation, amounting in the ag- 
 gregate to half a minute or so of time—changes which could 
 
102 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 be detected by a perfect clock kept going for a number of 
 years. But, as it takes many years for these changes to occur, 
 no clock yet made will detect them. 
 
 Yet another change not entirely accounted for on the the- 
 ory of gravitation occurs in the motion of the planet Mercury. 
 From a discussion of all the observed transits of this planet 
 across the disk of the sun, Leverrier has found that the mo- 
 tion of the perihelion of Mercury is about 40 seconds in a 
 century greater than that computed from the gravitation of 
 the other planets. This he attributes to the action of a group 
 of small planets between Mercury and the sun. In this form, 
 however, the explanation is not entirely satisfactory. In the 
 first place, it seems hardly possible that such a group of plan- 
 ets could exist without being detected during total eclipses of 
 the sun, if not at other times. In the next place, granting 
 them to exist, they must produce a secular variation in the 
 position of the orbit of Mercury, whereas this variation seems 
 to agree exactly with theory. Leverrier explains this by sup- 
 posing the group of asteroids to be in the same plane with the 
 orbit of Mercury, but it is exceedingly improbable that such 
 a group would be found in this plane. There is, however, an 
 allied explanation which is at least worthy of consideration. 
 The phenomenon of the zodiacal light, to be described here- 
 after, shows that there is an immense disk of matter of some 
 kind surrounding the sun, and extending out to the orbit of 
 the earth, where it gradually fades away. The nature of this 
 matter is entirely unknown, but it may consist of a swarm of 
 minute particles, revolving round the sun, and reflecting its 
 light, like planets. Ifthe total mass of these particles is equal 
 to that of a very small planet, say a tenth the mass of the 
 earth, it would cause the observed motion of the perihelion of 
 Mercury. The evidence on this subject will be considered 
 more fully in treating of Mercury. 
 
 With the exceptions just described, all the motions in the 
 solar system, so far as known, agree perfectly with the results 
 of the theory of gravitation. The little imperfections which 
 still exist in the astronomical tables seein to proceed mainly 
 
 ” 
 OO 
 
RELATION OF THE PLANETS AND STARS. 103 
 
 from errors in the data from which the mathematician must 
 start in computing the motion of any planet. ‘The time of 
 revolution of a planet, the eccentricity of its orbit, the position 
 of its perihelion, and its place in the orbit at a given time, can 
 none of them be computed from the theory of gravitation, but 
 must be derived from observations alone. If the observations 
 were absolutely perfect, results of any degree of accuracy 
 could be obtained from them; but the imperfections of all 
 instruments, and even of the human sight itself, prevent ob- 
 servations from attaining the degree of precision sought after 
 by the theoretical astronomer, and make the considerations of 
 “errors of observation” as well as of “errors of the tables” 
 constantly necessary. 
 
 § 7. Relation of the Planets to the Stars. 
 
 In Chapter I, § 3, it was stated that the heavenly bodies 
 belong to two classes, the one comprising a vast multitude of 
 stars, which always preserved their relative positions, as if they 
 were set in a sphere of crystal, while the others moved, each 
 in its own orbit, according to laws which have been described. 
 We now know that these moving bodies, or planets, form a 
 sort of family by themselves, known as the Solar System. 
 This system consists of the sun as its centre, with a number of 
 primary planets revolving around it, and satellites, or second- 
 ary planets, revolving around them. Before the invention of 
 the telescope but six primary planets were known, including 
 the earth, and one satellite, the moon. By the aid of that in- 
 strument, two great primary planets, outside the orbit of Sat- 
 urn, and an immense swarm of smaller ones between the or- 
 bits of Mars and Jupiter, have been discovered; while the 
 four outer planets— Jupiter, Saturn, Uranus, and Neptune — 
 are each the centre of motion of one or more satellites. The 
 sun is distinguished from the planets, not only by his immense 
 mass, which is several hundred times that of all the other bod- 
 ies of his system combined, but by the fact that he shines by 
 his own light, while the planets and satellites are dark bodies, 
 se only by reflecting the light of the sun. 
 
104 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 
 
 A remarkable symmetry of structure is seen in this system, 
 in that all the large planets and all the satellites revolve in 
 orbits which are nearly circular, and, the satellites of the two 
 outer planets excepted, nearly in the same plane. This family 
 of planets are all bound together, and kept each in its respec- 
 tive orbit, by the law of gravitation, the action of which is of 
 such a nature that each planet may make countless revolutions 
 without the structure of the system undergoing any change. 
 
 Turning our attention from this system to the thousands of 
 fixed stars which stud the heavens, the first thing to be consid- 
 ered is their enormous distance asunder, compared with the 
 dimensions of the solar system, though the latter are them- 
 selves inconceivably great. To give an idea of the relative 
 distances, suppose a voyager through the celestial spaces could 
 travel from the sun to the outermost planet of our system in 
 twenty-four hours. So enormous would be his velocity, that it 
 would carry him across the Atlantic Ocean, from New York 
 to Liverpool, in less than a tenth of a second of the clock. 
 Starting from the sun with this velocity, he would cross the 
 orbits of the inner planets in rapid succession, and the outer 
 ones more slowly, until, at the end of a single day, he would 
 reach the confines of our system, crossing the orbit of Neptune. 
 But, though he passed eight planets the first day, he would 
 pass none the next, for he would have to journey eighteen or 
 twenty years, without diminution of speed, before he would 
 reach the nearest star, and would then have to continue his 
 journey as far again before he could reach another. All the 
 planets of our system would have vanished in the distance, in 
 the course of the first three days, and the sun would be but an 
 insignificant star in the firmament. The conclusion is, that 
 our sun is one of an enormous number of self-luminous bodies 
 scattered at such distances that years would be required to 
 traverse the space between them, even when the voyager went 
 at the rate we have supposed. The solar and the stellar sys- 
 tems thus offer us two distinct fields of inquiry, into which we 
 shall enter after describing the instruments and methods by 
 which they are investigated. 
 
 es 
 
PART IIT—PRACTICAL ASTRONOMY. 
 
 INTRODUCTORY REMARKS. 
 
 Suouitp the reader ask what Practical Astronomy is, the 
 best answer might be given him by a statement of one of its 
 operations, showing how eminently practical our science is. 
 “Place an astronomer on board a ship; blindfold him ; carry 
 him by any route to any ocean on the globe, whether under 
 the tropics or in one of the frigid zones; land him on the 
 wildest rock that can be found; remove his bandage, and give 
 him a chronometer regulated to Greenwich or Washington 
 time, a transit instrument with the proper appliances, and the 
 necessary books and tables, and in a single clear night he can 
 tell his position within a hundred yards by observations of the 
 stars.” This, from a utilitarian point of view, is one of the 
 most important operations of Practical Astronomy. When we 
 travel into regions little known, whether on the ocean or on 
 the Western plains, or when we wish to make a map of a 
 country, we have no way of finding our position by reference 
 to terrestrial objects. Our only course is to observe the heav- 
 ens, and find in what point the zenith of our place intersects 
 the celestial sphere at some moment of Greenwich or Wash- 
 ington time, and then the problem is at once solved. The in- 
 struments and methods by which this is done may also be ap- 
 plied to celestial measurements, and thus we have the art and 
 science of Practical Astronomy. To speak more generally, 
 Practical Astronomy consists in the description and investiga- 
 tion of the instruments and methods employed by astronomers 
 in the work of exploring and measuring the heavens, and of 
 
106 PRACTICAL ASTRONOMY. 
 
 determining positions on the earth by observations of the heav- 
 enly bodies. The general construction of these instruments, 
 and the leading principles which underlie their use and em- 
 ployment, can be explained with the aid of a few technical 
 terms which we shall define as we have occasion for them. 
 
 The instruments employed by the ancients in celestial ob- 
 servations were so few and simple that we may dispose of 
 them very briefly. The only ones we need mention at pres- 
 ent are the gnomon and the astrolabe, or armillary sphere. 
 The former was little more than a large sun-dial of the sim- 
 plest construction, by which the altitude and position of the 
 sun were determined from the length and direction of the 
 shadow of an upright pillar. If the sun were a point to the 
 sight, this method would admit of considerable accuracy, be- 
 cause the shadow would then be sharply defined. In fact, 
 however, owing to the apparent size of the solar disk, the shad- 
 ow of any object at the distance of a few feet becomes ill-de- 
 fined, shading off so gradually that it is hard to say where it 
 ends. No approach to accuracy can therefore be attained by 
 the gnomon. 
 
 Notwithstanding the rudeness of this instrument, it seems 
 to have been the one universally employed by the ancients 
 for the determination of the times when the sun reached 
 the equinoxes and solstices. The day when the shadow was 
 shortest marked the summer solstice, and a comparison of 
 the length of the shadow with the height of the style gave, 
 by a trigonometric calculation, the altitude of the sun. The 
 day when the shadow was longest marked the winter solstice ; 
 and the day when the altitude of the sun was midway between 
 the altitudes at the two solstices marked the equinoxes. Thus 
 this rude instrument served the purpose of determining the 
 length of the year with an accuracy sufficient for the purposes 
 of daily life. But so immensely superior are our modern 
 methods in accuracy, that the astronomer can to-day compute 
 the position of the sun at any hour of any day 2000 years ago 
 with far greater accuracy than it could have been observed 
 with a gnomon. 
 
INTRODUCTORY REMARKS. 107 
 
 The armillary sphere consisted of a combination of three 
 circles, one of which could be set in the plane of the equator 
 or the ecliptic; that is, an arm moving around this circle 
 would always point towards some part of the equator or the 
 ecliptic, according to the way the instrument was set. The 
 circle in question, being divided into degrees, served the pur- 
 pose of measuring the angular distance of any two bodies in 
 or near the ecliptic, as the sun and moon, or a star and planet. | 
 It was by such measures that Hipparchus and Ptolemy were 
 able to determine the larger inequalities in the motions of the 
 sun, moon, and planets. | 
 
 & —— 
 ay ~ =——S 
 MME ([LoEZZE 
 
 Fig. 27.—Armillary sphere, as described by Ptolemy, and used by him and by Hipparchus. 
 The circle El is set in the plane of the ecliptic, the line PP being directed towards its 
 pole. The circle ApMp passes throngh the poles of both the ecliptic and the equator. 
 The inner pair of circles turn on the axis PP, and are furnished with sights which may 
 
 be directed on the object to be observed. The latitude and longitude of the object are 
 then read off by the position of the circles. 
 
108 PRACTICAL ASTRONOMY. 
 
 CHAPTER IL 
 THE TELESCOPE. 
 
 § 1. The First Telescopes. 
 
 Tue telescope is so essential a part of every instrument in- 
 tended for astronomical measurement, that, apart from its own 
 importance, it must claim the first place in any description of 
 astronomical instruments. The question, Who made the first 
 telescape ? was long discussed, and, perhaps, will never be con- 
 clusively settled. If the question were merely, Who is entitled 
 to the credit of the invention under the rules according to 
 which scientific credit is now awarded ? we conceive that the 
 answer must be, Galileo. The first publisher of a result or 
 discovery, supposing such result or discovery to be honestly 
 his own, now takes the place of the first inventor; and there 
 is little doubt that Galileo was the first one to show the world 
 how to make a telescope. But Galileo himself says that it 
 was through hearing that some one in France or Holland had 
 made an instrument which magnified distant objects, and 
 brought them nearer to the view, that he was led to inquire 
 how such a result could be reached. He seems to have ob- 
 tained from others the idea that the instrument was possible, . 
 but no hint as to how it was made. 
 
 As a historic fact, however, there is no serious question that 
 the telescope originated in Holland; but the desire of the in- 
 ventors, or of the authorities, or both, to profit by the posses- 
 sion of an instrument of such extraordinary powers, prevented 
 the knowledge of its construction from spreading abroad. The 
 honor of being the originator has been claimed for three men, 
 each of whom has lad his partisans. Their names are Metius, 
 
THE FIRST TELESCOPES. 109 
 
 Lipperhey, and Jansen; the last two being spectacle-makers 
 in the town of Middleburg, and the first a professor of mathe- 
 matics. 
 
 The claims of Jansen were sustained by Peter Borelli, au- 
 thor of a small book* on the subject,and on the strength of 
 his authority Jansen was long held to be the true inventor. 
 His story was that Jansen had shown a telescope sixteen inches 
 long to Prince Maurice and the Archduke Albert, who, per- 
 ceiving the importance of the invention in war, offered him 
 money to keep it a secret. If this story be true, it would be 
 interesting to know on what terms Jansen was induced to sell 
 out his right to immortality. But Borelli’s case rests on the 
 testimony of two or three old men who had known Jansen in 
 their youth, taken forty-five or fifty years after the occurrence 
 of the events, when Jansen had long been dead, and has there- 
 fore never been considered as fully proved. 
 
 About 1830, documentary evidence was discovered which 
 showed that Hans Lipperhey, whom Borelli claims to have 
 been a second inventor of the telescope, made application to 
 the States-general of Holland, on November 2d, 1608, for a 
 patent for an instrument to see with at a distance. About 
 the same time a similar application was made by James Me- 
 tius. The Government refused a patent to Lipperhey, on the 
 ground that the invention was already known elsewhere, but 
 ordered several instruments from him, and enjoined him to 
 keep their construction a secret. 
 
 It will be seen from this that the historic question, Who 
 made the first telescope? does not admit of being easily an- 
 swered; but that the powers of the instrument were well 
 known in Holland in 1608 seems to be shown by the refusal 
 of a patent to Lipperhey. The efforts made in that country 
 to keep the knowledge of the construction a secret were so 
 far successful that we must go from Holland to Italy to find 
 how that knowledge first became public property. About six 
 months after the petitions of Lipperhey and Metius, Galileo 
 
 * ‘*De Vero Telescopii Inventore,” The Hague, 1655. 
 
110 PRACTICAL ASTRONOMY. 
 
 was in Venice on a visit, and there received a letter from 
 Paris, in which the invention was mentioned. He at once set 
 himself to the reinvention of the instrument, and was so suc- 
 cessful that in a few days he exhibited a telescope magnify- 
 ing three times, to the astonished authorities of the city. Re- 
 turning to his home in Florence, he made other and larger 
 ones, which revealed to him the spots on the sun, the phases 
 of Venus, the mountains on the moon, the satellites of Jupiter, 
 the seeming handles of Saturn, and some of the myriads of 
 stars, separately invisible to the naked eye, whose combined 
 light forms the milky-way. But the largest of these instru- 
 ments magnified only about thirty times, and was so imper- 
 fect in construction as to be far from showing as much as 
 could be seen with a modern telescope of that power. The 
 Galilean telescope was, in fact, of the simplest construction, 
 consisting of the combination of a pair of lenses, of which the 
 larger was convex and the smaller concave, as shown in the 
 following figure: 
 O 
 
 B 
 
 Fic. 28.—The Galilean telescope. The dotted lines show the course of the rays through 
 the lenses. 
 
 The distance of the lenses was such that the rays of light 
 from a star passing through the large convex lens, or object- 
 glass, O56, met the concave lens, #, before reaching the focus. 
 The position of this concave lens was such that the rays 
 should emerge from it nearly parallel. This form of tele- 
 scope is still used in opera-glasses, because it can be made 
 shorter than any other. 
 
 The improvements in the telescope since Galileo can be 
 best understood if we give a brief statement of the princi- 
 ples on which all modern telescopes are constructed. The 
 properties of every such instrument depend on the power pos- 
 sessed by a lens or by a concave mirror of forming an im- 
 age of any distant object in its focus. This is done in the 
 
THE FIRST TELESCOPES. bi 
 
 ease of the lens by refracting the light which passes through 
 it, and in the case of the mirror by reflecting back the rays 
 which strike it. In order to form an image of a point, it is 
 necessary that a portion of the rays of light which emanate 
 from the point shall be collected and made to converge to 
 some other point. Jor instance, in the following figure, the 
 
 Fig. 29.—Formation of an image by a lens. 
 
 nearly parallel rays emanating from a distant point in the di- 
 rection from which the arrow is coming strike the lens, Z, 
 and as they pass through it are bent out of their course, and 
 made to converge to a point, #. Continuing their course, : 
 they diverge from F exactly as of F itself were a luminous point, 
 a cone of light being formed with its apex at / An observer 
 placing his eye within this cone of rays, and looking at F, 
 will there seem to see a shining point, although really there 
 is nothing there. This apparent shining point is, in the lan- 
 guage of astronomy, called the image of the real point. The dis- 
 tance, OF, is called the focal length of the lens. 
 
 If, instead of a simple point, we have an object of some 
 apparent magnitude, as the moon, a house, or a tree, then the 
 light from each point of the object will be brought to a cor- 
 responding point near / ‘To find where this corresponding 
 point is, we have only to draw a line from each point of an 
 object through the centre of the lens, and continue it as far as 
 the focus. Each point of the object will then have its own 
 point in the image. These points, or images, will be spread 
 out over the surface, YZ, which is called the focal plane, and 
 will make up a representation, or image, of the entire object 
 on a small scale, but in a reversed position, exactly as in the 
 camera of a photographer. An eye at B within the cone of 
 rays will then see all or a part of the object reversed in the 
 focal plane. The image thus formed may be viewed by the 
 
112 PRACTICAL ASTRONOMY. 
 
 eye as if it were a real object; and as a minute object may be 
 viewed by a magnifying lens, so such a lens may be used to 
 view and magnify the image formed in the focal plane. In » 
 the large lens of long focus to form the image in the focal 
 plane, and the small lens to view and magnify this image, we 
 have the two essential parts of a refracting telescope. The 
 former lens is called the objective, or object-glass, and the latter 
 the eye-prece, eye-lens, or ocular. 
 
 The magnifying power of a telescope depends upon the rel- 
 ative focal lengths of the objective and ocular. The greater 
 the focal length of the former—that is, the greater the distance 
 Of —the larger the image will be; and the less the focal length 
 of the eye-lens, the nearer the eye can be brought to the im- 
 age, and the more the latter will be magnified. The magnify- 
 ing power is found by dividing the focal length of the objec- 
 tive by that of the eye-lens. Tor instance, if the focal length 
 of an objective were 36 inches, and that of the eye-lens were 
 three-quarters of an inch, the quotient of these numbers would 
 be 48, which would be the magnifying power. If the focal 
 lengths of these lenses were equal, the telescope would not 
 magnify at all. By simply turning a telescope end for end, 
 and looking in at the objective, we have a reversed telescope, 
 which diminishes objects in the same proportion that it mag- 
 nifies them when not reversed. 
 
 From the foregoing rule it follows that we can, theoretical- 
 ly, make any telescope magnify as much as we please, by sim- 
 ply using a sufficiently small eye-lens. If, for instance, we 
 wish our telescope of 36 inches focal length to magnify 3600 
 times, we have only to apply to it an eye-lens of =45 of an inch. 
 focal length. But,in attempting to do this, a difficulty arises 
 with which astronomers have always had to contend, and 
 which has its origin in the imperfection of the image formed 
 by the object-glass. No lens will bring all the rays of light 
 to absolutely the same focus. When light passes through a 
 prism, the various colors are refracted unequally, red being 
 refracted the least, and violet the most. It is the same 
 when light is refracted by a lens, and the consequence is that 
 
Fig. 30.—A great telescope of the seventeenth century, after Blanchini. 
 
THE FIRST TELESCOPES. 115 
 
 the red rays will be brought to the farthest focus, and the vio- 
 let to the nearest, while the intermediate colors will be scat- 
 tered between. As all the light is not brought to the same 
 focus, it is impossible to get any accurate image of a star or 
 other object at which the telescope is pointed, the eye seeing 
 only a confused mixture of images of various colors. When 
 a sufficiently low magnifying power is used, the confusion will 
 be slight, the edges of the object being indistinct, and made 
 up of colored fringes. When the magnifying power is in- 
 creased, the object will indeed look larger, but these confused 
 fringes will look larger in the same proportion; so that the 
 observer will see no more than before. This separation of the 
 light in a telescope is termed chromatic aberration. 
 
 Such was the difficulty which the successors of Galileo en- 
 countered in attempting to improve the telescope, and which 
 they found it impossible to obviate. They found, however, 
 that they could diminish it by increasing the length of the tel- 
 escope, and the consequent size of the confused image. If 
 they made an object-glass of any fixed diameter, say six inches, 
 they found that the image was no more confused when the 
 focal length was sixty feet than when it was six, and the same 
 eye-lens could therefore be used in both cases. but the im- 
 age in the focus of the first was ten times as large as in the 
 ‘second, and thus using the same eye-lens would give ten times 
 the magnifying power. Huyghens, Cassini, Hevelius, and oth- 
 er astronomers of the latter part of the seventeenth century, 
 made telescopes a hundred feet or upwards in length. Some 
 astronomers then had to dispense with a tube entirely ;. the ob- 
 jective being mounted by Cassini on the top of a long pole, 
 while the ocular was moved along near the ground. Hevelius 
 kept his objective and ocular connected by a long rod which 
 replaced the tube. Very complicated and ingenious arrange- 
 ments were sometimes used in managing these huge instru- 
 ments, of which we give one specimen, taken from the work 
 of Blanchini, “Hesperi et Phosphori Nova Phenomena,” in which 
 that astronomer describes his celebrated observations on the 
 rotation of Venus. 
 
116 PRACTICAL ASTRONOMY. 
 
 § 2. The Achromatic Telescope. 
 
 A century and a half elapsed from the time when Galileo 
 showed his first telescope to the authorities of Venice before 
 any method of destroying the chromatic aberration of a lens 
 _was discovered. It is to Dollond, an English optician, that the 
 practical construction of the achromatic telescope is due, al- 
 though the principle on which it depends was first published 
 by Euler, the German mathematician. The invention of Dol- 
 lond consists in the combination of a convex and concaye lens 
 of two kinds of glass in such a way that their aberrations 
 shall counteract each other. How this is effected will be best 
 seen by taking the case of refraction by a prism, where the 
 same principle comes into play. The separation of the light 
 into its prismatic colors is here termed dispersion. Suppose, 
 now, that we take two prisms of glass, ABC and ACD, (Fig. 
 31), and join them in the manner shown in the figure. If a 
 
 Fig. 31.—Refraction through a compound prism. 
 
 ray, /2S, pass through the two, their actions on it will tend 
 to counteract each other, owing to the opposite directions in 
 which their angles are turned, and the ray will be refracted 
 only by the difference of the refractive powers, and dispersed 
 by the difference of the dispersive powers. If the dispersive 
 powers are equal, there will be no dispersion at all, the ray 
 passing through without any separation of its colors. If the 
 two prisms are made of the same kind of glass, their dispersive 
 powers can be made equal only by making them of the same 
 angle, and then their refractive powers will be equal also, and 
 the ray will pass through without any refraction. As our ob- 
 
THE ACHROMATIC TELESCOPE. 117 
 
 ject is to have refraction without dispersion,a combination of 
 prisms of the same kind of glass cannot effect it. 
 
 The problem which is now presented to us is, Can we make 
 two prisms of different kinds of glass such that their disper- 
 sive powers shall be equal, but their refractive powers un- 
 equal? The researches of Euler and Dollond answered this 
 question in the affirmative by showing that the dispersive 
 power of dense flint-glass is double that of crown-glass, while 
 its refractive power is nearly the same. Consequently, if we 
 make the prism ABC of crown glass, and the prism ACD of 
 flint, the angle of the flint at C Se half that of the crown 
 at A, the two opposite dispersions will neutralize each other, 
 and the rays will pass through without being broken up into 
 the separate colors. But the crown prism, with double the an- 
 gle, will have a more powerful refractive power than the flint ; 
 so that, by combining the two, we shall have refraction without 
 dispersion, which ce the pr shee 
 
 The manner in which this principle is applied to the con- 
 struction of an object-glass is this: a convex lens of crown is 
 combined with a concave lens of flint of about half the cur- 
 vature. No exact rule respecting the ratio of the two curva- 
 tures can be given, because the refractive powers of different 
 specimens of glass differ greatly, and the proper ratio must, 
 therefore, be found by trial in each case. Having found it, 
 the two lenses will then have equal aberrations, but in oppo- 
 site directions, while the crown refracting more powerfully 
 than the flint, the rays will be brought to a focus at a dis- 
 tance a little more.than double the focal distance of the former. 
 A combination of this sort is called an achromatic objective. 
 Some of the earlier achromatic objectives were made of three 
 lenses, a double concave lens of flint glass being fitted be- 
 tween two double convex ones of crown. At present, how- 
 ever, but two lenses are used, the forms of 
 which, as used in the smaller European tele- 
 scopes, and in all the telescopes of Mr. Alvan <p 
 Clark, are shown in Fig. 82. The crown- ev, eg a 
 glass is here a double convex lens, and the achromatic objective. 
 
118 PRACTICAL ASTRONOMY. 
 
 curvatures of the two faces are equal. The curvature of the 
 inside face of the flint is the same as that of the crown, so 
 that the two faces fit accurately together, while the outer face 
 is nearly flat. If the dispersive power of the flint were just 
 double that of the crown, this face, would have to be flat 
 to produce achromatism; but this is not generally the case. 
 The fact is that, as no two specimens of glass made at dif- 
 ferent meltings have exactly the same refractive and disper- 
 sive powers, the optician, in making a telescope, must find the 
 ratios of dispersion of his two glasses, and then give the outer 
 face of his flint such a degree of curvature as to neutralize 
 the dispersion of his crown glass. Usually, this face will have 
 to be slightly concave. 
 
 When the inner faces of the glasses are thus made to fit, it 
 is not uncommon to join the glasses together with a transpar- 
 ent balsam, in order to diminish the loss of light in passing 
 through the glass. Whenever light falls upon transparent 
 glass, between three and four per cent. of it is reflected back, 
 and when, after passing through, it leaves again, about the 
 saine amount is reflected back into the glass. Consequently, 
 about seven per cent. of the light is lost in passing through 
 each lens. But when the two lenses are joined with balsam 
 or castor-oil, the reflection from the second surface of the flint 
 and the first surface of the crown is greatly diminished, and a 
 loss of perhaps six per cent. of the light is avoided.* 
 
 As larger and more perfect achromatic telescopes were 
 made, a new source of aberration was discovered, no practical 
 method of correcting which is yet known. It arises from the 
 fact that flint glass, as compared with crown, disperses the blue 
 end of the spectrum more than the red end. If we make 
 
 * When there is no balsam, another inconvenience sometimes arises from a 
 double reflection of light from the inner surfaces of the glass. Of the light re- 
 flected back from the first surface of the crown, four per cent. is again reflected 
 from the second surface of the flint, and sent down to the focus of the telescope 
 with the direct rays. If there be the slightest misplacement of one of the lenses, 
 the reflected rays will come to a different focus from the direct ones, and every 
 bright star will seem to have a small companion star along-side of it. 
 
THE ACHROMATIC TELESCOPE. 119 
 
 lenses of flint and crown having equal dispersive power, we 
 shall find that the red end is longest in the crown-glass spec- 
 trum, and the blue end in the flint-glass spectrum. The con- 
 sequence is that when we join a pair of prisms in reversed 
 positions, as shown in Fig. 31, the two dispersions cannot be 
 made to destroy each other entirely. Instead of the refracted 
 light being all joined in one white ray, the spectrum will be 
 folded over, as it were, the red and indigo ends being joined 
 together, the faint violet light extending out by itself, while 
 the yellow and green are joined at the opposite end. This 
 end will, therefore, be of a yellowish green, while the other 
 end is purple. 
 
 The spectrum thus formed by the combination of a flint 
 and crown prism is termed the secondary spectrum. It is very 
 much shorter than the ordinary spectra formed by either the 
 crown or the flint glass, and a large portion of the light is con- 
 densed near the yellowish-green end. ‘The effect of it is that 
 the refracting telescope is not perfectly achromatic, though 
 very nearly so. In a small telescope the defect is hardly no- 
 ticeable, the only drawback being that a bright star or other 
 object is seen surrounded by a blue or violet areole, formed by 
 the indigo rays thrown out by the flint-glass. If the eye-piece 
 is pushed in, so that the star is seen, not as a point, but as a 
 small disk, the centre of this disk will be green or yellow, 
 while the border will be reddish purple. But, in the immense 
 refractors of two-feet aperture or upwards, of which a number 
 have been produced of late years, the secondary aberration 
 constitutes the most serious optical defect; and it is a defect 
 which, arising from the properties of glass itself, no art can 
 diminish. The difficulty may be lessened in the same way 
 that the chromatic aberration was lessened in the older tele- 
 scopes, namely, by increasing the length of the instrument. 
 In doing this, however, with glasses of such large size, engi- 
 neering difficulties are encountered which soon become insur- 
 mountable. We must, therefore, consider that, in the great 
 refractors of recent times, the limit of optical power for such 
 instruments has been very nearly attained. 
 
120 PRACTICAL ASTRONOMY. 
 
 The eye-piece of a telescope, as well as its objective, con- 
 sists of two glasses. A single lens will, indeed, answer all 
 the purposes of seeing an object in the centre of the field 
 of view, but the field itself will be narrow and indistinct at 
 the edges. An additional lens, term- 
 ed the field-lens, is therefore placed 
 very near the image, for the purpose 
 of refracting the outer rays into the 
 proper direction to form a distinct 
 image with the aid of the eye-lens. 
 In Fig. 83 such an eye-piece is rep- 
 resented, in which the field-lens is 
 between the image and the eye. This is called a positive 
 eye-piece. In the negative eye-piece the rays pass through 
 the field-lens just before coming to a focus, so that the image 
 is formed just within that lens. The positive eye-piece is © 
 used when it is required to use a micrometer in the focal 
 plane ; but for mere looking the negative ocular is best. All 
 telescopes are supplied with a number of eye-pieces, by 
 changing which the magnifying power may be altered to suit 
 the observer. 
 
 The astronomical telescope used with these eye-pieces al- 
 ways shows objects upside down and right side left. This 
 causes no inconvenience in celestial observations. But for 
 viewing terrestrial objects the eye-piece must have two pairs 
 of lenses, the first of which forms a new image of the object 
 restored to its proper position, which image is viewed by the 
 eye-piece formed of the second pair. This combination is 
 called an erecting or terrestrial eye-piece. 
 
 Fig. 33.—Section of eye-piece 
 of a telescope. 
 
 § 3. The Mounting of the Telescope. 
 
 If the earth did not revolve, so that each heavenly body 
 would be seen hour after hour and day after day in nearly 
 the same direction, the problem of using great telescopes 
 would be much simplified. The objective and the eye-piece 
 could be fixed so as to point at the object, and the observer 
 could scrutinize it at his leisure. But actually, when we use 
 
THE MOUNTING OF THE TELESCOPE. 121 
 
 a telescope, the diurnal revolution of the earth is apparently 
 increased in proportion to the magnifying power of the in- 
 strument; and if the latter is fixed, and a high power is used, 
 the object passes by with such rapidity that it is impossible to 
 scrutinize it. Merely to point a telescope at an object needs 
 many special contrivances, because, unless the pointing is ac- 
 curate, the object cannot be found at all. With a telescope, 
 and nothing more, an observer might spend half an hour in 
 vain efforts to point it at Sirius so accurately that the image 
 of the star should be brought into the field of view; and then, 
 before he got one good look, it might flit away and be lost 
 again. If this is the case with a bright star, how much harder 
 must it be to point at the planet Neptune, an object invisible 
 to the naked eye, which is not in the same direction two min- 
 utes in succession! It will readily be understood that, to make 
 any astronomical use of a large telescope, two things are abso- 
 lutely necessary: first, the means of pointing the telescope at 
 any object, visible or invisible ; and, second, the means of moy- 
 ing the telescope so that 5 
 it shall follow the object 
 in its diurnal motion, 
 and thus keep its image 
 in the field of view. The 
 following are the me- 
 chanical contrivances by 
 which these objects are 
 effected : 
 
 The object-glass is 
 placed in one end of a 
 tube, OF, the length of 
 the tube being nearly 
 equal to the focal length 
 of the objective. The 
 eye-piece is fitted into a 
 projection at the lower 
 end of the tube, 7. The 
 
 RS 
 
 : é Fig. 34.—Mode of mounting a telescope so as to fol- 
 object of the tube is to low a star in its diurnal motion, 
 
£22 PRACTICAL ASTRONOMY. 
 
 keep the glasses in their proper relative positions, and to pro- 
 tect the eye of the observer from stray light. 
 
 The tube has an axis, AB, firmly fastened to it at A near its 
 middle, which axis passes through a cylindrical case, C, into 
 which it neatly fits, and in which it can turn. By turning the 
 telescope on this axis, the end # can be brought towards the 
 reader, and O from him, or vice versa. This axis is called the 
 declination axis. The ease, C, is firmly fastened to a second 
 axis, DH, supported at D and # called the polar axis. This 
 axis points to the pole of the heavens, and, by turning it, the 
 whole telescope, with the part, A C, of the case, may be brought 
 towards the observer, while the end B will recede from him, 
 or vice versa. In order that the weight of the telescope may 
 not make it turn on the polar axis, it is balanced by a weight 
 at 5, on the other end of the declination axis. This weight 
 is commonly divided, a part being carried by the axis, and a 
 part by the case, C. The polar axis is carried by a frame, /, 
 well fastened on top of a pier of masonry. 
 
 Such is the general nature of the mechanism by which an 
 astronomical telescope is mounted. The essential point is 
 that there shall be two axes—one fixed, and pointing at the 
 pole, and one at right angles to it, and turning with it. In 
 the arrangement of these axes there are great differences in 
 the telescopes of different makers; but Fig. 84 shows what 
 is essential in the plan of mounting now very generally 
 adopted. 
 
 In the figure the telescope is represented as-east of the spec- 
 tator, and as pointed at the pole, and therefore parallel to the 
 polar axis. Suppose now that the telescope be turned on the 
 declination axis, A, through an are of 90°, the eye-piece, ZF, 
 being brought towards the spectator ; the object end will then 
 point towards the east horizon, and therefore towards the celes- 
 tial equator, the eye end pointing directly towards the spec- 
 tator. Then let the whole instrument be turned on the polar 
 axis, the eye-piece being brought downwards. The telescope 
 will then move along the celestial equator, or the path of a 
 star, 90° from the pole. And at whatever distance from the 
 
 % 
 
THE REFLECTING TELESCOPE. 123 
 
 pole we set it by turning it on the declination axis, if we 
 turn it on the polar axis it will describe a circle having the 
 pole at its centre; that is, the same circle which a star follows 
 by its diurnal motion. So, to observe a star with the telescope, 
 we have first to turn it on the declination axis to the polar dis- 
 tance of the star, and then on the polar axis till it points at 
 the star. This pointing is effected by circles divided into de- 
 grees and minutes, not shown in the figure, by which the dis- 
 tance which the telescope points from the pole and from the 
 meridian may be found at any time. — 
 
 In order that the star, when once found, may be kept in the 
 field of view, the telescope is furnished with a system of clock- 
 work, by which the polar axis is slowly turned at the rate of 
 one revolution a day. By starting this clock- work, the tele- 
 scope is made to follow the star in its diurnal motion; or, to 
 speak with greater astronomical precision, as the earth turns 
 on its axis from west to east, the telescope turns from east to 
 west with the same angular velocity, so that the direction in 
 which it points in the heavens remains unaltered. 
 
 In order to facilitate the finding or recognition of an object, 
 the telescope is furnished with a “finder,” 7, consisting of a 
 small telescope of low power pointing in the same direction 
 with the larger one. An object can be seen in the small tel- 
 escope without the pointing being so accurate as is necessary 
 in the case of the large one; and, when once seen, the tele- 
 scope is moved until the object is in the middle of the field 
 of view, when it is also in the field of view of the large one. 
 
 § 4. The Reflecting Telescope. 
 
 Two radically different kinds of telescopes are made: the 
 one just described, known as the refracting telescope, because 
 dependent on the refraction of light through glass lenses; and 
 the other, the reflecting telescope, so called because it acts by 
 reflecting the light from a concave mirror. The name of the 
 first inventor of this instrument is disputed; but Sir Isaac 
 Newton was among the first to introduce it. It was designed 
 by him to avoid the difficulty growing out of the chromatic 
 
124 ; PRACTICAL ASTRONOMY. 
 
 aberration of the refracting telescopes of his time, which, it 
 will be remembered, were not achromatic. If parallel rays of 
 light from a distant object fall upon a concave mirror, as shown 
 in Fig. 35, they will all be reflected back to a focus, F, half- 
 way between the centre of curvature, G', and the surface of 
 
 NS ae eet 
 
 a pe a a se 
 
 Fie. 35.—Speculum bringing rays to a single focus by reflection. 
 
 the mirror. In order that the rays may be all reflected to 
 absolutely the same focus, the section of the mirror must be 
 a parabola, and the point where the rays meet will be the 
 focus of the parabola. If the rays emanate from the various 
 points of an object, an image of this object will be formed 
 in and near the focus, as in the case of a lens. This image 
 is to be viewed with a magnifying eye-piece like that of a 
 refracting telescope. Such a mirror is called a speculum. — 
 
 Here, however, a difficulty arises. The image is formed on 
 the same side of the mirror on which the object lies; and in or- 
 der that it may be seen directly, the eye of the observer and 
 the eye-piece must be between / and G, directly in the rays 
 of light emanating from the object. By placing the eye here, 
 not only would a great deal of the light be cut off by the body 
 of the observer, but the definition of the image would be great- 
 ly injured by the interposition of so large an object. Three 
 plans have been devised for evading this difficulty, which are 
 due, respectively, to Gregory, Newton, and Herschel. 
 
 The Herschelian Telescope.—In this form of telescope the 
 mirror is slightly tipped, so that the image, instead of being 
 formed in the centre of the tube, is formed near one side of 
 it, as in Fig. 86. The observer can then view it without put- 
 ting his head inside the tube, and, therefore, without cutting 
 off any material portion of the light. In observation, he must 
 stand at the upper, or outer, end of the tube, and look into it, 
 his back being turned towards the object. From his looking 
 
THE REFLECTING TELESCOPE. £25 
 
 directly into the mirror, it was also called the “ front-view ” 
 telescope. The great disadvantage of this arrangement is that 
 
 Fie. 36.—Herschelian telescope. 
 
 the rays cannot be brought to an exact focus when they are 
 thrown so far to one side of the axis, and the injury to the 
 definition is so great that the front-view plan is now entirely 
 abandoned. 
 
 Lhe Newtonian Telescope—The plan proposed by Sir Isaac 
 Newton was to place a small plane mirror just inside the fo- 
 cus, inclined to the telescope at an angle of 45°, so as to throw 
 the rays to the side of the tube, where they come to a focus, 
 and form the image. An opening is made in the side of the 
 tube, just below where the image is formed in which the eye- 
 piece is inserted. This mirror cuts off some of the light, but 
 not enough to be a serious defect. An improvement which 
 lessens this defect has been made by Professor Henry Draper. 
 
 Fie. 37.—Horizontal section of a Newtonian telescope. This section shows how the lumi- 
 nous rays reflected from the parabolic mirror M meet a small rectangular prism ™ n, 
 which replaces the inclined plane mirror used in the old form of Newtonian telescope. 
 After undergoing a total reflection from m n, the rays form at a b a very small image 
 of the heavenly body. 
 
 The inclined mirror is replaced by a small rectangular prism, 
 by reflection from which the image is formed very near the 
 prism. <A pair of lenses are then inserted in the course of 
 
126 PRACTICAL ASTRONOMY. 
 
 the rays, by which a second image is formed at the opening 
 in the side of the tube, and this second image is viewed by 
 an ordinary eye-piece. ‘The four lenses together form an 
 erecting eye-piece. 
 
 The Gregorian Telescope.—This is a form proposed by James 
 Gregory, who probably preceded Newton as an inventor of the 
 reflecting telescope. Behind the focus, /', a small concave 
 mirror, /, is placed, by which the light is reflected back again 
 
 Fig. 38.—Section of the Gregorian telescope. 
 
 down the tube. The larger mirror, J/, has an opening through 
 its centre, and the small mirror, A, is so adjusted as to form a 
 second image of the object in this opening. This image is 
 then viewed by an eye-piece which is screwed into the opening, | 
 
 The Cassegrainian Telescope—In principle the same with the 
 Gregorian, differs from it only in that the small mirror, £, is 
 convex, and is placed inside the focus, /, so that the rays are 
 reflected from it before reaching the focus, and no image is 
 formed until they reach the opening in the large mirror. 
 This form has an advantage over the Gregorian in that the 
 telescope may be made shorter, and the small mirror can be 
 more easily shaped to the required figure. It has therefore 
 entirely superseded the original Gregorian form. 
 
 Optically, these forms of telescope are inferior to the New- 
 tonian. But the latter is subject to the inconvenience that the 
 observer must be stationed at the upper end of the telescope, 
 where he looks into an eye-piece screwed into the side of the 
 tube. If the telescope is a small one, this inconvenience is 
 not felt; but with large telescopes, twenty feet long or up- 
 wards, the case is entirely different. Means must then be pro- 
 vided by which the observer may be carried in the air at a 
 height equal to the length of the instrument, and this requires 
 considerable mechanism, the management of which is often 
 
THE PRINCIPAL TELESCOPES OF MODERN TIMES. 12% 
 
 very troublesome. On the other hand, the Cassegrainian tele- 
 scope is pointed directly at the object to be viewed, like a re- 
 fractor, and the observer stands at the lower end, and looks in 
 at the opening through the large mirror. This is, therefore, 
 the most convenient form of all in management. One draw- 
 back is, that there are two mirrors to be looked after, and, un- 
 less the figure of both is perfect, the image will be distorted. 
 Another is the great size of the image, which forces the ob- 
 server to use either a high magnifying power, or an eye-piece 
 of corresponding size.* But these defects are of little impor- 
 tance compared with the great advantage of convenient use. 
 
 § 5. The Principal Great Reflecting Telescopes of Modern Times. 
 
 The reflecting telescopes made by Newton and his contem- 
 poraries were very small indeed, none being more than a few 
 inches in diameter. Though vastly more manageable than the 
 immensely long refractors of Huyghens, they do not seem to 
 have exceeded them in effectiveness. We might, therefore, 
 have expected the achromatic telescope to supersede the re- 
 flector entirely, if it could be made of large size. But in the 
 time of Dollond it was impossible to produce disks of flint-glass 
 of sufficient uniformity for a telescope more than a very few 
 inches in diameter. An achromatic of four inches aperture 
 was then considered of extraordinary size, and good ones of 
 more than two or three inches were rare. Consequently, for 
 the purpose of seeing the most faint and difficult objects, the 
 earlier achromatics were little, if any, better than the long 
 telescopes of Huyghens and Cassini. As there were no such 
 obstacles to the polishing of large mirrors, it was clear that it 
 was to the reflecting telescope that recourse must be had for 
 any great increase jn optical power. Before the middle of 
 the last century the reflectors were little larger than the re- 
 fractors, and had not exceeded them in their optical perform- 
 ance. But a genius now arose who was to make a wonderful 
 improvement in their construction. 
 
 * The Melbourne telescope has an eye-lens six inches in diameter. 
 
 G 10 
 
128 PRACTICAL ASTRONOMY. 
 
 William Herschel, in 1766, was a church-organist and teach- 
 er of music of very high repute in Bath, who spent what little 
 leisure he had in the study of mathematics, astronomy, and 
 optics. By accident a Gregorian reflector two feet long fell 
 into his hands, and, turning it to the heavens, he was so enrapt- 
 ured with the views presented to him that he sent to London 
 to see if he could not purchase one of greater power. The 
 price named being far above his means, he resolved to make 
 one for himself. After many experiments with metallic al- 
 loys, to learn which would reflect most light, and many efforts 
 to find the best way of polishing his mirror, and giving it a 
 parabolic form, he produced a five-foot Newtonian reflector, 
 which revealed to him a number of interesting celestial phe- 
 nomena, though, of course, nothing that was not already known. 
 Determined to aim at nothing less than the largest telescope 
 ' that could be made, he attempted vast numbers of mirrors of 
 constantly increasing size. The large majority of the individ- 
 ual attempts were failures; but among the results of the suc- 
 cessful attempts were telescopes of constantly increasing size, 
 until he attained the hitherto unthought-of aperture of two feet, 
 with a length of twenty feet. With one of these he discov- 
 ered the planet Uranus. The fame of the musician-astrono- 
 mer reaching the ears of King George III., that monarch gave 
 him a pension of £200 per annum, to enable him to devote 
 his life to a career of astronomical discovery. He now made 
 the greatest stride of all by completing a reflector four feet 
 in diameter and forty feet long, with which he discovered two 
 new satellites of Saturn. 
 
 Herschel now found that he had attained the limit of man- 
 ageable size. The observer had to be suspended perhaps thir- 
 ty or forty feet in the air, in a room large enough to hold, not 
 only himself, but all the means necessary for recording his 
 observations; and this room had to follow the telescope as it 
 moved, to keep a star in the field. To this was added the 
 difficulty of keeping the mirror in proper figure, the mere 
 change of temperature in the night operating injuriously in 
 this respect. We need not, therefore, be surprised to learn 
 
THE PRINCIPAL TELESCOPES OF MODERN TIMES. 129 
 
 Fig. 39.—Herschel’s great telescope. 
 
 that Herschel made very little use of this instrument, and pre- 
 ferred the twenty-foot' even in scrutinizing the most difficult 
 objects.* 
 
 * Herschel’s great instrument is still preserved, but is not mounted for use; 
 indeed, it is probable that the mirror lost all its lustre long years ago. In 1839, 
 Sir John Herschel dismounted it, laid it in a horizontal position, and closed it up 
 after a family celebration inside the tube, at which the following song was sung: 
 
 THE OLD TELESCOPE. 
 
 [To be sung on New-1ear’s-eve, 1839-40, by Papa, Mamma, Madame Gerlach, and all the Litile 
 Bodies in the Tube thereof assembled.) 
 
 In the old Telescope’s tube we sit, 
 And the shades of the past around us flit; 
 His requiem sing we with shout and din, 
 While the old year goes ont, and the new comes in, 
 Chorus.—Merrily, merrily let us all sing, 
 And make the old telescope rattle and ring! 
 
130 PRACTICAL ASTRONOMY. 
 
 The only immediate successor of Sir William Herschel in 
 the construction of great telescopes was his son, Sir John Her- 
 schel. But the latter made none to equal the largest of his 
 father’s in size, and it is doubtful whether they exceeded them 
 in optical power. 
 
 The first decided advance on the great telescope was the 
 celebrated reflector of the Earl of Rosse,* at Parsonstown, Ire- 
 
 Full fifty years did he Jaugh at the storm, 
 
 And the blast could not shake his majestic form ; 
 
 Now prone he lies, where he once stood high, 
 
 And searched the deep heaven with his broad, bright eye. 
 
 Chorus.—Merrily, merrily, etc., etc. 
 
 There are wonders no living sight has seen, 
 Which within this hollow have pictured been ; 
 Which mortal record can never recall, 
 
 And are known to Him only who made them all. 
 
 Chorus.—Merrily, merrily, etc., etc. 
 
 Here watched our father the wintry night, 
 
 And his gaze has been fed with preadamite light. 
 His labors were lightened by sisterly love, 
 
 And, united, they strained their vision above. 
 
 Chorus.—Merrily, merrily, etc., ete. 
 
 He has stretched him quietly down, at length, 
 To bask in the starlight his giant strength; 
 And Time shall here a tough morsel find 
 
 For his steel-devouring teeth to grind. 
 
 Chorus.—-Merrily, merrily, etc., ete. 
 
 He will grind it at last, as grind it he must, 
 
 And its brass and its iron shall be clay and rust; 
 But scathless ages shall roll away, 
 
 And nurture its frame, and its form’s decay. 
 
 Chorus.—Merrily, merrily, etc., etc. 
 
 A new year dawns, and the old year’s past ; 
 God send it, a happy one like the last 
 (A little more sun and a little less rain 
 To save us from cdugh and rheumatic pain). 
 
 Chorus.—Merrily, merrily, etc., etc. 
 God grant that its end this group may find 
 In love and in harmony fondly joined! 
 
 And that some of us, fifty years hence, once more 
 May make the old Telescope’s echoes roar. 
 
 Chorus.—Merrily, merrily, etc., etc. 
 
 * William Parsons, third Earl of Rosse, the original constructor of this tele- 
 scope, died in 1867. The work of the instrument is continued by his son, the pres- 
 ent earl. 
 
a 
 
 5 
 2 
 4 
 : 
 f 
 
i 
 WW 
 | | i 
 
 ASIC, 
 
 ee 
 
 FA 
 
 N ESL ALBEE 
 
 = 
 eT 
 \ NN 
 
 N\\ 
 \\ 
 
 i ‘hie iN 
 Ase 
 
 SS 
 
 , is > : ee 
 iy | at \ 
 i | il iil, iY 
 
 | 4 A 
 i i hi ie 
 Hi fe 
 
 Fie. 40.—Lord Rosse’s great telescope. 
 
THE PRINCIPAL TELESCOPES OF MODERN TIMES. too 
 
 land. The speculum of this telescope is six feet in diameter, 
 and about fifty-four feet focal length, and was cast in 1842. 
 One of the great improvements made by the Earl of Rosse 
 was the introduction of steam machinery for grinding and 
 polishing the great mirror, an instrumentality of which Her- 
 schel could not avail himself. The mounting of this telescope 
 is decidedly different from that adopted by Herschel. The 
 telescope is placed between two walls of masonry, which only 
 allow it to move about 10° on each side of the meridian, and 
 it turns on a pivot at the lower end of the tube. It is moved 
 north and south in the meridian by an’ ingenious combination 
 of chains,and may thus be set at the polar distance of any 
 star which it is required to observe. It is then moved slowly 
 towards the west, so as to follow the star, by a long screw 
 driven by an immense piece of clock-work. It is commonly 
 used as a Newtonian, the observer looking into the side of the 
 tube near the upper end. ‘To enable him to reach the mouth 
 of the tube, various systems of movable platforms and staging 
 are employed. One of the platforms is suspended south of 
 the piers; it extends east and west by the distance between 
 the walls, and may be raised by machinery so as to be directly 
 under the mouth of the telescope so long as the altitude of the 
 latter is less than 45°. When the altitude is greater than this, 
 the observer ascends a stairway to the top of one of the walls, 
 where he mounts one of several sliding stages, by which he 
 can be carried to the mouth of the telescope, in any position 
 of the latter. This instrument has been employed principal- 
 ly in making drawings of lunar scenery and of the planets 
 and nebulee. Its great light-gathering power peculiarly fits it 
 for the latter object. 
 
 Other Reflecting Telescopes.— Although no other reflector ap- 
 proaching the great one of the Earl of Rosse in size has ever 
 been made, some others are worthy of notice, on account of 
 their perfection of figure and the importance of the discov- 
 eries made with them. Among these the first place is due to 
 the great reflectors of Mr. William Lassell, of England. This 
 gentleman made a reflector of two feet aperture about the 
 
134 PRACTICAL ASTRONOMY. 
 
 same time that Rosse constructed his immense six-foot. The 
 perfection of figure of the mirror was evinced by the discov- 
 ery of two satellites of Uranus, which had been previously un- 
 known and unseen, unless, as is possible, Herschel and Struve 
 caught glimpses of them on a few occasions. He afterwards 
 made one of four feet aperture, which, in 1863, he took to the 
 island of Malta, where he made a series of observations on 
 satellites and nebule. 
 
 =) Z- 
 i= 
 
 (i—|/= 
 
 pa 
 
 ==; 
 
 = 
 
 j= 
 
 SSS = 
 
 A, 
 WA 
 
 y W2 | 
 Za 
 yam TTT 
 
 — 
 HA 
 
 Fig. 41.—Mr. Lassell’s great four-foot reflector, as mounted at Malta. 
 
 In 1870, a reflecting telescope four feet in diameter, on the 
 Cassegrainian plan, was made by Thomas Grubb & Son, of 
 Dublin, for the Observatory of Melbourne, Australia. This 
 instrument is remarkable, not only for its perfection of figure, 
 but as being probably the most easily managed large reflector 
 ever made. 
 
HUIECTTETIT 
 
 | 7 | : YY 
 BM S iI =| 
 TIT] rel 7 — ! WZ =| 
 {4 LTTE TH 
 : 9 eemahe 
 | 
 WAH 
 1) if 
 1 |. { . ms 
 | lf i 
 Hi Boe 
 | 
 
 At 
 
 = — —_"=— 
 
 Fig. 42.—The new Paris reflector. 
 
THE PRINCIPAL TELESCOPES OF MODERN TIMES. 137 
 
 The only American who has ever successfully undertaken 
 the construction of large reflecting telescopes is Professor Hen- 
 ry Draper, of New York, who has one of twenty-eight inches 
 aperture, the work of his own hands. This instrument was 
 mounted about 1872 in the owner’s private observatory at 
 Hastings, on the Hudson. The mirror is not of speculum 
 metal, but of silvered glass, and is almost perfect in figure. 
 This telescope has been principally employed in making pho- 
 tographs of celestial objects, and can be used either as a New- 
 tonian or a Cassegrainian. 
 
 An attempt has recently been made at the Paris Observa- 
 tory to construct a reflecting telescope with a mirror of sil- 
 vered glass, as large as the great specula of Lassell and the 
 Melbourne Observatory. The diameter of the glass is 120 
 centimetres, a fraction of an inch short of four English feet. 
 It was figured, polished, and silvered at the Paris Observa- 
 tory by M. Martin, using the methods devised by Foucault. 
 It was mounted in 1875; but, unfortunately, the proper meas- 
 ures were not taken to prevent the glass from bending under 
 its own weight, and thus destroying the perfection of the 
 parabolic figure which M. Martin had succeeded in obtain- 
 ing. It was therefore taken from its tube to have this defect 
 of mounting remedied. The machinery for supporting and 
 moving this telescope being in some respects peculiar, we pre- 
 sent a view of it in Fig. 42, on page 134. 
 
 § 6. Great Refracting Telescopes. 
 
 We have already remarked that, in the early days of the 
 achromatic telescope, its progress was hindered by the diffi- 
 culty of making large disks of flint-glass. About the begin- 
 ning of the present century, Guinand, a Swiss mechanic, after 
 a long series of experiments, discovered a method by which 
 he could produce disks of flint-glass of a size before unheard 
 of. The celebrated Fraunhofer was then commencing busi- 
 ness as an optician in Munich, and hearing of Guinand’s suc- 
 cess induced him to come to Munich and commence the man- 
 ufacture of optical glass. Fraunhofer was a physicist of a 
 
138 PRACTICAL ASTRONOMY. 
 
 Z 
 
 Tn 
 | 
 
 —_ 
 
 | 
 
 : a ET 
 
 LE 
 
 ai 
 
 H —S 
 
 t 
 | 
 
 if 
 
 ——S 
 
 1 
 \ 
 I 
 
 = = = 
 
 Fig. 43.—The great Melbourne reflector. T, the tube containing the great mirror near its 
 lower end. Y, the small mirror throwing the light back to the eye-piece, y. C N, the 
 polar axis. U, the counterpoise at the end of the declination axis. Z, the clock-work 
 which moves the telescope by the jointed rods z e e E, and the clamp F. 
 
 high order, and made a more careful and exhaustive study of 
 
 the optical qualities of glass, and the conditions for making 
 
 the best telescope, than any one before him had ever attempted. 
 
 With the aid of the large disks furnished by Guinand, he was 
 
 able to carry the aperture of his telescopes up to ten inches. 
 
 Dying in 1826, his successors, Merz and Mahler, of Munich, 
 
 made two telescopes of fifteen inches aperture, which were 
 
 then considered most extraordinary. One of these belongs 
 
 : 
 
GREAT REFRACTING TELESCOPES. 139 
 
 to the Pulkowa Observatory, in Russia; and the other was 
 purchased by a subscription of citizens of Boston for the ob- 
 servatory of Harvard University. 
 
 No rival of the house of Fraunhofer in the construction of 
 great refractors arose until he had been dead thirty years, and 
 then it arose where least expected. In 1846, Mr. Alvan Clark 
 was a citizen of Cambridgeport, Massachusetts, unknown to 
 fame, who made a modest livelihood by pursuing the self- 
 taught art of portrait-painting, and beguiled his leisure by 
 the construction of small telescopes. ‘Though without the 
 advantage of a mathematical education, he had a perfect 
 knowledge of optical principles to just the extent necessary 
 to enable him to make and judge a telescope. Having been 
 led by accident to attempt the grinding of lenses, he soon pro- 
 duced objectives equal in quality to any ever made, and, if 
 he had been a citizen of any other civilized country, would 
 have found no difficulty in establishing a reputation. But 
 he had to struggle ten years with that neglect and incre- 
 dulity which is the common lot of native genius in this coun- 
 try; and, extraordinary as it may seem, it was by a foreigner 
 that his name and powers were first brought to the notice 
 of the astronomical world. Rev. W. R. Dawes, one of the 
 leading amateur astronomers of England, and an active mem- 
 ber of the Royal Astronomical Society, purchased an object- 
 glass from Mr. Clark in 1853. He found it so excellent that 
 in the course of the next two or three years he ordered several 
 others, and, finally, an entire telescope. He also made several 
 communications to the Astronomical Society, giving lists of 
 difficult double stars detected by Mr. Clark with telescopes of 
 his own construction, and showing that Mr. Clark’s oe 
 were almost perfect in definition. 
 
 The result of this was that the American artist iat to be 
 appreciated in his own country; and in 1860 he received an 
 order from the University of Mississippi, of which Dr. F. A. 
 P. Barnard* was then president, for a refractor of eighteen 
 
 * Now President of Columbia College, New York City. 
 
140 PRACTICAL ASTRONOMY. 
 
 inches aperture, which was three inches greater than the larg- 
 est that had then been made. Before the glass was finished, 
 it was made famous by the discovery of the companion of 
 Sirius, a success for which the Lalande medal was awarded 
 by the French Academy of Sciences. The University of 
 Mississippi was prevented from taking this telescope by the 
 civil war. It was sold to the Astronomical Society of Chi- 
 cago, and is now mounted at the University in that city. 
 
 This instrument did not long retain its supremacy. The 
 firm of Thomas Cooke & Sons, of York, England, in 1870, 
 mounted a refractor of twenty-five inches clear aperture for 
 R.S. Newall, Esq., of Gateshead, England, of which the defi- 
 nition is very good. In the summer of 1874 it was used by 
 Mr. Lockyer, in a study of Coggia’s comet. 
 
 Up to 1870 the Naval Observatory of the United States 
 had no large telescope except a Munich refractor of nine and 
 a half inches, such as Fraunhofer used to make early in the 
 century. In that year Congress authorized the construction 
 of a telescope of the largest size of American manufacture. 
 A contract was soon after made with the firm of Alvan 
 Clark & Sons to construct the telescope. The aperture 
 agreed upon was twenty-six inches, exceeding that of Mr. 
 Newall’s telescope by only one inch. The rough disks were 
 ordered from Messrs. Chance & Co., of Birmingham, Eng- 
 land; but so great was the difficulty of making large masses 
 of glass of the necessary purity, that they did not arrive until 
 December, 1871. The work of figuring and polishing them 
 was commenced immediately. The glasses were completed 
 in October, 1872, and the remainder of the instrument during 
 the year following. It was finally mounted and ready for ob- 
 servation in November, 1873. This telescope has since be- 
 come famous by the discovery of the satellites of Mars. 
 
 When this telescope was ordered from the Messrs. Clark 
 they were negotiating with Mr. L. P. McCormick, of Chicago, 
 for a telescope of equal size. This instrument has since been 
 completed, and presented by its owner to the University of 
 Virginia. Thus the two greatest telescopes yet made in 
 
MAGNIFYING POWERS OF. TELESCOPES. 141 
 
 America are mounted within a hundred and fifty miles of 
 each other. 
 
 Up to the year 1881 the Great Washington Telescope re- 
 mained the largest and most successful refractor in the world. 
 But during this year an instrument of one inch greater aper- 
 ture was completed by Mr. Howard Grubb, of Dublin, for 
 the Austrian Government. It has just been mounted in the 
 Imperial Observatory at Vienna, but up to the time of send- 
 ing these pages to press no actual observations have been 
 made with it. 
 
 § 7. The Magnifying Powers of the Two Classes of Telescopes. 
 
 Questions which now very naturally arise are, Which of the 
 two classes of telescopes we have described is the more power- 
 ful, the reflector or the refractor? and is there any limit to the 
 magnifying power of either? To these questions it is difficult 
 to return a decided answer, because each class has its peculiar 
 advantages, and in each class many difficulties lie in the way 
 of obtaining the highest magnifying power. The fact is, that 
 very exaggerated ideas of the magnifying power of great tele- 
 scopes are entertained by the public. It will, therefore, be 
 instructive to state what the circumstances are which prevent 
 these ideas from being realized, and what the conditions are 
 on which the seeing power of telescopes depends. 
 
 We note, first, that when we look at a luminous point—a star, 
 for instance—without a telescope, we see it by the aid of the 
 cone of light which enters the pupil of the eye. The diameter 
 of the pupil being about one-fifth of an inch, as much light 
 from the star as falls on a circle of this diameter is brought to 
 a focus on the retina, and unless this quantity of light is suffi- 
 cient to be perceptible, the star will not be seen. Now, we 
 may liken the telescope to a “ Cyclopean eye,” of which the 
 object-glass is the pupil, because, by its aid, all the ight which 
 falls on the object-glass is brought to a focus on the retina, 
 provided that a sufficiently small eye-piece is used. Of course, 
 we must except that portion of the light which is lost in pass- 
 ing through the glasses. Since the quantity of light which 
 
142 PRACTICAL ASTRONOMY. 
 
 falls on a surface is proportional to the extent of the surface, 
 and therefore to the square of its diameter, it follows that, 
 because a telescope of one-inch clear aperture has five times 
 the diameter of the pupil, it will admit 25 times the light; a 
 six-inch will admit 900 times the hght which the pupil will; 
 and so with any other aperture. A star viewed with the 
 telescope will, therefore, appear brighter than to the naked 
 eye in proportion to the square of the aperture of the in- 
 strument. But the star will not be magnified like a planet, 
 because a point is only a point, no matter how often we mul- 
 tiply it. It is true that a bright star in the telescope some- 
 times appears to have a perceptible disk; but this is owing to 
 various imperfections of the image, having their origin in the 
 air, the instrument, and the eye, all of which have the effect of 
 slightly scattering a portion of the light which comes from the 
 star. Hence, with perfect vision the apparent brilliancy of a 
 star. will be proportional to the square of the aperture of the 
 telescope. It is said that Sir William Herschel, at a time when 
 by accident his telescope was so pointed that Sirius was about 
 to enter its field of view, was first apprised of what was com- 
 ing by the appearance of a dawn like the morning. ‘The light 
 increased rapidly, until the star itself appeared with a dazzling 
 splendor which reminded him of the rising sun. Indeed, in 
 any good telescope of two feet aperture or upwards, Sirius is 
 an almost dazzling object to an eye which has rested for some 
 time in darkness. 
 
 But in order that all the light which falls on the object- 
 glass, or mirror, of a telescope may enter the pupil of the eye, 
 it is necessary that the magnifying power be at least equal to 
 the ratio which the aperture of the telescope bears to that of 
 the pupil. The latter is generally about one-fifth of an inch. 
 We must, therefore, employ a magnifying power of at least 
 five for every inch of aperture, or we will not get the full ad- 
 vantage of our object-glass. The reason of this will be appar- 
 ent by studying Fig. 29, p. 109, from which it will be seen that 
 a pencil of parallel rays falling on the object-glass, and pass- 
 ing through the eye-piece, will be reduced in diameter in the 
 
MAGNIFYING POWERS OF TELESCOPES. 143 
 
 ratio of the focal distance of the objective to that of the eye- 
 piece, which is the same as the magnifying power. [or in- 
 stance, if to a twenty-four-inch telescope we attached an eye- 
 piece so large that the magnifying power was only 48, and 
 pointed it at a bright star, the “emergent pencil” of rays from 
 the eye-piece would be half an inch in diameter, and the whole 
 of them could not possibly enter the pupil. By increasing the 
 magnifying power, we would increase the apparent brilliancy 
 of the star, until we reached the power 120, after which no 
 further increase of brilliancy would be possible. 
 
 All this supposes that we are viewing a star or other lumi- 
 nous point. If the object has a sensible surface, like the moon, 
 or a large nebula, and we consider its apparent superficial 
 brilliancy, the case will be in part reversed. The object will 
 then appear equally illuminated, with all powers below five 
 for each inch of aperture, but will begin to grow darker when 
 we pass above that limit. The reason of this is, that as we 
 increase the magnifying power the light is spread over a larger 
 surface of the retina, and is thus enfeebled. So long as our 
 magnifying power is below the limit, the increased quantity 
 of light which enters the pupil by an increase of magnifying 
 power just compensates for the greater surface over which it 
 is spread, so that the brilliancy is constant. Above the limit 
 of five to the inch, the surface over which the light is spread, 
 or the apparent magnitude of the object, still increases with 
 the magnifying power, but there is no increase of light ; hence, 
 the object looks fainter. What may at first sight seem para-. 
 doxical is, that the degree of iUlumination to which we now 
 refer can never be increased by the use of the telescope, but, 
 at the best, will be the same as to the naked eye. Indeed, 
 as some light is necessarily lost in passing through any tele- 
 scope, the illumination is always less with the telescope. With 
 the best reflectors of speculum metal, the illumination will be 
 reduced to one-half, or less, if the polish is not perfect; and 
 with refractors it will be reduced to seven or eight tenths. As 
 examples of these conclusions, the sky can never be made to 
 appear as bright through a telescope as to the naked eye; the 
 
 at 
 
144 PRACTICAL ASTRONOMY. 
 
 moon or a large nebula will appear more brightly illuminated 
 through a refracting telescope than through a reflector. If 
 the object is a very brilliant one, like the sun or Venus, the 
 loss of brilliancy by magnifying, which we have described, will 
 not cause any inconvenience; but the outer planets and many 
 of the nebule are so faintly illuminated that a magnifying 
 power many times exceeding the limit cannot be used with 
 advantage. 
 
 Still another cause which places a limit to the power of 
 telescopes is diffraction. When the “emergent pencil” is 
 reduced below -4; of an inch in diameter—that is, when the 
 magnifying power is greater than 50 for every inch of aper- 
 ture of the object-glass—the outlines of every object observed 
 become confused and indistinct, no matter how bright the il- 
 lumination or how perfect the glass may be. The effect is the 
 same as if we looked throngh a small pin-hole in a card, an 
 experiment which anyone may try. This effect is owing to 
 the diffraction of the light at the edge of the object-glass.or 
 mirror, and it increases so rapidly with the magnifying power 
 that when we carry the latter above 100 to the inch, the in- 
 crease of indistinctness neutralizes the increase of power. If, 
 then, we multiply the aperture of the telescope in inches by 
 100, we shall have a limit beyond which there is no use in 
 magnifying. Indeed, it is doubtful if any real advantage is 
 gained beyond 60 to the inch. In a telescope of two feet (24 
 inches) aperture this limit would be 2400. Such a limit can- 
 not be set with entire exactness; but,even under the most fa- 
 vorable circumstances, the advantage in attempting to surpass 
 a power of 70 to the inch will be very slight. 
 
 The foregoing remarks apply to the most perfect telescopes, 
 used under the most favorable circumstances. But the best 
 telescope has imperfections which would nearly always pre- 
 vent the use of the highest magnifying powers in astronomical 
 observations. In the refracting telescope the principal defect 
 arises from the secondary aberration already explained, which, 
 arising from an inherent quality of the glass itself, cannot be 
 obviated by perfection of workmanship. In the case of the re- 
 
MAGNIFYING POWERS OF TELESCOPES. 145 
 
 flector, the corresponding difficulty is to keep the mirror in per- 
 fect figure in every position. As the telescope is moved about, 
 the mirror is liable to bend, through its own weight and elas- 
 ticity, to such an extent as greatly to injure or destroy the im- 
 age in the focus; and, though this liability is greatly dimin- 
 ished by the plan now adopted, of supporting the mirror on a 
 system of levers or on an air-cushion, it is generally trouble- 
 some, owing to the difficulty of keeping the apparatus in order. 
 
 If we compare the refracting and reflecting telescopes which 
 have hitherto been made, it is easy to make a summary of 
 their relative advantages. If properly made and attended to, 
 the refractor is easy to manage, convenient in use, and al- 
 ways in order for working with its full power. If its greatest 
 defect, the secondary spectrum, cannot be diminished by skill, 
 neither can it be increased by the want of skill on the part of 
 the observer. So important is this certainty of operation, that 
 far the greater part of the astronomical observations of the 
 present century have been made with refractors, which have 
 always proved themselves the best working instruments. Still, 
 the defects arising from the secondary spectrum are inherent 
 in the latter, and increase with the aperture of the glass to 
 such an extent that no advantage can ever be gained by carry- 
 ing the diameter of the lenses beyond a limit which may be 
 somewhere between 80 and 36 inches. On the other hand, 
 when we consider mere seeing-power, calculation at least gives 
 the preference to the reflector. It is easy to compute that 
 Lord Rosse’s “ Leviathan,” and the four-foot reflectors of Mr. 
 Lassell and of the Paris and Melbourne observatories, must 
 collect from two to four times the light of the great Washing- 
 ton telescope. But when, instead of calculation, we inquire 
 what difficult objects have actually been seen with the two 
 classes of instruments, the result seems to indicate that the 
 greatest refractor is equal in optical power to the great reflect- 
 ors. No known object seen with the latter is too faint to be 
 seen with the former. Why this discrepancy between the 
 calculated powers of the great reflectors and their actual per- 
 formance? The only causes we can find for it are imperfec- 
 
146 PRACTICAL ASTRONOMY. 
 
 tions in the figure and polish of the great mirrors. The great 
 refractors are substantially perfect in their workmanship; the 
 reflectors do not appear to be perfect, though what the imper- 
 fections may be, it is impossible to say with entire certainty. 
 Whether the great telescope of the future shall belong to the 
 one class or the other must depend upon whether the imper- 
 fections of the reflecting mirror can be completely overcome. 
 Mr. Grubb, the maker of the great Melbourne telescope, thinks 
 he has completely succeeded in this, so as to insure a mirror 
 of six, seven, or even eight feet in diameter which shall be as 
 perfect as an object-glass. If he is right—and there is no 
 mechanician whose opinion is entitled to greater confidence— 
 then he has solved the problem in favor of the reflector, so far 
 as optical power is concerned. But so large a telescope will 
 be so difficult to manipulate, that we must still look to the re- 
 fractor as the working instrument of the future as well as of 
 the past; though, for the discovery and examination of very 
 faint objects, it may be found that the advantage will all be 
 on the side of the future great reflector. 
 
 The great foe to astronomical observation is one which 
 people seldom take into account, namely, the atmosphere. 
 When we look at a distant object along the surface of the 
 ground on a hot summer day, we notice a certain waviness of 
 outline, accompanied by a slight trembling. If we look with 
 a telescope, we shall find this waving and trembling magnified 
 as much as the object is, so that we can see little better with 
 the most powerful telescope than with the naked eye. The 
 cause of this appearance is the mixing of the hot air near the 
 ground with the cooler air above, which causes an irregular 
 and constantly changing refraction, and the result is that as- 
 tronomical observations requiring high magnifying power can 
 very rarely be advantageously made in the daytime. By 
 night the air is not so much disturbed, yet there are always 
 currents of air of slightly different temperatures, the crossing 
 and mixing of which produce the same effects in a small de- 
 gree. To such currents is due the twinkling of the stars; 
 and we may lay it down as a rule, that when a star twinkles 
 
MAGNIFYING POWERS OF TELESCOPES. 147 
 
 the finest observation of it cannot be made with a telescope of 
 high power. Instead of presenting the appearance of a bright, 
 well-defined point, it will look like a blaze of light flaring 
 about in every direction, or like a pot of molten boiling metal ; 
 and the higher the magnifying power, the more it will flare 
 and boil. The amount of this atmospheric disturbance varies 
 greatly from night to night, but it is never entirely absent. 
 If no continuous disturbance of the image could be seen with 
 a power of 400, most astronomers would regard the night as a 
 very good one; and nights on which a power of more than 
 1000 can be advantageously employed are quite rare, at least 
 in this climate. 
 
 It has sometimes been said that Sir William Herschel em- 
 ployed a power as high as 6000 with one of his great tele- 
 scopes, and, on the strength of this, that the moon may have 
 been brought within an apparent distance of forty miles. If 
 such a power was used on the moon, we must suppose, not 
 merely that the moon was seen as if at the distance of forty 
 miles, even if Herschel used his largest telescope — that of 
 four feet aperture—but that the vision would be the same as 
 if he had looked through a pin-hole +35 of an inch in diam- 
 eter, and through several yards of running water, or many 
 miles of air. It is doubtful whether the moon has ever been 
 seen with any telescope so well as it could be seen with the 
 naked eye at a distance of 500 miles. If such has been the 
 case, we may be sure that the magnifying power did not ex- 
 ceed 1000. | 
 
 If seeing depended entirely on magnifying power, we could 
 not hope to gain much by further improvement of the tele- 
 scope, unless we should mount our instrument in some place 
 where there is less atmospheric disturbance than in the re- 
 gions where observatories have hitherto been built. It is *sup- 
 posed that, on the mountains or table-lands in the western and 
 south-western regions of North: America, the atmosphere is 
 clear and steady in an extraordinary degree; and if this sup- 
 position is entirely correct, a great gain to astronomy might 
 result from establishing an observatory in that region. 
 
148 PRACTICAL ASTRONOMY. 
 
 CHAPTER II. 
 
 APPLICATION OF THE TELESCOPE TO CELESTIAL MEASUREMENTS. 
 
 § 1. Circles of the Celestial Sphere, and their Relations to Positions 
 on the Karth. 
 
 Iy the opening chapter of this work it was shown that all 
 the heavenly bodies seem to lie and move on the surface of a 
 sphere, in the interior of which the earth and the observer are 
 placed. The operations of Practical Astronomy consist large- 
 ly in determining the apparent positions of the heavenly bod- 
 ies on this sphere. These positions are defined in a way anal- 
 ogous to that in which the position of a city or a ship is de- 
 fined on the earth, namely, by a system of celestial latitudes 
 and longitudes. That measure which, in the heavens, corre- 
 sponds most nearly to terrestrial longitude is called Right As- 
 cension, and that which corresponds to terrestrial latitude is 
 called Declination. 
 
 In Fig. 45 let the globe be the celestial sphere, represented 
 as if viewed from the outside by an observer situated towards 
 the east, though we necessarily see the actual sphere from the 
 centre. is the north pole, AB the horizon, Q the south pole 
 (invisible in northern latitudes because below the horizon), #/’ 
 the equator, 7 the zenith. The meridian lines radiate from 
 the north pole in every direction, cross the equator at right 
 angles, and meet again at the south pole, just like meridians 
 on the earth. The meridian from which right ascensions are 
 counted, corresponding in this respect to the meridian of 
 Greenwich on the surface of the earth, is that which passes 
 through the vernal equinox, or point of crossing of the equa- 
 tor and ecliptic. It is called the first meridian. Three bright 
 
CIRCLES OF THE CELESTIAL SPHERE. 149 
 
 stars near which this meridian now passes may be seen during 
 the autumn: they are a Andromede and y Pegasi, on Maps 
 II. and V.,and 3 Cassiopeize,on Map I. The right ascension 
 of any star on this meridian is zero, and the right ascension 
 of any other star is measured by the angle which the merid- 
 ian passing through it makes with the first meridian, this angle 
 being always counted towards the east. For reasons which 
 will soon be explained, right ascension is generally reckoned, 
 not in degrees, but in hours, minutes, and seconds of time. 
 
 \ 
 S2Ga 
 BAH 
 
 NZ 
 
 WE 
 @® 
 Fia. 44.—Circles of the celestial sphere. 
 
 IJ is the ecliptic, crossing the equator at its point of inter- 
 section with the first meridian, and making an angle of 234° 
 with it. The declination of a star is its distance from the 
 celestial equator, whether north or south, exactly as latitude 
 on the earth is distance from the earth’s equator. Thus, when 
 the right ascension and declination of a heavenly body are 
 given, the astronomer knows its position in the celestial sphere, 
 just as we know the position of a city on the earth when its 
 longitude and latitude are given. 
 
 It must be observed that the declinations of the heavenly 
 
150 PRACTICAL ASTRONOMY. 
 
 bodies are, in a certain sense, referred to the earth. In as- 
 tronomy the equator is regarded as a plane passing through 
 the centre of the earth, at right angles to its axis, and dividing 
 it into two hemispheres. The line where this plane intersects 
 the surface of the earth is our terrestrial, or geographical, equa- 
 tor. If an observer standing on the geographical equator im- 
 agines this plane running east and west, and cutting into and 
 through the earth, where he stands he will have the astro- 
 nomical equator, which differs from the geographical equator 
 only in being the plane in which the latter is situated. Now 
 imagine this plane continued in every direction without limit 
 till it cuts the infinite celestial sphere as in Fig. 17, page 62. 
 The circle in which it intersects this sphere will be the celes- 
 tial equator. It will pass directly over the head of the ob- 
 server at the equator. 
 
 There is a general correspondence between latitude on the 
 earth and declination in the heavens, which may be seen by 
 referring to the same figure. Here the reader must conceive 
 of the earth as a globe, ep, situated in the centre of the celes- 
 tial sphere, 4PQS, which is infinitely larger than the earth. 
 The plane represented by HQ'is the astronomical equator, di- 
 viding both the earth and the imaginary celestial sphere into 
 two equal hemispheres. Suppose, now, that the observer, in- 
 stead of standing under the equator, is standing under some 
 other parallel, say that of 45° N. (Being in this latitude means 
 that the plumb-line where he stands makes an angle of 45° 
 with the plane of the equator.) The point over his head will 
 then be in 45° celestial declination. If we imagine a pencil 
 of infinite length rising vertically where the observer stands 
 so that its point shall meet the celestial sphere in his zenith, 
 and if, as the earth performs its diurnal revolution on its axis, 
 we imagine this pencil to leave its mark on the celestial sphere, 
 this mark will be the parallel of 45° N. declination, or a cir- 
 cle everywhere equally distant from the equator and from the 
 pole. ‘The same observer will see the celestial pole at an eleva- 
 tion equal to his latitude, that is,at the angle 45°. We have now 
 the following rules for determining the latitude of a place: 
 
CIRCLES OF THE CELESTIAL SPHERE. 151 
 
 1. The latitude ts equal to the declination of the observer's zenith. 
 
 2. It ws also equal to the altitude of the pole above his horizon. 
 
 Hence, if the astronomer at any unknown station wishes to 
 determine his latitude, he has only to find what parallel of 
 declination passes through his zenith, the latter being marked 
 by the direction of the plumb-line, or by the perpendicular to 
 the surface of still water or quicksilver. If he finds a star 
 passing exactly in his zenith, and knows its declination, he has 
 his latitude at once, because it is the same as the star’s dec- 
 lination. Practically, however, an observer will never find a 
 known star exactly in his zenith; he must therefore find at 
 what angular distance from the zenith a known star passes his 
 meridian, and by adding or subtracting this distance from the 
 star’s declination he has his latitude. If he does not know 
 the declination of any star, he measures the altitudes above 
 the horizon at which any star near the pole passes the merid- 
 ian, both above the pole and under the pole. The mean of 
 the two gives the latitude. 
 
 Let. us now consider the more complex problem of deter- 
 mining longitudes. If the earth did not revolve, the obsery- 
 er’s longitude would correspond to the right ascension of his 
 zenith in the same fixed manner that his latitude corresponds 
 to its declination. But, owing to the diurnal. motion, there is 
 no such fixed correspondence. It is therefore necessary to 
 have some means of representing the constantly varying rela- 
 tion. 
 
 Wherever on the earth’s surface an observer may stand, his 
 meridian, both terrestrial and celestial, is represented*astronom- 
 ically by an imaginary plane similar to the plane of the equa- 
 tor. This plane is vertical to the observer, and passes through 
 the poles. It divides the earth into two hemispheres, and is 
 perpendicular to the equator. In Fig. 17, the celestial and ter- 
 restrial spheres are supposed to be cut through by this plane; 
 it cuts the earth when the observer stands in a line running 
 north and south from pole to pole, and thus forms a terrestrial 
 meridian. The same plane intersects the celestial sphere in a 
 great circle, which, rising above the observer’s horizon in the 
 
 H 
 
152 PRACTICAL ASTRONOMY. 
 
 north, passes through the pole and the zenith, and disappears at 
 the south horizon. Two observers north and south of each 
 other have the same meridian; but in different longitudes they 
 have different meridians, which, however, all pass through each 
 pole. 
 
 In consequence of the earth’s diurnal motion, the meridian 
 of every place is constantly moving among the stars in such a 
 way as to make a complete revolution in 23 hours 56 minutes 
 4.09 seconds. The reader will find it more easy to conceive 
 of the celestial sphere as revolving from east to west, the ter- 
 restrial meridian remaining at rest; the effect being geomet- 
 rically the same whether we conceive of the true or the ap- 
 parent motion. There are, then, two sets of meridians on 
 the celestial sphere. One set (that represented in Fig. 45) is 
 fixed among the stars, and is in constant apparent motion 
 from east to west with the stars, while the other set is fixed 
 by the earth, and is apparently at rest. 
 
 As differences of latitude are measured by angles in the 
 heavens, so differences of terrestrial longitude are measured by 
 the time it takes a celestial meridian to pass from one terres- 
 trial meridian to another; while differences of right ascension 
 are measured by the time it takes a terrestrial meridian to 
 move from one celestial meridian to another. Ordinary solar 
 time would, however, be inconvenient for this measure, because 
 a revolution does not take place in an exact number of hours. 
 A different measure, known as sidereal time, is therefore in- 
 troduced. The time required for one revolution of the celes- 
 tial meridian is divided into 24 hours, and these hours are 
 subdivided into minutes and seconds. Srdereal noon at any 
 place is the moment at which the vernal equinox passes the 
 meridian of that place, and sidereal time is counted round 
 from 0 hour to 24 hours, when the equinox will have returned 
 to the meridian, and the count is commenced over again. 
 Since right ascensions in the heavens are. counted from the 
 equinox, when it is sidereal noon, or 0 hour, all celestial ob- 
 jects on the meridian of the place are in 0° of right ascension. 
 At 1 hour sidereal time, the meridians have moved 15°, and 
 
CIRCLES OF THE CELESTIAL SPHERE. 153 
 
 objects now on the meridian are in 15° of right ascension. 
 Throughout its whole diurnal course the right ascension of the 
 meridian constantly,increases at the rate of 15° per hour, so 
 that the right ascension is always found by multiplying the 
 sidereal time by 15. To avoid this constant multiplication, it 
 is customary in astronomy to express both right ascensions and 
 terrestrial longitudes by hours. Thus the Pleiades are said to 
 be in 3 hours 40 minutes right ascension, meaning that they are 
 on the meridian of any place at 3 hours 40 minutes sidereal 
 time. The longitude of the Washington Observatory from 
 Greenwich is 77° 3’; but in astronomical language the longi- 
 tude is said to be 5 hours 8 minutes 12 seconds, meaning that 
 it takes 5 hours 8 minutes 12 seconds for any celestial merid- 
 ian to pass from the meridian of Greenwich to that of Wash- 
 ington. In consequence, when it is 0 hour, sidereal time at 
 Washington, it is 5 hours 8 minutes 12 seconds sidereal time 
 at Greenwich. 
 
 About March 22d of every year, sidereal 0 hour occurs very 
 nearly at noon. On each successive day it occurs about 3 min- 
 utes 56 seconds earlier, which in the course of a year brings 
 it back to noon again. Since the sidereal time gives the posi- 
 tion of the celestial sphere relatively to the meridian of any 
 place, it is convenient to know it in order to find what stars 
 are on the meridian. The following table shows the sidereal 
 time of mean, or ordinary civil, noon at the beginning of each 
 month: 
 
 Hrs. Min. Hrs. Min. 
 BILIALY si rukee naes dee eses dade: Be LOREEN el ULVesesseigessacerets arpsdase cuaes anes 6 38 
 MEEDEURI YAU cecedc svete ees peneda ts RE ATAU LUBED cae cdenasaciccsetdateres nds +es 8 40 
 Lh SUTIN ar oe ae Oe eer Heme L OR A 2ek Goda OOPLCM DOT aataettns Aitiwssescy ce 10 438 
 WE rath e <epe snes sidiavas ssinnyiees spe vn AOi | etober ihc o decane ts 22 ocachos cae res 12 41 
 DEMME ota s.es jt cs senelso cle sties Seah ot IOV OI DG Ee tar tacidgace cesta rees «>< 14 43 
 CLT oy ie a a 4 PAO VT DECCMDEL cre ccc viaccess seve ses cs ease 16 42 
 
 The sidereal time at any hour of the year may be found 
 from the preceding table by the following process within a 
 very few minutes: To the number of the preceding table 
 corresponding to the month add 4 minutes for each day of 
 the month, and the hour past noon. The sum of these num- 
 
154 PRACTICAL ASTRONOMY. 
 
 bers, subtracting 24 hours if the sum exceeds that quantity, 
 will give the sidereal time. As an example, let it be required 
 to find the sidereal time corresponding to November 13th at 
 3AM. This is 15 hours past noon. So we have 
 
 Hrs. Min. 
 
 November tram Wabre. uy.w eel vapc abs ls <aecew ete eemeem eet 14 438 
 AB COAV ED Aone sa tec exes at corde dis ccyedeg Sara ree seter 0 52 
 PASEO one cars teats esas sei cied on odeonp Th pereaaeatee enka eee 15 0 
 MMUDN staat bse siden fees < eicedmmsta een tasers Maetera 30 35 
 
 SOD CEs aye a vce b aa fee bak das ol viatgteci inet eeclen tae ean tere 24 0 
 Sidereal timie required: ..sc.sshstctesst aetacsuae 6 35 
 
 The sidereal time obtained in this way will seldom or never 
 be more than five minutes in error during the remainder of 
 this century. In every observatory the principal clock runs 
 by sidereal time, so that by looking at its face the astronomer 
 knows what stars are on or near the meridian. Having the 
 sidereal time, the stars which are on the meridian may be 
 found by reference to the star maps, where the right ascen- 
 sions are shown on the borders of the maps. 
 
 § 2. The Meridian Circle, and its Use. 
 
 As a complete description of the various sorts of instru- 
 ments used in astronomical measurements, and of the modes 
 of using them, would interest but a small class of readers, 
 we shall confine ourselves for the present to one which may 
 be called the fundamental instrument of modern astronomy, 
 the application of which has direct and immediate reference 
 to the circles of the celestial sphere described in the preceding 
 section. This one is termed the Meridian Circle, or Transit Cir- 
 cle. Its essential parts are a moderate-sized telescope balanced 
 on an axis passing through its centre, with a system of fine 
 
 lines in the eye-piece; one or two circles fastened on the axis, ’ 
 
 revolving with the telescope, and having degrees and subdi- 
 visions cut on their outer edges; and a set of microscope mi- 
 crometers for measuring between the lines so cut. It is abso- 
 lutely necessary that every part of the instrument shall be of 
 the most perfect workmanship, and that the masonry piers on 
 
 — 
 
 ie te bie 
 
THE MERIDIAN CIRCLE, AND ITS USE. 155 
 
 which it is mounted shall be as stable as it is possible to make 
 them. 
 
 There are many differences of detail in the construction 
 and mounting of different meridian circles, but they all turn 
 on an east and west horizontal axis, and therefore the telescope 
 moves only in the plane of the meridian. Tig. 45 shows the 
 
 Fia. 45.—The Washington transit circle. 
 
 construction of the great circle in the Naval Observatory, 
 Washington. The marble piers, PP, are supported on a mass 
 of masonry under the floor, the bottom of which is twelve feet 
 below the surface of the ground. The middle of the telescope 
 is formed of a large cube, about fifteen inches on each side. 
 From the east and west side of this cube extend the trunn- 
 ions, which are so large next the cube as to be nearly conical 
 in shape. The outer ends terminate in finely ground steel 
 pivots two and a half inches in diameter, which rest on brass 
 V’s firmly fixed to heavy castings set into the piers with hy- 
 
156 PRACTICAL ASTRONOMY. 
 
 draulic cement. In order that the delicate pivots may not 
 be worn by the whole weight of the instrument resting on 
 them, the counterpoises, Bb, support all the weight except 30 
 or 40 pounds. Near the ends of the axis are the circles, seen 
 edgewise, which are firmly screwed on the trunnions, and there- 
 fore turn with the instrument. ach pier carries four arms, 
 and each of these arms carries a microscope, marked m, hav- 
 ing in its focus the face of the circle on which the lines are 
 cut. These lines divide the circle into 360°, and each degree 
 into thirty spaces of two minutes each, so that there are 10,800 
 lines cut on the circle. They are cut in a silver band, and are 
 so fine as to be invisible to the naked eye unless the light is 
 thrown upon them in a particular way. On each side of the 
 instrument, in a line with the axis, is a lamp which throws 
 light into the telescope so as to illuminate the field of view. 
 Reflecting prisms inside of the pier throw some of the light 
 upon those points of the circle which are viewed by the mi- 
 croscopes, so as to illuminate the fine divisions on the circle. 
 Being thus limited in its movements, an object can be seen 
 with the telescope only when on, or very near, the meridian. 
 The sole use of the instrnment is to observe the exact times 
 at which stars cross the meridian, and their altitudes above 
 the horizon, or distances from the zenith, at the time of cross- 
 ing. To give precision to these observations, the eye-piece of 
 the instrument is supplied with a system of fine black lines, 
 usually made of spider’s web, as 
 shown in Fig. 46. These lines 
 are set in the focus, so that the 
 image of a star crossing the me- 
 ridian passes over them. The 
 middle vertical spider line marks 
 the meridian; and to find the 
 time of meridian transit of a star 
 it is only necessary to note the 
 moment of passage of its image 
 Fig. 46. 6 geder lines in field of view of ties this line. But, to give great- 
 
 a meridian circle. er precision and certainty to his 
 
‘ 
 
 THE MERIDIAN CIRCLE, AND ITS USE. 157 
 
 observation, the astronomer generally notes the moments of 
 transit over five or more lines, and takes the average of them 
 all. 
 
 Formerly the astronomer had to find the times of transit by 
 listening to the beat of his sidereal clock, counting the sec- 
 onds, and estimating the tenths of a second at which the tran- 
 sit over a line took place. If, for instance, he should find that 
 the star had not reached the line when the tick of twenty- 
 three seconds was heard, but crossed before the twenty-fourth 
 second was ticked, he would know that the time was twenty- 
 three seconds and some fraction, and would have to estimate 
 what that fraction was. A skilful observer will generally 
 make this estimate within a tenth of a second, and will only 
 on rare occasions be in error by as much as two tenths. 
 
 Shortly after the introduction of the electric-telegraph, the 
 American astronomers of that day introduced a much easier 
 method of determining the time of transit of a star, by means 
 of the electro-chronograph. As now made, this instrument con- 
 sists of a revolving cylinder, having a sheet of paper wrapped 
 around it, and making one revolution per minute. A pen 
 or other marker is connected with a telegraphic apparatus in 
 such a way that whenever a signal is sent to the pen it makes 
 a mark on the moving paper. This pen moves lengthwise of 
 the cylinder at the rate of about an inch in ten minutes, so 
 that, in consequence of the turning of the cylinder on its axis, 
 the marks of the pen will be along a spiral, the folds of which 
 are one-tenth of an inch apart. The galvanic circuit which 
 works the pen is connected with the sidereal clock, so that the 
 latter causes the pen to make a signal every second. The 
 same pen may be worked by a telegraphic key in the hand 
 of the observer. The latter, looking into his telescope, and 
 watching the approach of the image of the star to each wire, 
 makes a signal at the moment at which the star crosses. ‘This 
 signal is recorded on the chronograph in its proper place 
 among the clock signals, from which it may be distinguished 
 by its greater strength. The record is permanent, and the 
 sheet may be taken off and read at leisure, the exact tenth of 
 
158 PRACTICAL ASTRONOMY. 
 
 a second at which each signal was made being seen by its 
 position among the clock signals. The great advantages of 
 this method are, that great skill and practice are not required 
 to make good observations, and that the observer need not see 
 either the clock or his book, and can make a great number of 
 observations in the course of the evening which may be read 
 off at leisure. In the case of the most skilful observers there 
 is no great gain in accuracy, for the reason that they can esti- 
 mate the fraction of a second by the eye and ear with nearly 
 the same accuracy that they can give the signal. 
 
 The zenith distance of the star, from which its declination 
 is determined, is observed by having in the reticule a hori- 
 zontal spider line which is made to bisect the image of the 
 star as it passes the meridian line. The observer then goes to 
 the microscopes, ascertains what lines cut on the circle are un- 
 der them, and what number of seconds the nearest line is from 
 the proper point in the field of the microscope. The mean of 
 the results from the four microscopes is called the czrcle-reading, 
 and can be determined within two or three tenths of a second 
 of are, or even nearer, if all the apparatus is in the best order. 
 The minuteness of this angle may be judged by the circum- 
 stance that the smallest round object a keen eye can see sub- 
 tends an angle of about forty seconds. 
 
 We have described only the leading operations necessary in 
 determinations with a meridian circle. To complete the de- 
 termination of the position of a star as accurately as a prac- 
 tised observer can bisect it with the spider line is a much more 
 complicated matter, owing to the unavoidable errors and im- 
 perfections of his instrument. It is impossible to set the lat- 
 ter in the meridian with mathematical precision, and, if it were 
 done, it would not remain so a single day. When the astron- 
 omer comes to tenths of seconds, he has difficulties to contend 
 with at every step. The effects of changes of temperature 
 and motions of the solid earth on the foundations of his in- 
 strument are such as to keep it constantly changing; his clock 
 is so far from going right that he never attempts to set it per- 
 fectly right, but only determines its error from his observa- 
 
DETERMINATION OF TERRESTRIAL LONGITUDES. 159 
 
 tions. Every observation must, therefore, be corrected for a 
 number of instrumental errors before the result is accurate, 
 an operation many times more laborious than merely making 
 the observation. 
 
 § 3. Determination of Terrestrial Longitudes. 
 
 The telegraphic mode of recording observations, described 
 in the last section, affords a method of determining differences 
 of longitude between places connected by telegraph of ex- 
 traordinary elegance and perfection. We have already shown 
 that the difference of longitude between two points is meas- 
 ured by the time it takes a star to move from the meridian of 
 the easternmost point to that of the westernmost point. We 
 have also explained in the last section how an observer with a 
 meridian circle determines and records the passage of a star 
 over his meridian within a tenth of a second. Since the ze- 
 nith distance of the star is not required in this observation, the 
 circles and microscopes may be dispensed with, and the instru- 
 ment is then much simpler in construction, and is termed a 
 Transit Instrument. When the observer makes a telegraphic 
 record of the moment of transit of a star by striking a key in 
 the manner described, it is evident that the electro-chrono- 
 graph on which his taps are recorded may be at any distance 
 to which the electric current can carry his signal. It may, 
 therefore, be in a distant city. There is no difficulty in a 
 Washington observer recording his observations in Cincinnati. 
 
 On this system, the mode of operation is about as follows: 
 the Washington and Cincinnati stations each has its transit in- 
 strument, its observer, and its chronograph; but the chrono- 
 graphs are connected by telegraph, so that any signal made 
 by either observer is recorded on both chronographs. As 
 the Washington observer sees a star previously agreed on pass 
 over the lines in the focus of his instrument, he makes sig- 
 nals with his telegraphic key, which are recorded both on his 
 own chronograph and on that of Cincinnati. When the star 
 reaches the meridian of the latter city, the observer there sig- 
 
 nals the transit of the star in like manner, and the moment 
 12 
 
160 PRACTICAL ASTRONOMY. 
 
 of passage over each line in the focus of his instrument is 
 recorded, both in Cincinnati and Washington. The elapsed 
 time is then found by measuring off the chronograph sheets. 
 
 The reason for having all the observations recorded on both 
 chronographs is that the results may be corrected for the time 
 it takes the electric current to pass between the two cities, 
 which is quite perceptible at great distances. In consequence 
 of this “ wave-time,” the Washington observation will be re- 
 corded a little too late at Cincinnati, so that the difference of 
 longitude on the Cincinnati chronograph willbe too small. 
 The Cincinnati observation, which comes last, being recorded 
 a little too late at Washington, the difference of time on the 
 Washington chronograph will be a little too great. The mean 
 of the results on the two chronographs will be the correct 
 longitude, while their difference will be twice the time it takes 
 the electric current to pass between the two cities. The re- 
 sults thus obtained for the velocity of electricity are by no 
 means accordant, but the larger number do not differ very 
 greatly from 8000 miles per second. 
 
 A celestial meridian moves over the earth’s surface at the 
 rate of fifteen degrees an hour, or a minute of arc in four sec- 
 onds of time. More precisely, this is the rate of rotation of 
 the earth. The length of a minute of are in longitude de- 
 pends on the latitude. It is about 6000 feet, or a mile and a 
 sixth at the equator, but diminishes whether we go north or 
 south, owing to the approach of the meridians on the globular 
 earth, as can be seen on a globe. In the latitude of our Mid- 
 dle States it is about 4600 feet, so that the surface of the earth 
 there moves over 1150 feet a second. At the latitude of 
 Greenwich it is 3800 feet, so that the motion is 950 feet per 
 second. Two skilful astronomers, by making a great num- 
 ber of observations, can determine the time it takes the stars 
 to pass from one meridian to another within one or two hun- 
 dredths of a second of time, and can therefore make sure of 
 the difference of longitude fees two distant cities wy 
 six or eight yards. 
 
 Of ate the telegraphic method of determining longitudes 
 
DETERMINATION OF TERRESTRIAL LONGITUDES. 161 
 
 has been applied in a way a little different, though resting on 
 the same principles. Instead of recording the transits of stars 
 on both chronographs, each observer determines the error of 
 his clock by transits of stars of which the right ascension has 
 been carefully determined. Each clock is then connected with 
 both chronographs by means of the telegraphic lines, and made 
 to record its beats for the space of a few minutes only. Thus 
 the difference between the sidereal times at the two stations 
 for the same moment of absolute time can be found, and this 
 difference is the difference of longitude in time. A few years 
 ago, when the difference of longitude between points on the 
 Atlantic and Pacific coasts was determined by the Coast 
 Survey, a clock in Cambridge was made to record its beats on 
 a chronograph in San Francisco, and vice versa. In 1866, as 
 soon as the Atlantic cable had been successfully laid, Dr. B. A. 
 Gould went to Europe, under the auspices of the Coast Survey, 
 to determine the difference of longitude between Europe and 
 America. Owing to the astronomical importance of this de- 
 termination, it has since been twice repeated, once under the 
 direction of Mr. Dean, and, lastly, under that of Mr. Hilgard, 
 both of the Survey. These three campaigns gave the follow- 
 ing separate results for the difference of longitude between 
 the Royal Observatory, Greenwich, and the Naval Observato- 
 ry, Washington: 
 Hrs. Min. Sec. 
 
 IE Ould CLG heer eet are reste aah pchdeceeie cbavat Soe LL 
 DITRLICAD LOL Ust meget tes fiaradesisotersvetveaastbbers 5 8 12.16 
 INE ERAUS URES SLES 2 tase siciatsOs tise vases ae uaweesies sone tes 5 8 42709 
 
 The extreme difference, it will be seen, is less than a tenth of 
 a second, and would probably have been smaller but for the 
 numerous difficulties attendant on a determination through a 
 long ocean cable, which are much greater than through a land 
 line. 
 
 The use of the telegraph for the determination of longitude 
 is necessarily limited, and other methods must therefore gen- 
 erally be used. The general problem of determining a longi- 
 tude, whether that of a ship upon the ocean or of a station 
 
162 PRACTICAL ASTRONOMY. 
 
 upon the land, depends on two requirements: (1) a knowledge 
 of the local time at the station, and (2) a knowledge. of the 
 corresponding time at Greenwich, Washington, or some other 
 standard meridian. The difference of these two represents 
 the longitude. . 
 
 The first determination, that of the local time, is not a diffi- 
 cult problem when the utmost accuracy is not required. We 
 have already shown how it is determined with a transit instru- 
 ment. But this instrument cannot be used at all at sea, and 
 is somewhat heavy to carry and troublesome to set up on the 
 land. For ships and travellers it is, therefore, much more con- 
 venient to use a sextant, by which the altitude of the sun or of 
 a star above the horizon can be measured with very little time 
 or trouble. To obtain the time, the observation is made, not 
 when the object is on the meridian, but when it is as nearly as 
 practicable east or west. Having found the altitude, the calcu- 
 lation of a spherical triangle from the data given in the Vau- 
 tical Almanac at once gives the local time, or the error of the 
 chronometer on local time. 
 
 The difficult problem is to determine the Greenwich time. 
 So necessary to navigation is some method of doing this, that 
 the British Government long had a standing offer of a reward 
 of £10,000 to any one who would find a successful method 
 of determining the longitude at sea. When the office of As- 
 tronomer Royal was established, which was in 1675, the duty 
 of the incumbent was declared to be “to apply himself with 
 the most exact care and diligence to the rectifying the Ta- 
 bles of the Motions of the Heavens, and the places of the 
 Fixed Stars, in order to find out the so much desired Longi- 
 tude at Sea for the perfecting the Art of Navigation.” The 
 reward above referred to was ultimately divided between an 
 astronomer, Tobias Mayer, who made a great improvement in 
 the tables of the moon, and a watch-maker who improved the 
 marine chronometer. 
 
 The moon, making her monthly circuit of the heavens, may 
 be considered a sort of standard clock from which the astron- 
 omer can learn the Greenwich time, in whatever part of the 
 
DETERMINATION OF TERRESTRIAL LONGITUDES. 163 
 
 world he may find himself. This he does by observing her po- 
 sitions among the stars. The Nautical Almanac gives the pre- 
 dicted distance of the moon from certain other bodies—sun, 
 planets or bright stars—for every three hours of Greenwich 
 time; and if the astronomer or navigator measures this dis- 
 tance with a sextant, he has the means of finding at what 
 Greenwich time the distance was equal to that measured. Un- 
 fortunately, however, this operation is much like that of deter- 
 mining the time froma clock which has nothing but an hour- 
 hand. The moon moves among the stars only about 13° in 
 a day, and her own diameter in an hour. If the observer wants 
 his Greenwich time within half a minute, he must determine 
 the position of the moon within the hundred and twentieth of 
 her diameter. This is about as near as an ordinary observer 
 at sea can come with a sextant; and yet the error would be 74 
 miles of longitude. Even this degree of exactness can be ob- 
 tained only by having the moon’s place relatively to the stars 
 predicted with great accuracy; and here we meet with one of 
 the most complex problems of astronomy, the efforts to solve 
 which have already been mentioned. 
 In addition to the uncertainty of which we have spoken, 
 this method is open to the objection of being difficult, owing 
 to the long calculation necessary to free the measured distance 
 from the effects of the refraction of both bodies by the atmos- 
 phere, and of the parallax of the moon. On ordinary voyages 
 navigators prefer to trust to their chronometers. The error of 
 the chronometer on Greenwich time and its daily rate are 
 determined at ports of which the longitude is known, and the 
 navigator can then calculate this error on the supposition that 
 the chronometer gains or loses the same amount every day. 
 On voyages between Europe and America a good chronome- 
 ter will not generally deviate more than ten or fifteen seconds 
 from its calculated rate, so that it answers all the purposes of 
 navigation. 
 Still another observation by which Greenwich time may be 
 obtained to a minute in any part of the world is that of the 
 eclipses of Jupiter’s first satellite. The Greenwich or Wash- 
 
164 PRACTICAL ASTRONOMY. 
 
 ington times at which the eclipses are to occur are given in 
 the Nautical Almanac, so that if the traveller can succeed in 
 observing one, he has his Greenwich time at once, without any 
 calculation whatever. But the error of his observation may 
 be half a minute, or even an entire minute, so that this meth- 
 od is not at all accurate. 
 
 Where an astronomer can fit up a portable observatory, the 
 observation of the moon affords him a much more accurate 
 longitude than it does the navigator, because he can use better 
 instruments. Jf he has a transit instrument, he determines 
 from observation the right ascension of the moon’s limb as 
 she passes his meridian, and then, referring to the Nautical 
 Almanac, he finds at what Greenwich time the limb had this 
 right ascension. <A. single transit would, if the moon’s place 
 were correctly predicted, give a longitude correct within six 
 or eight seconds of time. It is found, however, that, owing to 
 the errors of the moon’s tables, it is necessary for the astron- 
 omer to wait for corresponding observations of the moon at 
 some standard observatory before he can be sure of this de- 
 gree of accuracy. 
 
 § 4. Mean, or Clock, Time. 
 
 We have hitherto described only sidereal time, which corre- 
 sponds to the diurnal revolution of the starry sphere, or, more 
 exactly yet, of the vernal equinox. Such a measure of time 
 would not answer the purposes of civil life, and even in astron- 
 omy its use is generally confined-to the determination of right 
 ascensions. Solar time, regulated by the diurnal motion of the 
 sun, is almost universally used in astronomical observations as 
 well as in civil life. Jormerly, solar time was made to con- 
 form absolutely to the motion of the sun; that is, it was noon 
 when the sun was on the meridian, and the hours were those 
 that would be given by a sundial. If the interval between 
 two consecutive transits of the sun were always the same, 
 this measure would have been adhered to. But there are two 
 sources of variation in the motion of the sun in right ascen- 
 sion, the effect of which is to make these intervals unequal: 
 
MEAN, OR CLOCK, TIME. 165 
 
 1. The eccentricity of the earth’s orbit. In consequence 
 of this, as already explained, the angular motion of the earth, 
 round the sun is more rapid in December, when the earth is 
 nearest the sun, than in June, when it is farthest. The aver- 
 age, or mean, motion is such that the sun is 3 minutes 56 sec- 
 onds longer in returning to the meridian than a star is. But, 
 owing to the eccentricity, this motion is actually one-thirtieth 
 greater in December, and the same amount less in June; so 
 that it varies from 3 minutes 48 seconds to 4 minutes 4 sec- 
 onds. 
 
 2. The principal source of the inequality referred to is the 
 obliquity of the ecliptic. When the sun is near the equinoxes, 
 his motion among the stars is oblique to the direction of the 
 diurnal motion; while the latter motion is directly to the 
 west, the former is 234° north or south of east. If, then, sun 
 and star cross the meridian together one day near the equinox, 
 he will not be 3 minutes 56 seconds later than the star in 
 crossing the next day, but about one-twelfth less, or 20 sec- 
 onds. ‘Therefore, at the times of the equinoxes, the solar days 
 are about 20 seconds shorter than the average. At the sol- 
 stices, the opposite effect is produced. The sun, being 234° 
 nearer the pole than before, the diurnal motion is slower, and 
 it takes the sun 20 seconds longer than the regular interval of 
 3 minutes 56 seconds for that motion to carry the sun over 
 the space which separates him from the star which culminat- 
 ed with him the day before. The days are then 20 seconds 
 longer than the average, from this cause. 
 
 So long as clocks could not be made to keep time within 
 20 seconds a day, these variations in the course of the sun 
 were not found to cause any serious inconvenience. But 
 when clocks began to keep time better than the sun, it be- 
 came necessary either to keep putting them ahead when the 
 sun went too fast, and behind when he went too slow, or to 
 give up the attempt to make them correspond. The latter 
 course is now universally adopted, where accurate time is re- 
 quired ; the standard sun for time being, not the real sun, but 
 a “mean sun,” which is sometimes ahead of the real one, and 
 
166 PRACTICAL ASTRONOMY. 
 
 sometimes behind it. The irregular time depending on the 
 motion of the true sun, or that given by a sundial, is called 
 Apparent Time, while that given by the mean sun, or by a 
 clock going at a uniform rate, is called Mean Time. The two 
 measures coincide four times ina year; during two interme- 
 diate seasons the mean time is ahead, and during two it is 
 behind. The following are the dates of coincidence, and of 
 maximum deviation, which vary but slightly from year to 
 
 year: 
 
 Piepriarys 1Oth....:hcesstaredecugeeneee True sun 15 minutes slow. 
 RNIEI AGIs cyiv > Save'ePedtcusarters senate Do. | tiple tC ORLCCLe 
 
 DRY L4G, os sseseve cas sees pees bereretes . ‘** §* 4 minutes fast. 
 ene: Leth cet nec eve weeree sce ete Srl at gen a OCONT ORES 
 
 duly: 25th)... /2oeosecterty ets toactiene . ‘* §&¢ 6 minutes slow. 
 August.Sl st: cs ssgssgeuenes + desea te $f Sf correct: 
 November 200.92 vcscteccesvasestnaces se £* 16 minutes fast. 
 December 24th fo.ecesssessaasere eee yt beet  COTTECE, 
 
 When the sun is slow, it passes the meridian after mean noon, 
 and the clock is faster than the sundial, and vice versa. These 
 wide deviations are the result of the gradual accumulations of 
 the deviations of a few seconds from day to day, the cause of 
 which has just been explained. Thus, during the interval be- 
 tween November 2d and February 12th, the sun is constantly 
 falling behind the clock at an average rate of 18 or 19 seconds 
 a day, which, continued through 100 days, brings it from 16 
 minutes fast to 15 minutes slow. 
 
 This difference between the real and the mean sun is called 
 the Hquation of Time. One of its effects, which is frequently 
 misunderstood, is that the interval from sunrise until noon, as 
 given in the almanacs, is not the same as that between noon 
 ‘and sunset. This often leads to the inquiry whether the fore- 
 noons can be longer or shorter than the afternoons. If by 
 “noon” we meant the passage of the real sun across the me- 
 ridian, they could not; but the noon of our clocks being some- 
 times 15 minutes before or after noon by the sun, the former 
 may be half an hour nearer to sunrise than to sunset, or vice 
 versa. 
 
 | 
 : 
 
PARALLAX IN GENERAL. 167 
 
 CHAPTER III. 
 MEASURING DISTANCES IN THE HEAVENS. 
 
 $1. Parallax in General. 
 
 Tue determination of the distances of the heavenly bodies 
 from us is a much more complex problem than merely deter- 
 mining their apparent positions on the celestial sphere. ‘The 
 latter depend entirely on the direction of the bodies from the 
 observer; and two bodies which lie in the same direction will 
 seem to occupy the same position, no matter how much farther 
 one may be than the other. Notwithstanding the enormous 
 differences between the distances of different heavenly bodies, 
 there is no way of telling even which is farthest and which 
 nearest by mere inspection, much less. can the absolute dis- 
 tance be determined in this way. 
 
 The distances of the heavenly bodies are generally deter- 
 mined from their Parallax. Parallax may be defined, in the 
 most general way, as the difference between the 
 
 \y 
 directions of a body as seen from two different 3 = B 
 points. Other conditions being equal, the AA 
 more distant the body, the less this differ- / / Ne \ 
 ence, or the less the parallax. To show, in pees a" 
 
 direction depends on distance, suppose an 
 observer at O to see two lights, A and B, at 
 night. He cannot tell by mere inspection /o Ee 
 which is the more distant. But suppose he gye.47,—Diagram illus- 
 walks over to the point P. Both lights wil] ting parallax. 
 
 then seem to change their direction, moving in the direction 
 opposite to that in which he goes. But the light A will change 
 more than the light B, for, being to the right of B when the 
 
 the most elementary way, how difference of / / \\ 
 / 
 i/ 
 
168 PRACTICAL ASTRONOMY. 
 
 observer was at O, it is now to the left of it. The observer 
 can then say with entire certainty that A is nearer than B. 
 
 As a steamship crosses the ocean, near objects at rest 
 change their direction rapidly, and soon flit by, while more 
 distant ones change very slowly. The stars are not seen to 
 change at all. If, however, the moon did not move, the pas- 
 senger would see her to have changed her apparent position 
 about one and a half times her diameter in consequence of 
 the journey. If, when the moon is near the meridian, an ob- 
 server could in a moment jump from New York to Liverpool, 
 keeping his eye fixed upon her, he would see her apparently 
 jump in the opposite direction about this amount. 
 
 Astronomically, the direction of an object from an observer 
 is determined by its position on the celestial sphere; that is, 
 by its right ascension and declination. In consequence of 
 parallax, the declination of a body is not the same when seen 
 from different parts of the earth. As the moon passes the 
 meridian of the Cape of Good Hope, her measured declina- 
 tion may be a degree or more farther north than it is when 
 she passes the meridian of Greenwich. The determination of 
 the parallax of the moon was one of the objects of the British 
 Government in establishing.an observatory at the Cape, and 
 so well has this object been attained that the best determina- 
 tions of the parallax have been made by comparing the Green- 
 wich and Cape observations of the moon’s declination. 
 
 The determination of the distance of a celestial object from 
 the parallax depends on the solution of a triangle. If, in Fig. 
 48, we suppose the circle to represent the earth, and imagine 
 an observer at A to view a celes- 
 tial object, JZ, he will see it pro- 
 jected on the infinite celestial 
 sphere in the direction A con- 
 tinued. Another observer at A’ 
 will see it in the direction A’M. 
 The difference of these directions 
 is the angle at JZ Knowing all 
 Fra, 48,—Diagram illustrating parallax. the angles of the quadrilateral 
 
PARALLAX IN GENERAL. 169 
 
 ACA’M, and the length of the earth’s radius, C/A, the dis- 
 tance of the object from the three points, A, A’, and C, can 
 be found by solving a simple problem of trigonometry. 
 
 The term parallax is frequently used in a more limited 
 sense than that in which we have just defined and elucidated 
 it. Instead of the difference of directions of a celestial body 
 seen from any two points, the astronomer generally means the 
 difference between the direction ,, 
 of the body as it would appear u’ 
 from the centre of the earth, and 
 the direction seen by an observer 
 at the surface. Thus,in Fig. 49, 
 an observer at the centre of the 
 earth, C, would see the object J/’ 
 in the direction CZ’, while one 
 on the surface at P will see it in 
 the direction PM’. The differ- 
 ence of these directions is the Fre. 49.—Variation of parallax with the 
 angle PM’C. If the observer ce et 
 should be at the point where the line W/’C intersects the sur- 
 face of the earth, there would be no parallax: in this case, 
 the object would be in his geocentric zenith. If, on the other 
 hand, the observer has the object in his horizon, so that the 
 line PM” is tangent to the surface of the earth, the angle 
 CM" P is called the horizontal parallax. The horizontal paral- 
 lax is equal to the angle which the radius of the earth subtends as 
 seen from the object. When we say that the horizontal parallax 
 of the moon is 57’, and that of the sun 8”’.85, it is the same 
 thing as saying that the diameter of the earth subtends twice 
 those angles as seen from the moon and sun respectively. 
 
 Owing to the ellipticity of the earth, all its diameters will 
 not subtend the same angle; the polar diameter being the 
 shortest of all, and the equatorial the longest. The equatorial 
 diameter is, therefore, adopted by astronomers as the standard 
 for parallax. The corresponding parallax, that is, the equato- 
 rial radius of the earth as seen from a celestial body, is called 
 the Hguatorial Horizontal Parallax of that body. 
 
170 PRACTICAL ASTRONOMY. 
 
 To measure directly the distance of the moon or any other 
 heavenly body, the line PC must be replaced by the line join- 
 ing the positions of the two observers, called the base-line. 
 Knowing the length and direction of this base-line, and the 
 difference of directions, or parallax, the distance is at once ob- 
 tained. If the absolute length of the base-line should not be 
 known, the astronomer could still determine the proportion 
 of the distance of the object to the base-line, leaving the final 
 determination of the absolute distances to be made when the 
 base-line could be measured. 
 
 It is not always necessary for two observers actually to sta- 
 tion themselves in two distant parts of the earth to determine 
 a parallax. If the observer himself could move along the 
 base-line, and keep up a series of observations on the object, to 
 see how it seemed to move in the opposite direction, he would 
 still be able to determine its distance. Now, every observer is 
 actually carried along by two such motions, because he is on 
 the moving earth. He is carried round the sun every year, 
 and round the axis of the earth every day. We have already 
 shown how, in consequence of the first motion, all the planets 
 seem to describe a series of epicycles. This apparent motion 
 is an effect of parallax, and by means of it the proportions of 
 the solar system can be determined with extreme accuracy. 
 The base-line is the diameter of the earth’s orbit. But the 
 parallax in question does not help us to determine this base- 
 line. ‘To find it, we must first know the distance of the earth 
 from the sun, and here we have no base-line but the diameter 
 of the earth itself. Nor can the annual motion of the earth 
 round the sun enable us to determine the distance of the 
 moon, because the latter is carried round by the same motion. 
 
 The result of the daily revolution of the observer round the 
 earth’s axis is, that the apparent movement of the planet along 
 its course is not perfectly uniform: when the observer is east, 
 the planet is a little to the west, and vice versa. By observing 
 the small inequalities in the motion of the planet correspond- 
 ing to the rotation of the earth on its axis, we have the means 
 of observing its distance with the earth’s diameter as a base- 
 
PARALLAX IN GENERAL. yg 
 
 line, and this diameter is well known. Unfortunately, how- 
 ever, the earth is so small compared with the distances of the 
 planets, that the parallax in question almost eludes measure- 
 ment, except in the case of those planets which are nearest 
 the earth, and even then it is so minute that its accurate de- 
 termination is one of the most difficult problems of modern 
 astronomy. 
 
 The principal difficulty in determining a parallax from the 
 revolution of the observer around the earth’s axis is that the 
 observations are not to be made in the meridian, but when the 
 planet is near the horizon in the east and west. Hence the 
 most accurate and convenient instrument of all, the meridian 
 circle, cannot be used, and recourse must be had to methods 
 of observation subject to many sources of error. 
 
 In measuring very minute parallaxes, it may be doubtful 
 whether the position of the body on the celestial sphere can 
 be determined with the necessary accuracy. In this case re- 
 sort is sometimes had to relative parallax. By this is meant 
 the difference between the parallaxes of two bodies lying near- 
 ly in the same direction. The most notable example of this 
 is afforded by a transit of Venus over the face of the sun. 
 To determine the absolute direction of Venus when nearest 
 the earth with the accuracy required in measurements of par- 
 allax has not hitherto been found practicable, because the ob- 
 servation must be made in the daytime, when the atmosphere 
 is much disturbed by the rays of the sun, and also because 
 only a small part of the planet can then be seen. But if the 
 planet is actually between us and the sun, so as to be seen pro- 
 jected on the sun’s face, the apparent distance of the planet 
 from the centre or from the limb of the sun may be found 
 with considerable accuracy. Moreover, this distance will be 
 different as seen from different parts of the earth’s surface at 
 the same moment, owing to the effect of parallax; that is, dif- 
 ferent observers will see Venus projected on different parts of 
 the sun’s face. But the change thus observed will be only 
 that due to the difference of the parallaxes of the two bodies; 
 while both change their directions, that nearest the observer 
 
172 PRACTICAL ASTRONOMY. 
 
 changes the more, and thus seems to move past the other, ex- 
 actly as in the diagram of the lights. : 
 
 It may be asked how the parallax of the sun can be found 
 from observations of the transit of Venus, if such observations 
 show only the difference between the parallax of Venus and 
 that of the sun. We reply that the ratio of the parallaxes of 
 the two bodies is known with great precision from the propor- 
 tions of the system. We have already shown that these pro- 
 portions are known with great accuracy from the third law of 
 Kepler, and from the annual parallax produced by the revolu- 
 tion of the earth round the sun. It is thus known that at the 
 time of the transit of Venus, in 1874, the sun was nearly four 
 times the distance of Venus, or, more exactly, that he was 
 3.783 times as far as that planet. Consequently, the parallax 
 of Venus was then 3.783 times that of the sun. The differ- 
 ence of the parallaxes, that is, the relative parallax, must then 
 have been 2.783 times the sun’s parallax. Consequently, we 
 have only to divide the relative parallax found from the ob- 
 servations by 2.783 to have the parallax of the sun itself. 
 
 Still another parallax, seldom applied except to the fixed 
 stars,is the Annual Parallax. This is the parallax already ex- 
 plained as due to the annnal revolution of the earth in its or- 
 bit. It is equal to the angle subtended by the line joining the 
 earth and sun, as seen from the star or other body. When we 
 say that the annual parallax of a star is one second of are, it is 
 the same thing as saying that at the star the line joining the 
 earth and sun would subtend an apparent angle of one sec- 
 ond, or that the diameter of the earth’s orbit would appear un- 
 der an angle of two seconds. 
 
 It will be seen that the measurement of the heavens involves 
 two separate operations. The one consists in the determina- 
 tion of the distance between the earth and the sun, which is 
 made to depend on the solar parallax, or the angle which the 
 semidiameter of the earth subtends as seen from the sun, and 
 which is the unit of distance in celestial measurements. The 
 other consists in the determination of the distances of the stars 
 and planets in terms of this unit, which gives what we may 
 
MEASURES OF THE DISTANCE OF THE SUN. 173 
 
 call the proportions of the universe. Knowing this proportion, 
 we can determine all the distances of the universe when the 
 length of our unit or the distance of the sun is known, but not 
 before. The determination of this distance is, therefore, one 
 of the capital problems of astronomy, as well as one of the most 
 difficult, to the solution of which both ancient and modern as- 
 tronomers have devoted many efforts. 
 
 § 2. Measures of the Distance of the Sun. 
 
 We have already shown, in describing the phases of the 
 moon, how Aristarchus attempted to determine the distance 
 of the sun by measuring the angle between the sun and the 
 moon, when the latter appeared half illuminated. From this 
 measure, the sun was supposed to be twenty times as far as 
 the moon; a result which arose solely from the accidental er- 
 rors of the observations. 
 
 Another method of attacking the problem was applied by 
 Ptolemy, but is probably due to Hipparchus. It rests on a 
 very ingenious geometrical construction founded on the prin- 
 ciple that the more distant the sun, the narrower will be the 
 shadow of the earth at the distance of the moon. The actual 
 diameter was determined from an ingenious combination of 
 two partial eclipses of the moon, in one of which half of the 
 moon was south of the limit of the shadow, while in the other 
 three-fourths of her diameter was north of the limit; that is, 
 one fourth of the moon’s disk was eclipsed. Itwas thus found 
 that the moon’s apparent diameter was 313’, and the appar- 
 ent diameter of the shadow 402’. The former number was 
 certainly remarkably near the truth. From this it was con- 
 cluded that the sun’s parallax was 3’ 11”, and his distance 1210 
 radii of the earth. This result was an entire mistake, arising 
 from the uncertainty of any measure of so small an angle. 
 Really, the parallax is so minute as to elude all measurement 
 with any instrument in which the vision is not assisted by the 
 use of a telescope. Yet this result continued to figure in as- 
 tronomy through the fourteen centuries during which the “Al- 
 magest” of Ptolemy was the supreme authority, without, appar- 
 
174 PRACTICAL ASTRONOMY. 
 
 ently, any astronomer being bold enough to seriously under- 
 take its revision. 
 
 Kepler and his contemporaries saw clearly that this distance 
 must be far too small; but all their estimates fell short of the 
 truth. Wendell came nearest the truth, as he claimed that 
 the parallax could not exceed 15’. But the best estimate of 
 the seventeenth century was made by Huyghens,* the reason 
 why it was the best being that it was not founded on any 
 attempt to measure the parallax itself, which was then real- 
 ly incapable of measurement, but on the probable magnitude 
 of the earth as a planet. The parallax of the sun is, as al- 
 ready explained, the apparent semidiameter of the earth as 
 seen from the sun. If, then, we can find what size the earth 
 would appear if seen from the sun, the problem would at once 
 be solved. The apparent magnitudes of the planets, as seen 
 from the earth, are found by direct measurement with the 
 telescope. The proportions of the solar system being known, 
 as already explained, it is very easy to determine the magni- 
 tudes of all the planets as seen from the sun, the earth alone 
 excepted. The idea of Huyghens was that the earth, being a 
 planet, its magnitude would probably be somewhere near that 
 of the average of the two planets on each side of it, namely, 
 Venus and Mars. So, taking the mean of the diameters of 
 Venus and Mars, and supposing this to represent the diameter 
 of the earth, he found the angle which the semidiameter of 
 the supposed earth would subtend from the sun, which would 
 be the solar parallax. 
 
 Although this method may look like a happy mode of 
 guessing, it was much more reliable than any which had be- 
 fore been applied, for the reason that, in supposing the mag- 
 nitude of the earth to be between those of Venus and Mars, 
 he was likely to be nearer the truth than any measure of an 
 angle entirely invisible to the naked eye would be. 
 
 An attempt of the same kind made by Horrox, celebrated 
 in the history of astronomy as the first observer of a transit 
 
 * At the close of his “Systema Saturnium.” 
 
MEASURES OF THE DISTANCE OF THE SUN. 175 
 
 of Venus, is also worthy of mention. He held a theory, which 
 we now know to be erroneous, that the diameters of the plan- 
 ets were proportional to their distances. from the sun, so that 
 their angular diameter as seen from the sun would be the 
 same for them all. This angular diameter he estimated at 
 28’. The solar parallax being equal to the semi-diameter of 
 the earth, as seen from the sun, it would follow from this that 
 the solar parallax was 14”. This result, though much farther 
 from the truth than that of Huyghens, was a great advance 
 on any that had preceded it. 
 
 We now come to the modern methods of measuring the 
 parallax of the sun. These consist, not in measuring this par- 
 allax directly, because this cannot even now be done with any 
 accuracy, but in measuring the parallax of one of the planets 
 Venus and Mars when nearest the earth. These planets pass- 
 ing from time to time much nearer to us than the sun does, 
 have then a much larger parallax, and one which can easily 
 be measured. Having the parallax of the planet, that of the 
 sun is determined from the known proportion between their 
 respective distances. 
 
 The first application of this method was made by the French 
 astronomers to the planet Mars. In 1671 they sent an ex- 
 pedition to the colony of Cayenne, in South America, which 
 made observations of the position of Mars during the opposi- 
 tion of 1672, while corresponding observations were made at 
 the Paris Observatory. The difference of the two apparent 
 positions, reduced to the same moment, gave the parallax of 
 Mars. From a discussion of these observations, Cassini con- 
 cluded the parallax of the sun to be 9’.5, corresponding to a 
 distance of the sun equal to 21,600 semidiameters of the earth. 
 This distance was as much too small as Huyghens’s was too 
 great, so that, as we now know, no real improvement was 
 made. Still, the data were much more certain than those on 
 which the estimate of Huyghens was made, and for a hundred 
 years it was generally considered that the sun’s parallax was 
 about 10”, and his distance between 80 and 90 millions of miles. 
 
 The method by observations of Mars is still, in some of its 
 I 13 | 
 
176 PRACTICAL ASTRONOMY. 
 
 forms, among the most valuable which have been applied to 
 the determination of the solar parallax. About once in six- 
 teen years Mars approaches almost as near the earth as Venus 
 does at the times of her transits, the favorable times being 
 those when Mars at opposition is near his perihelion. His 
 distance outside the earth’s orbit is then only 0.373 of the as- 
 tronomical unit, or 844 millions of miles, while at his aphe- 
 lion the distance is nearly twice as great. At the nearest op- 
 positions, his parallax is over 23’,an angle which can be meas- 
 ured with some accuracy. The displacement of the planet 
 due to parallax is then found by comparing the results of ob- 
 servations in the two hemispheres. 
 
 An expedition of this sort was that of Captain James M. 
 ' Gilliss, late of the United States Navy, who went ont to Chili in 
 1849, and remained till 1852, for the purpose of observing the 
 parallaxes of both Venus and Mars. The most recent expe- 
 dition was that made to the Island of Ascension, in the year 
 1877, by Mr. David Gill, now Astronomer Royal at the Cape 
 of Good Hope. In that year the opposition of Mars occurred 
 within a few days of the time of his passing perihelion, so that 
 he approached nearer the earth than at any time within the 
 last thirty years. Mr. Gill took advantage of this cireum- 
 stance to determine the parallax by the aid of the heliometer. 
 He did not, however, depend upon corresponding observations 
 in other regions of the earth, but planned out his work so as 
 to measure the change in the direction of Venus as the ob- 
 server was carried around by the rotation of the earth. In 
 consequence of this, when Mars was near either horizon he 
 would appear lower down than if he were viewed from the 
 centre of the earth. The Island of Ascension being near the 
 equator, the direction down when Mars was in the east would 
 be nearly opposite the corresponding direction when Mars 
 was in the west. Consequently, the motion of Mars would 
 not be perfectly uniform and regular, but there would be a 
 daily oscillation due to parallax which Mr. Gill undertook to 
 measure. The final result of his observations gave 8’.78 for 
 the solar parallax. 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 177 
 
 § 3. Solar Parallax from Transits of Venus. 
 
 The most celebrated method of determining the solar paral- 
 lax has been by transits of Venus over the face of the sun, by 
 which the difference between the parallax of the planet and 
 that of the sun can be found, as explained in §1. We know 
 from our astronomical tables that this phenomenon has recur- 
 red in a certain regular cycle four times every 243 years for 
 many centuries past. This cycle is made up of four intervals, 
 the lengths of which are, in regular order, 1053 years, 8 years, 
 1214 years, 8 years, after which the intervals repeat them- 
 selves. The dates of occurrence for eight centuries are as 
 follows: 
 
 MID Ocha, ¢ dncce size ccnaree ete June 2d. LSCascees asthee reece . December 6th. 
 Deke Ore ea, cvapaicwnices ne eeaae June Ist. AOE, Fer cieiee wince sane .June 8th. 
 
 hes ee teucs cave Gs oe ere neenene Precemuer (tn, |-2O1 22.0: .csnsceedsseeoadsse .June 6th. 
 
 A Gore Pocc cha siete iene emus Preceamber funy QIU Tick ., secs adiees ss caese December 11th. 
 Le GAB S ees Ss tana eaccas semen June 5th. Ul ARE Rhea fas. Rar RPE ae December 8th. 
 BLO OSes tir thee oes: June 3d. VA RE OTE Soiree RE CER .June 11th. 
 
 VS Cah cones sda dpedrices DiSCONi mer SEN. A200. 6s ooscsarsavsrecrce arts June 9th. 
 
 It has been only in comparatively recent times that this phe- 
 nomenon could be predicted and observed. In the years 1518 
 and 1526 the idea of looking for such a thing does not seem 
 to have occurred to any one. The following century gave 
 birth to Kepler, who so far improved the planetary tables 
 as to predict that a transit would occur on December 6th, 
 1631. But it did not commence until after sunset in Enu- 
 rope, and was over before sunrise next morning, so that it 
 passed entirely unobserved. Unfortunately, the tables were 
 so far from accurate that they failed to indicate the. transit 
 which occurred eight years later, and led Kepler to announce 
 that the phenomenon would not recur till 1761. The transit 
 of 1639 would, therefore, like all former ones, have passed 
 entirely unobserved, had it not been for the talent and enthu- 
 siasm of a young Englishman. Jeremiah Horrox was then a 
 young curate of eighteen, residing in the North of England, 
 who, even at that early age, was a master of the astronomy of 
 
178 PRACTICAL ASTRONOMY. 
 
 his times. Comparing different tables with his own observa- 
 tions of Venus, he found that a transit might be expected to 
 occur on December 4th, and prepared to observe it, after the 
 fashion then in vogue, by letting the image of the sun passing 
 through his telescope fall on a screen behind it. Unfortu- 
 nately, the day was Sunday, and his clerical duties prevented 
 his seeing the ingress of the planet upon the solar disk—a cir- 
 cumstance which science has mourned for a century past, and 
 will have reason to mourn for a century to come. When he 
 returned from church, he was overjoyed to see the planet upon 
 the face of the sun, but, after following it half an hour, the ap- 
 proach of sunset compelled him to suspend his observations. 
 
 During the interval between this and the next transit, which 
 occurred in 1761, exact astronomy made very rapid progress, 
 through the discovery of the law of gravitation and the ap- 
 plication of the telescope to celestial measurements. A great 
 additional interest was lent to the phenomenon by Halley’s 
 discovery that observations of it made from distant points of 
 the earth could be used to determine the distance of the sun. 
 
 The principles by which the parallaxes, and therefore the 
 distances, of Venus and the sun are determined by Halley’s 
 method are quite simple. In consequence of the parallax of 
 Venus, two observers at distant points of the earth’s surface, 
 watching her course over the 
 solar disk, will see her describe 
 slightly different paths, as shown 
 in Fig.50. It is by the distance 
 between these paths that the par- 
 allax has hitherto been deter- 
 mined. 
 
 The essential principle of Hal- 
 ley’s method consists in the mode 
 Fie. 50.—Apparent paths of Venus across of determining the distance be- 
 
 the sun, as seen from different stations tween these apparent paths. An 
 
 during the transit of 1874. Theupper , - e 
 path is that seen from a southern sta- inspection of the fioure will show 
 
 tion; the lower is that seen from a 
 northern station, but the distance be- that the path farthest from the 
 
 tween the paths is exaggerated. sun’s centre is shorter than the 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 179 
 
 other, so that Venus will pass over the sun more quickly when 
 watched from a southern station than when watched from a 
 northern one. Halley therefore proposed that the different ob- 
 servers should, with a telescope and a chronometer, note the 
 time it took Venus to pass over the disk, and the difference be- 
 tween, these times, as seen from different stations, would give 
 the means of determining the difference between the parallaxes 
 of Venus and the sun. The ratio between the distances of 
 the planet and the sun is known with great exactness by Kep- 
 ler’s third law, from which, knowing the differences of paral- 
 laxes, the distance of each body can be determined. 
 
 By this plan of Halley the observer must note with great 
 exactness the times both of beginning and end of the transit. 
 There are two phases which may be observed at the beginning 
 and two at the end, making four in all. 
 
 The first is that when the planet first touches the edge of 
 the-solar disk, and begins to make a notch in it, as at a, Fig. 50. 
 This is called first external contact. 
 
 The second is that when the planet has just entered entirely 
 upon the sun, as at b. This is called first internal contact. 
 
 The third contact is that in which the planet, after crossing 
 the sun, first reaches the edge of the disk, and begins to go 
 off,as atc. This is called second internal contact. 
 
 The fourth contact is that in which the planet finally disap- 
 pears from the face of the sun,as at d. This is called second 
 external contact. 
 
 Now, it was the opinion of Halley, and a very plausible one, 
 too, that the internal contacts could be observed with far great- 
 er accuracy than the external ones. He founded this opinion 
 on his own experience in observing a transit of the planet Mer- 
 cury at St. Helenain 1677. It will be seen by inspecting Fig. 
 51, which represents the position of the planet just before first 
 internal contact, that as the planet moves forward on the solar 
 disk the sharp horns of light on each side of it approach each 
 other, and that the moment of internal contact is marked by 
 these horns meeting each other, and forming a thread of light 
 all the way across the dark space, as in Fig.52. This thread 
 
180 PRACTICAL ASTRONOMY. 
 
 of light is indeed simply the extreme edge of the sun’s disk 
 coming into view behind the planet. In observing the tran- 
 sit of Mercury, Halley felt 
 sure that he could fix the 
 moment at which the horns 
 met, and the edge of the 
 sun’s disk appeared un- 
 broken, within a single sec- 
 ond; and he hence con- 
 cluded that observers of 
 the transit of Venus could 
 observe the time required 
 Fig. 51.—Venus approaching internal contact on for Venus to pass aclOss 
 the face of the sun. The planet is supposed the sun within one or two 
 to be moving upward. 
 seconds. ‘These times would 
 differ in different parts of the earth by fifteen or twenty min- 
 utes, in consequence of parallax. ence it followed, that if 
 Halley’s estimate of the de- 
 gree of accuracy attainable 
 were correct, the parallax of 
 Venus and the sun would be 
 determined by the proposed 
 system of observations within 
 the six hundredth of its whole 
 amount. 
 
 When the long-expected 5th 
 of June, 1761, at length ap- 
 proached, which was a gener- 
 ation after Halley’s death. ex- big, 52.—Internal contact of the limb of Ve- 
 
 3 nus with that of the sun. 
 
 peditions were sent to distant 
 
 parts of the world by the principal European nations to make 
 the required observations. The French sent out from among 
 their astronomers, Le Gentil to Pondicherry; Pingré to Rod- 
 riguez Island, in the neighborhood of the Mauritius; and the 
 Abbé Chappe to Tobolsk, in Siberia. The war with England, 
 unfortunately, prevented the first two from reaching their sta- 
 tions in time, but Chappe was successful. From England, Ma- 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 181 
 
 son—he of the celebrated Mason and Dixon’s Line—was sent 
 to Sumatra; but he, too, was stopped by the war: Maskelyne, 
 the Astronomer Royal, was sent to St. Helena. Denmark, 
 Sweden, and Russia also sent out expeditions to various points 
 in Europe and Asia. 
 
 With those observers who were favored by fine weather, the 
 entry of the dark body of Venus upon the limb of the sun 
 was seen very well until the critical moment of internal con- 
 tact approached. Then they were perplexed to find that the 
 planet, instead of preserving its circular form, appeared to 
 assume the shape of a pear or a balloon, the elongated portion 
 being connected with the limb of the sun. We give two fig- 
 ures, 52 and 53, the first showing how the planet at to tek 
 fonked, the last how it really did look. Now, we can readily 
 see at the observer, looking 
 at such an appearance as 7 
 Fig. 53, would be unable to 
 say whether internal contact 
 had or had not taken place. 
 The round part of the planet 
 is entirely within the sun, so 
 that if he judged from this 
 alone, he would say that in- 
 ternal contact is passed. But 
 the horns are still separated 
 by this dark elongation, or 
 “black drop,” as it is general- 
 ly called, so that, judging from this, internal contact has not 
 taken place. The result was an uncertainty sometimes amount- 
 ing to nearly a minute in observations which were expected to 
 be correct within a single second. 
 
 When the parties returned home, and their observations 
 were computed by various astronomers, the resulting values 
 of the solar parallax were found to range from 8”.5, found by 
 Short of England, to 10.5, found by Pingré, of France, so 
 that there was nearly as much uncertainty as ever in the value 
 of the element sought. Nothing daunted, however, prepara- 
 
 Fig. 53.—The black drop, or ligament. 
 
182 PRACTICAL ASTRONOMY. 
 
 tions yet more extensive were made to observe the transit of 
 1769. Among the observers was one whose patience and 
 whose fortune must excite our warmest sympathies. We have 
 said that Le Gentil, sent out by the French Academy to ob- 
 serve the transit of 1761 in the East Indies, was prevented 
 from reaching his station by the war with England. Finding. 
 the first port he attempted to reach in the possession of the 
 English, his commander attempted to make another, and, 
 meeting with unfavorable winds, was still at sea on the day of 
 the transit. He thereupon formed the resolution of remain- 
 ing, with his instruments, to observe the transit of 1769. He 
 was enabled to support himself by some successful mercantile 
 adventures, and he also industriously devoted himself to scien- 
 tific observations and inquiries. The long-looked-for morning 
 of June 4th, 1769, found him thoroughly prepared to make 
 the observations for which he had waited eight long years. 
 The sun shone out in a cloudless sky, as it had shone for a 
 number of days previously. but just as it was time for the 
 transit to begin, a sudden storm arose, and the sky became 
 covered with clouds. When they cleared away the transit 
 was over. It was two weeks before the ill-fated astronomer 
 could hold the pen which was to tell his friends in Paris the 
 story of his disappointment. 
 
 In this transit the ingress of Venus on the limb of the sun 
 occurred just before the sun was setting in Western Europe, 
 which allowed numbers of observations of the first two phases 
 to be made in England and France. The commencement was 
 also visible in this country—which was then these colonies— 
 under very favorable circumstances, and it was well observed 
 by the few astronomers we then had. The leader among 
 these was the talented and enthusiastic Rittenhouse, who was 
 already well known for his industry as an observer. The ob- 
 servations were organized under the auspices of the American 
 Philosophical Society, then in the vigor of its youth, and par- 
 ties of observers were stationed at Norristown, Philadelphia, 
 and Cape Henlopen. These observations have every appear- 
 ance of being among the most accurate made on the transit; 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 183 
 
 but they have not received the consideration to which they are 
 entitled, partly, we suppose, because the altitude of the sun 
 was too great to admit of their being of much value for the 
 determination of parallax, and partly because they were not 
 very accordant with the European observations. 
 
 The phenomena of the distortion of the planet and the 
 “black drop,” already described, were noticed in this, as in 
 the preceding transit. It is strongly indicative of the ill 
 preparation of the observers that it seems to have taken them 
 all by surprise, except the few who had observed the preced- 
 ing transit. The cause of the appearance was first pointed 
 out by Lalande, and is briefly this: when we look at a bright 
 object on a dark ground, it looks a little larger than it real- 
 ly is, owing to the encroachment of the light upon the dark 
 border. This encroachment, or irradiation, may arise from a 
 number of causes—imperfections of the eye, imperfections of 
 the lenses of the telescope when an instrument is used, and 
 the softening effect of the atmosphere when we look at a ce- 
 lestial object near the horizon. To understand its effect, we 
 have only to imagine a false edge painted in white around the 
 borders of the bright object, the edge becoming narrower and 
 darker where the bright object is reduced to a very narrow 
 line. Thus, by painting around the borders of the light por- 
 tions of Fig. 51, we have formed Fig. 53, and produced an ap- 
 pearance quite similar to that described by the observers of 
 the transit. The better the telescope and the steadier the at- 
 mosphere, the narrower this border will be, and the more the 
 planet will seem to preserve its true form, as in Fig.52. In 
 the observations of the recent transit of Venus with the im- 
 proved instruments of the present time, very few of the more 
 experienced observers noticed any distortion at all. 
 
 The results of the observations of 1769 were much more 
 accordant than those of 1761, and seemed to indicate a paral- 
 lax of about 8’.5. Curious as it may seem, more than half a 
 century elapsed after the transit before its results were com- 
 pletely worked up from all the observations in an entirely 
 satisfactory manner. This was at length done by Encke, in 
 
184 PRACTICAL ASTRONOMY. 
 
 1824, for both transits, the result giving 8’’.5776 for the solar 
 parallax. Some suspicion, however, attached to some of the 
 observations, which he was not at that time able to remove. 
 In 1885, having examined the original records of the observa- 
 tions in question, he corrected his work, and found the follow- 
 ing separate results from the two transits: 
 
 Parallax from the observations Of 1761.......ccsseccsccececssvecs 8.53 
 Parallax from the observations Of 1769.......-.ssssseseeeeeeeees .8".59 
 Most probable result from both transits. .........cccseeseeceeeees oO .TL 
 
 The probable error of the result was estimated at 0/037, 
 which, though larger than was expected, was much less than 
 the actual error has since proved to be. The corresponding 
 distance of the sun is 95,370,000 miles, a classic number 
 adopted by astronomers everywhere, and familiar to every 
 one who has read any work on astronomy. 
 
 This result of Encke was received without question for 
 more than thirty years.. But in 1854 the celebrated Hansen, 
 completing his investigations of the motions of the moon, 
 found that her observed positions near her first and last quar- 
 ters could not be accounted for except by supposing the par- 
 allax of the sun increased, and therefore his distance dimin- 
 ished, by about a thirtieth of its entire amount. ‘The exist- 
 ence of this error has since been amply confirmed in several 
 ways. The fact is, that although a century ago a transit of 
 Venus afforded the most accurate way of obtaining the dis- 
 tance of the sun, yet the great advances made during the 
 present generation in the art of observing, and the applica- 
 tion of scientific methods, have led to other means of greater 
 accuracy than these old observations. It is remarkable that 
 while nearly every class of observations is now made with 
 a precision which the astronomers of a century ago never 
 thought possible, yet this particular observation of the interior 
 contact of a planet with the limb of the sun has never been 
 made with any thing like the accuracy which Halley himself 
 thought he attained in his observation of the transit of Mer- 
 cury two centuries ago. 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 185 
 
 The knowledge of this error in the fundamental astronom- 
 ical unit gave increased interest.to the transit of Venus which 
 was to occur on December 8th, 1874. The rarity of the phe- 
 nomenon was an advantage, in that it led to an amount of | 
 public interest being taken in it which could not have been 
 excited by any other astronomical event, and thus secured 
 from various governments the grants necessary to fit out the 
 necessary parties of observation. Plans of observation began 
 to be worked out very far in advance. In 1857, Professor 
 Airy sketched a general plan of operations for the observation 
 of the transits, and indicated the regions of the globe in which 
 he considered the observations should be made. In 1870, be- 
 fore any steps whatever were taken in this country, he had ad- 
 vanced so far in his preparations as to have his observing huts 
 all ready, and his instruments in process of construction. In 
 1869, the Prussian Government appointed a commission, con- 
 sisting of six or eight of its most eminent astronomers, to de- 
 vise a plan of operations, and report it to the Government 
 with an estimate of the expenses. About the same time the 
 Russian Government began making extensive preparations 
 for observing the transit from a great number of stations in 
 Siberia. 
 
 Active preparations for the observations in question were 
 commenced by the United States Government in 1871. An 
 account of the method of observation adopted by the Com- 
 mission to whom the matter was intrusted may not be devoid 
 of interest. The observations of the older transits having 
 failed in giving results of the accuracy now required, it be- 
 came necessary to improve upon the system then adopted. 
 In this system, the parallax depended entirely on observations 
 of contacts, the uncertainty of which we have already shown. 
 Besides this uncertainty, Halley’s method was open to the ob- 
 jection that, unless both contacts were observed at each sta- 
 tion, the path of Venus could not be determined, and no re- 
 sult could be deduced. It was therefore proposed by De 
 Isle early in the last century, that the observers should de- 
 termine the longitudes of their stations, in order that, by 
 
186 PRACTICAL ASTRONOMY. 
 
 means of it, they could find the actual intervals between the 
 moments at which any given contact was seen at the different 
 stations. This method was an improvement on Halley’s, in 
 that it diminished the chances of total failure. Still, it de- 
 pended entirely upon making an accurate observation of the 
 moment of contact, and was liable to fail from any accident 
 which might interfere with such an observation—a passing 
 cloud, or a disarrangement of some of the instruments of ob- 
 servation. Besides, it was not yet certain whether the obser- 
 vations could be made with the necessary accuracy. It was, 
 therefore, desirable that, instead of depending on contacts 
 alone, some method should be adopted of finding the position 
 of Venus on the face of the sun as often as possible during 
 the four hours which she should occupy in passing. ‘The 
 easiest and most effective way of doing this seemed to be to 
 take photographs of the sun with Venus on his disk, which 
 photographs could be brought home, compared, and measured 
 at leisure. 
 
 This mode of astronomical measurement has been brought 
 to great perfection in this country by Mr. L. M. Rutherfurd 
 and others, and has been found to give results exceeding in 
 accuracy any yet attained by ordinary eye observations. The 
 advantages of the photographic method are so obvious that 
 there could be no hesitation about employing it, and, so far 
 as is known, it was applied by every European nation which 
 sent out parties of observation. But there is a great and 
 essential difference between the methods of photographing 
 adopted by the Americans and by most of the Europeans. 
 The latter seem to have devoted all their attention to the 
 problem of securing a good sharp photograph, taking it for 
 granted that when this photograph was measured there would 
 be no further difficulty. But the measurement at home is 
 necessarily made in inches and fractions, while the distance 
 we must know is to be found in minutes and seconds of an- 
 gular measure. If we have a map by measurements on which 
 we desire to know the exact distance of two places, we must 
 first know the exact scale on which the map is laid down, 
 
it intel 
 
 SOLAR PARALLAX FROM TRANSITS OF VENUS. 187 
 
 with a degree of accuracy corresponding to that of our meas- 
 ures. Just so with our photographs taken at various parts of 
 the globe. We must know the scale on which the images are 
 photographed before we can derive any conclusions from our 
 measures. While the determination of this scale with suffi- 
 cient precision for ordinary purposes is quite.easy, this is by 
 no means the case with a problem where so much accuracy 
 was required, so that here lay the greatest difficulty which the 
 photographic method offered. 
 
 In the mode of photographing adopted by the Americans 
 this difficulty was met by using a telescope of great length 
 —nearly forty feet. So long a telescope would be too un- 
 wieldy to point at the sun; it was therefore fixed in a hor- 
 izontal position, the rays of the sun being thrown into it by a 
 mirror. The scale of the picture was determined by actually 
 measuring the distance between the object-glass and the pho- 
 tograph-plate. Each station was supplied with special appa- 
 ratus by which this measurement could be made within the 
 hundredth of an inch. Then, knowing the position of the op- 
 tical centre of the glass, it is easy to calculate exactly how 
 many inches any given angle will subtend on the photograph- 
 plate. The following brief description of the apparatus will 
 be readily understood by reference to the figures: 
 
 The object-glass and the support for the mirror are mount- 
 ed on an iron pier extending four feet into the ground, and 
 firmly embedded in concrete. The mirror is in a frame at 
 the end of an inclined cast-iron axis, which is turned with a 
 very slow motion by a simple and ingenious piece of clock- 
 work. The inclination of the axis and the rate of motion are 
 so adjusted that, notwithstanding the diurnal motion of the 
 sun —or, to speak more accurately, of the earth —the sun’s 
 rays will always be reflected in the same direction. This re- 
 sult is not attained with entire exactness, but it is so near that 
 it will only be necessary for an assistant to touch the screws 
 of the mirror at intervals of fifteen or twenty minutes during 
 the critical hours of the transit. The reflector is simply a 
 piece of finely polished glass, without any silvering whatever. 
 
188 PRACTICAL ASTRONOMY. 
 
 It only reflects about a twentieth of the sun’s light; but so in- 
 tense are his rays that a photograph can be taken in less than 
 the tenth of a second. The polishing of this mirror was the 
 most delicate and difficult operation in the construction of 
 the apparatus, as the slightest deviation from perfect flatness 
 would be fatal. For instance, if a straight edge laid upon the 
 glass should touch at the edges, but be the hundred-thou- 
 sandth of an inch above it at the centre, the reflector would 
 be useless. It might have seemed hopeless to seek for such a 
 degree of accuracy, had it not been for the confidence of the 
 Commission in the mechanical genius of Alvan Clark & Sons, 
 to whom the manufacture of the apparatus was intrusted. 
 The mirrors were tested by observing objects through a tele- 
 scope, first directly, and then by reflection from the mirror. 
 If they were seen with equally good definition in the two 
 cases, it would show that there were no irregularities in the 
 surface of the mirror; while if it were either concave or con- 
 vex, the focus of the telescope would seem shortened or 
 lengthened. The first test was sustained perfectly, while the 
 
 4v1S6!14 
 
 i] w3q70H SAV Ta. 
 
 OWTANCE 
 28 AND A FRACTION, = G— EN S_subavs My: 
 
 Min 
 
 Saul rf 4 
 
 Ws Me 
 
 ey y ee aA 
 
 F 1a. 54.—Method of photographing the transit of Venus used by the French and Ameri- 
 can observers, and by Lord Lindsay. 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 189 
 
 circles of convexity or concavity indicated by the changes of 
 focus of the photographic telescope were many miles in di- 
 ameter. 
 
 Immediately in front of the mirror is the object-glass. The 
 curves of the lenses of which it is formed are so arranged that 
 it is not perfectly achromatic for the visual rays, but gives the 
 best photographic image. Thirty-eight feet and a fraction 
 from the glass is the focus, where an image of the sun abont 
 four and a quarter inches in diameter is formed. Here an- 
 other iron pier is firmly embedded in the ground for the sup- 
 port of the photographic plate-holder. This consists of a 
 brass frame seven inches square on the inside, revolving on a 
 vertical rod, which passes through the iron plate on top of the 
 pier. Into this frame is cemented a square of plate-glass, just 
 as a pane of glass is puttied in a window. The glass is divided 
 into small squares by very fine lines about one-five-hundredth 
 of an inch thick, which were etched by a process invented and 
 perfected by Mr. W. A. Rogers, of the Cambridge Observatory. 
 The sensitive plate goes into the other side of the frame, and 
 when in position for taking the photograph, there is a space 
 of about one-eighth of an inch between the ruled lines and 
 the plate. The former are, therefore, photographed on every 
 picture of the sun which is taken, and serve to detect any 
 contraction of the collodion film on the glass plate. 
 
 The rod on which the plate-holder turns, and the frame it- 
 self, are perforated from top to bottom by a vertical opening 
 one-sixth of an inch in diameter. Through the centre of this 
 opening, passing between the ruled plate and the photograph 
 plate, hangs a plumb-line of very fine silver wire. In every 
 picture of the sun this plumb-line is also photographed, and 
 this marks a truly vertical line on the plate very near the mid- 
 dle vertical etched line. A spirit-level is fixed to the top of 
 the frame, and serves to detect any changes in the inclination 
 of the ruled lines to the horizon. 
 
 One of the most essential features of the arrangement is 
 that the photographic object-glass and plate-holder are on the 
 same level, and in the meridian of the transit instrument with 
 
é 
 
 190 PRACTICAL ASTRONOMY. 
 
 which the time is determined. The central ruled line on the 
 plate-holder is thus used as a meridian mark for the transit. 
 The great advantage of this arrangement is, that it permits 
 “the angle which the line joining the centres of the sun and 
 , Venus makes with the meridian to be determined with the 
 greatest precision by means of the image of the plumb-line 
 which is photographed across the picture of the sun.* 
 Although the contact observations were not wholly relied 
 on, they were by no means neglected. On the contrary, the 
 greatest pains were taken to avoid the sources of error which 
 caused so much trouble in 1769. To learn what these errors 
 probably were, and to practise the observers in making their 
 observations so as to avoid them, an artificial planet was con- 
 structed to move over an artificial representation of a portion 
 of the solar disk by clock-work. The apparatus was mounted 
 on the top of a building about 3300 feet distant, in order to: 
 give the effect of atmospheric undulations and softening of 
 the edges of the planet. The planet was represented by-a 
 black disk one foot in diameter, which made its apparent mag- 
 nitude the same as that 
 of Venus in transit. The 
 sun was represented by 
 a white screen behind 
 the artificial Venus, the 
 portions of the edge of 
 the disk where Venus 
 entered and left being formed by the sloping edges of a black 
 triangle, as shown in the figure. There was no need of a rep- 
 resentation of the entire sun. The motion was so regulated 
 that the time occupied by the disk in passing from external to 
 
 [Alaa 
 A KADY, 
 
 Fig. 55.—Artificial transit of Venus. 
 
 * The method of photographing the sun by a fixed horizontal telescope with a 
 reflector in front of it is believed to have been first proposed in France by Captain 
 Laussedat. It was independently invented by the late Professor Winlock, who 
 put it into actual operation at the Harvard College Observatory in 1869, and, so 
 far as the author is aware, was the first one to do so. It was employed not only 
 by the American observers, but by the French, and by Lord Lindsay, M.P., of 
 Scotland. The latter gentleman fitted out a finely equipped expedition at his own 
 expense to observe the transit of Venus at the Mauritius. 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 191 
 
 internal contact, and the angle its motion made with the edges 
 of the triangle, were the same as they would be in the actual 
 transit as viewed from some point where it occurred near the 
 zenith. The disk was put at such a height that it was only 
 about three minutes from internal contact at ingress to inter- 
 nal contact at egress, instead of four hours. ‘ 
 
 At each American station the scientific corps consisted of 
 a chief of party, an assistant astronomer, and three photog- 
 raphers. The instruments at all the stations were precisely 
 similar, and the operations and observations the same at. all. 
 This system was adopted to secure two great advantages: first, 
 to run the least risk of entire failure from bad weather; and, 
 second, to have all the observations strictly comparable. Much 
 pains and trouble were devoted to these objects. 
 
 One of the most important features of the preparations, 
 which distinguishes them from the preparations to observe 
 the former transits, was the previous training of the observers. 
 All the members of the observing parties assembled at Wash- 
 ington to practise together before leaving to make the obser- 
 vations. They took all their multitudinous instruments and 
 apparatus out of their boxes, mounted them, and proceeded to 
 practise with them in the same way they were to be used at 
 the stations. Photographs of the sun were taken from day to 
 day in the same way as on the 8th of December, and each 
 chief of party was instructed in all the delicate operations 
 necessary to secure the entire success of his operations. 
 
 To know where a party could be sent, it had first to be 
 known when and where the transit would be visible. We 
 give a small map of the world showing this at a glance. 
 Could we have seen the planet Venus from the Eastern States 
 on the afternoon of December 8th, 1874, we should have seen 
 her approaching nearer and nearer the sun as the latter ap- 
 proached the horizon. In San Francisco, where sunset is three 
 hours later than here, she would have been so near the sun as 
 almost to seem to touch it. About an hour later she actual- 
 ly reached the solar disk. The sun was then shining on the 
 whole Pacific Ocean, except that portion nearest the Ameri- 
 
 14 
 
192 PRACTICAL ASTRONOMY. 
 
 4 A Pe 
 THE WHOLE FRANSES 5 
 
 VISIBLE — 
 USTRAL. 
 
 Yy Uy, 
 4 ¢ tiy 
 + PAN Gy Yj 
 & Z l iy, 
 “iy < 
 ~ 
 eer te Athed cassoon 
 
 Fig. 56.—Map of the earth, showing the areas of visibility of the transit of 1874. 
 
 can coast, and on Eastern Asia, Australia, and the Indian and 
 Antarctic oceans to the sonth pole. Venus was about four 
 and a half hours passing over the face of the sun, and during 
 this time the latter had set across the entire northern portion | 
 of the Pacific Ocean, and had risen as far west as Moscow 
 and Vienna, from which cities the planet might have been 
 seen to leave the disk just as the sun rose. 
 
 The stations which the American parties finally occupied, 
 with the names of the chiefs of party, are as follows: 
 
 NorTHERN HEMISPHERE. 
 
 Wladiwostok, Siberia...........- Professor ASAPH Hatt, U.S. N. 
 Peking, CHinas.c.- scepter rapen nse Professor J. C. WaTSon. 
 Nagasaki, Japan............sec0e Professor GEorGE Davipson, U. S. Coast Survey. 
 
 SOUTHERN STATIONS. 
 
 Kerguelen Island...............+. Commander G. P. Ryan, U.S.N. 
 
 Hobart-town, T'asmania....... .-Professor W. Harkness, U.S. N. 
 
 Campbelltown, ‘Tasmania*.....Captain C. W. Raymonp, Engineer Corps, U.S. A. 
 Queenstown, New Zealand.....Professor C. H. F. PErrers. 
 
 Chatham Jslands.....:..s<00dy ses Epwin Smiru, Esq., U. S. Coast Survey. 
 
 The southern parties were all carried to their respective sta- 
 tions by the U.S. steamer Swatara, Captain Ralph Chandler, 
 U.S. N., commanding. 
 
 * Captain Raymond’s party was designed for the Crozet Islands, but the Swa- 
 tara failed to effect a landing there. 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 193 
 
 The only thing which seriously interfered with the observa- 
 tions was the weather. Some photographs were obtained at 
 every station, but the full number at none. Altogether, there 
 were only about half the expected number obtained. No 
 contacts at all were observed at Hobart-town or Chatham Isl- 
 and, but one or more were observed at each of the remaining 
 six stations. Peking was, however, the only one at which all 
 four were observed. Among the parties sent out by other 
 nations, the most fortunate, as regards weather, were the Ger- 
 mans, who were successful at all six of their stations. The 
 English, French, and Russians were, on the average, about as 
 successful as the Americans. 
 
 The work of reducing the observations of a transit of Venus 
 with all the precision required by modern astronomy is one 
 involving an immense mass of calculations, and much tedious 
 investigation. Before the final result can be attained, it is 
 necessary that all the observations made under the auspices of 
 the several governments which took part in the work shall be 
 reduced and published, and, after this is done, that some one 
 shall.combine them all,so as to obtain the most probable re- 
 sult. Partial results, founded upon a portion of the observa- 
 tions, may, indeed, be deduced without waiting for all the 
 material; but the majority of the leading astronomers con- 
 ceive that these results will not have any scientific interest ; 
 and at a meeting of the International Astronomical Society 
 (the Astronomische Gesellschaft), held at Leyden, it was voted » 
 that their publication should be discouraged as injurious to 
 science. This view has not, however, been universally ac- 
 cepted, and three values of the solar parallax from the obser- 
 vations of the transit of 1874 have already appeared, one from 
 the French, and two from the English observations. 
 
 - The French observations here referred to were those made 
 at two stations, Peking and St. Paul’s Island. They were cal- 
 culated by M. Puiseux,a member of the French Academy of 
 Sciences, in 1875, and led to 8’’.88 as the value of the solar 
 parallax. 
 
 The British observations of contacts were worked up, under 
 
194 PRACTICAL ASTRONOMY. 
 
 the direction of Sir George Airy, in 1877, and were found to 
 lead to the surprisingly small result, 8’.76. But Mr. E. J. 
 Stone took the very same observations, and, by treating and 
 interpreting them in a different way, obtained the result 8’’.88. 
 That two results so different could be obtained from the same 
 observations must cast doubt upon their value, and raise ques- 
 tions which can be decided only by the combination of all the 
 observations. 
 
 Transit of December 6th, 1882.—The region of visibility 
 of this transit will be quite different from that of the last one, 
 as it will include the whole American continent, except those 
 portions lying in the Arctic zone where the sun will not rise 
 during the winter season. The beginning will also be visible 
 over a large part of Africa, and the end over most of the Pa- 
 cific Ocean. As almost every reader will be able to see either 
 the whole or some part of this transit, we present a map show- 
 ing the region of visibility of the different phases. 
 
 Within the shaded region marked “ whole transit invist- 
 ble” the entire transit will take place with the sun below the 
 horizon. It will be noticed that this region includes the 
 whole continent of Asia, but scarcely any other land except 
 the western half of Australia and the islands of the East In- 
 dies. This region is bounded on the west by a line marked 
 “transit begins at sunset.” Observers immediately west of 
 this line will see the transit begin a few minutes before the 
 sun sets; and the farther west they are the greater the time 
 during which they may see Venus on the sun’s disk. It will 
 be seen that the British Islands and the western half of Eu- 
 rope are in this region, the transit beginning at times vary- 
 ing from sunset to two hours before sunset. But in all this 
 region the sun will set before the transit is over. 
 
 Now, crossing the Atlantic towards the west, we come to the 
 line marked “ ¢ranszt ends at sunset.” An observer immedi- 
 ately to the east of this line will see the sun setting just be- 
 fore Venus is passing off his limb, while immediately to the 
 west the planet will leave the limb before the sun sets, so that 
 he will see the whole transit. The next line to the west is 
 
SOLAR PARALLAX FROM TRANSITS OF VENUS. 195 
 
 “transit begins at sunrise.” Observers east of this line, but 
 west of that last described, will see the whole transit. This 
 region includes the whole United States, except those portions 
 in the extreme north-west and on the Pacific coast. Tracing 
 the two lines to the north, it will be seen that they cross each 
 other on the shore of Hudson’s Bay, in 60° of north latitude. 
 At the point of crossing the transit begins at sunrise and ends 
 at sunset, so that Venus is on the sun’s disk exactly the whole 
 day, and neither more nor less, the length of the day being 
 equal to the time of the transit. 
 
 North of this point, and south of the Arctic circle, there 
 is a comparatively small triangular region within which the 
 transit will begin before sunrise and continue until after sun- 
 set. Therefore Venus will be on the sun’s limb during the 
 whole of the short day, though neither egress nor ingress 
 will be seen. It will be interesting to note the correspond- 
 ing region in the southern hemisphere, bounded by the Ant- 
 arctic circle and the lines “¢ranszt ends at sunrise” and “tran- 
 sit begins at sunset.” Within this region an observer would 
 see the transit just before sunset. After a night of only a few — 
 hours the sun would rise with Venus still on his disk and 
 about to leave it. Thus ingress and egress would both be vis- 
 ible, but the intermediate phases would be wholly or partly 
 invisible. | , | | 
 
 Passing still farther west we have a region where only the 
 end of the transit is visible. Immediately west of the line 
 “transit begins at sunrise” the sun will rise with Venus just 
 having entered on its disk; all the rest of the transit will be 
 seen. The farther west we go the longer Venus will have 
 been on the sun before sunrise, until, when we reach the line 
 “transit ends at sunrise,’ Venus will be passing off. There- 
 fore, in the Sandwich Islands and over all the Southern Pa- 
 cific Ocean, the end of the transit, but no other phase, is 
 visible. 
 
 Amateur observers within the United States may know 
 when to look for the appearance of Venus on the sun’s limb 
 by noting that the first impression of the planet will occur 
 
196 PRACTICAL ASTRONOMY. 
 
 over the whole United States near the same moment of ab- 
 solute time—namely, about five minutes before nine o’clock 
 on the morning of December 6th, Washington mean time. To 
 this time apply the longitude of the observer from Washing- 
 ton, and his local time will be given. Owing to the errors of 
 the tables of Venus we cannot predict within a minute the 
 time of beginning. It may occur at any moment between 
 three minutes and five minutes before nine, or even a fraction 
 of a minute outside these limits. The ending will occur from 
 three o’clock to two or three minutes past three, Washington 
 mean time. It will, however, occur from three to four min- 
 utes later on the Pacific coast than in the Northern States. 
 
 The apparent diameter of Venus will be a little more than 
 a minute of arc; it will, therefore, be visible to the naked eye 
 through a smoked glass as an exceedingly small dot. 
 
 § 4. Other Methods of determining the Sun's Distance, and their 
 Results. > : 
 
 The methods of determining the astronomical unit which 
 we have described rest entirely upon measures of parallax, an 
 angle which hardly ever exceeds 20”, and which it is there- 
 fore exceedingly difficult to measure with the necessary ac- 
 curacy. If there were no other way than this of determining 
 the sun’s distance, we might despair of being sure of it with- 
 in 200,000 miles. But the refined investigations of modern 
 science have brought to light other methods, by at least two 
 of which we may hope, ultimately, to attain a greater degree 
 of accuracy than we can by measuring parallaxes. Of these 
 two, one depends on the gravitating force of the sun upon the 
 moon, and the other upon the velocity of light. 
 
 Parallactic Equation of the Moon.—The motion of the moon 
 around the earth is largely affected by the gravitating force 
 of the sun, or,to speak more exactly, by the difference of the 
 gravitating force of the sun upon the moon and upon the 
 earth. A part of this difference depends upon the proportion 
 between the respective distances of the moon and the sun, so 
 that when this force is known, the proportion can be deter- 
 
Yj Ui) j CY M 
 ; ¢ d y is 
 Yi iif pe Yj AU 
 yy i Y , Oehe, 
 ) Ascensi in, A Uf 
 Y Yy Yi fy y 
 
 Bociety ote S \ ; 
 Jslands** 7 '.|+" , 9 nen 
 : 1. 
 
 Fra. 57.—Map of the world, showing the regions in which the transit of Venus will be visible on December 6th, 1882. 
 
METHODS OF DETERMINING THE SUN’S DISTANCE. 199 
 
 mined. ‘The distance of the moon being known with all nec- 
 essary precision, we have only to multiply it by the proportion 
 thus obtained to get the distance of the sun. The force in 
 question shows itself by producing a certain inequality in the 
 moon’s motion, by which she falls two minutes behind her 
 mean place near the first quarter, and is two minutes ahead 
 near her last quarter. In determining this inequality, we have 
 to measure an angle about six times as great as the average 
 of the planetary parallaxes on which the sun’s distance de- 
 pends; so that, if we could measure both angles with the same 
 precision, the error, by using the moon, would be only one- 
 sixth as great as in direct measures of parallax. But it seems 
 as if nature had determined to allow mankind no royal road 
 to a knowledge of the sun’s distance. It is the position of 
 the moon’s centre which we require for the purpose in ques- 
 tion, and this can never be directly fixed. We have to make 
 our observations on the limb or edge of the moon, as illu- 
 minated by the sun, and must reduce our observations to the 
 moon’s centre, before we can use them. The worst of the 
 matter is, that one limb is observed at the first quarter, and 
 another at the third quarter, so that we cannot tell with abso- 
 lute certainty how much of the observed inequality is real, 
 and how much is due to the change from one limb to the other. 
 So great is the uncertainty here that, previous to 1854, it was 
 supposed that the inequality in question was about 122”, 
 agreeing with the theoretical inequality from Encke’s errone- 
 ous value of the solar parallax. Hansen then found that it 
 was really about 4” greater, and thus was led to the conclusion 
 that the parallax of the sun must be increased, and his distance 
 diminished, by one-thirtieth of the whole amount. 
 
 It is quite likely that by adopting improved modes of ob- 
 servation, it will be found that tHe sun’s distance can be more 
 accurately measured in this way than through the parallaxes 
 of the planets. Some pains have already been taken to deter- 
 mine the exact amount of the inequality from observations, 
 the result being 125’.5. The entire seconds may here be re- 
 lied on, but the decimal is quite uncertain. We can only say 
 
 K 
 
200 PRACTICAL ASTRONOMY. 
 
 that we are pretty surely within three or four tenths of a sec- 
 ond of the truth. Irom this value the parallax of the sun is 
 found to be 8.83, with an uncertainty of two or three hun- 
 dredths of a second. 
 
 Sun's Distance from the Velocity of Inght.— There is an ex- 
 traordinary beauty in this method of measuring the sun’s dis- 
 tance, arising from the contrast between the simplicity of the 
 principle and the profoundness of the methods by which alone 
 the principle can be applied. Suppose we had a messenger 
 whom we could send to and fro between the sun and the 
 earth, and who could tell, on his return, exactly how long it 
 took him to perform his journey; suppose, also, we knew the 
 exact rate of speed at which he travelled. Then, if we mul- 
 tiply his speed by the time it took him to go to the sun, we 
 shall at once have the sun’s distance, just as we could deter- 
 mine the distance of two cities when we knew that a train 
 running thirty miles an hour required seven hours to pass be- 
 tween them. Such a messenger is light. It has been found 
 practicable to determine, experimentally, about how fast light 
 travels, and to find from astronomical phenomena how long 
 it takes to come from the sun to the earth. How these de- 
 terminations are made will be shown in the next chapter; 
 here we shall stop only to give results. 
 
 In 1862 Foucault found by experiment that light travelled 
 about 298,000 kilometres, or 185,200 miles per second. 
 
 In 1874 Cornu found by a different series of experiments 
 a velocity of 300,400 kilometres per second. 
 
 In 1879 Ensign A. A. Michelson, U. 8. Navy, found the ve- 
 locity to be 299,940 kilometres per second. 
 
 This result of Michelson’s is far more reliable than either 
 of the preceding ones. Combining them all, Professor D. P. 
 Todd, in 1880, concluded the most probable value of the ve- 
 locity to be 299,920 kilometres, or 186,360 miles per second. 
 Now, we know from the phenomena of aberration, hereafter 
 to be described, that light passes from the sun to the earth in 
 about 498 seconds. The product of these two numbers gives 
 the distance of the sun in miles. Making all necessary cor- 
 
 . 
 
METHODS OF. DETERMINING THE SUN’S DISTANCE. 201 
 
 rections, and using Struve’s constant of aberration, the sun’s 
 parallax was found by Mr. Todd to be 8’.811. 
 
 These two methods of determining the distance of the sun 
 may fairly be regarded as equal in accuracy to that by tran- 
 sits of Venus when they are employed in the best manner. 
 There are also two or three minor methods which, though 
 less accurate, are worthy of mention. One of the most in- 
 genious of these was first applied by Leverrier. It is known 
 from the theory of gravitation that the earth, in consequence 
 of the attraction of the moon, describes a small monthly orbit 
 around the common centre of gravity of these two bodies, cor- 
 responding to the monthly revolution of the moon around the 
 earth, or, to speak with more precision, around the same com-— 
 mon centre of gravity. If we know the mass (or weight) of 
 the moon relatively to that of the earth, and her distance, we 
 can thus calculate the radius of the little orbit referred to. 
 In round numbers, it is 8000 miles. This monthly oscillation 
 of the earth will cause a corresponding oscillation in the lon- 
 gitude of the sun, and by measuring its apparent amount we 
 ean tell how far the sun must be placed to make this amount 
 correspond to, say 5000 miles. Leverrier found the oscilla- 
 tions in are to be 6.50. From this he concluded the solar 
 parallax to be 8.95. But Mr. Stone,* of Greenwich, found 
 two errors in Leverrier’s computation,t and, when these are 
 corrected, the result is reduced to 8.85. 
 
 Another recondite method has been employed by Leverrier. 
 It is founded on the principle that when the relative masses 
 of the sun and earth are known, their distance can be found 
 by comparing the distance which a heavy body will fall in 
 one second at the surface of the earth with the fall of the lat- 
 _ ter towards the sun in the same time. The mass of the earth 
 was found by its disturbing action on the planets Venus and 
 Mars, as explained in the chapter on Gravitation. Leverrier 
 
 * Mr. E. J. Stone was then first assistant at the Royal Observatory, Green- 
 wich, but has been Astronomer Royal at the Cape of Good Hope since 1870. 
 
 + ** Monthly Notices of the Royal Astronomical Society,” vol. xxvii., p. 241, 
 and vol. xxviil., pp. 22, 23. 
 
202 PRACTICAL -ASTRONOMY. 
 
 concluded that this method gave the value of the solar paral- 
 lax as 8.86. But one of his numbers requires a small correc- 
 tion, which reduces it to 8.83. Another determination of the 
 mass of the earth relative to that of the sun has recently been 
 made by Von Asten, of Pulkowa, from the action of the earth 
 upon Encke’s comet. The solar parallax thence resulting is 
 9°”.009, the largest recent value; but the anomalies in the ap- 
 parent motions of this comet are such that very little reliance 
 can be placed upon this result. 
 
 Yet another method of determining the solar parallax has 
 been proposed and partially carried out by Dr. Galle.* It 
 _ consists in measuring the parallax of some of the small plan- 
 ets between Mars and Jupiter at the times of their nearest 
 approach to the earth, by observations in the northern and 
 southern hemispheres. The least distance of the nearest of 
 these bodies from us is little less than that of the sun, so that 
 in this respect they are far less favorable than Venus and 
 Mars. But they have the great advantage of being seen in 
 the telescope only as points of light, like stars, and, in conse- 
 quence, of having their position relative to the surrounding 
 stars determined with greater precision than can be obtained 
 in the case of disks ike those of Venus and Mars. Observa- 
 tions of Flora were made in this way at a number of observa- 
 tories in both hemispheres during the opposition of 1874, from 
 which Dr. Galle has deduced 8.875 as the value of the solar 
 parallax. 
 
 Most Probable Value of the Sun’s Paraliaz.—lt will be 
 seen that, although many of the preceding results are dis- 
 cordant, those which are most reliable generally fall between 
 the limits 8.76 and 8’.85. Taking them all into considera- 
 tion, there can be no reasonable doubt that the parallax lies 
 between the limits 8.79 and 8’.88. We may therefore say 
 that the most probable value of the sun’s parallax is 8’.81, 
 but this result is still subject to an uncertainty of two-hun- 
 
 * Dr. J. G. Galle, now director of the observatory at Breslau, Eastern Prussia. 
 He was formerly assistant at the Observatory of Berlin, where he became cele- 
 brated as the optical discoverer of the planet Neptune. 
 
STELLAR PARALLAX. 203 
 
 dredths of a second, or we might say an uncertainty of 345 
 of its whole amount. ‘Translated into distance, we may place 
 the distance of the sun between the limits 92,500,000 and 
 93,000,000 of miles. We may, therefore, call the distance of 
 the sun 92? millions of miles, with the uncertainty, perhaps, 
 of nearly one quarter of a million. Within the next ten years 
 we may hope to see the result fixed with greater certainty, but 
 this is as near as we can approach it in the present state of 
 astronomy. 
 
 In many recent works the distance in question will be found 
 stated at 91,000,000 and some fraction. This arises from the 
 circumstance that into several of the first determinations by 
 the new methods small errors and imperfections crept, which, 
 by a singular coincidence, all tended to make the parallax too 
 great, and therefore the distance too small. For instance, 
 Hansen’s original computions from the motion of the moon, 
 led him to a parallax of 8.96. This result has been proved 
 to be too large from various causes. 
 
 The observations of Mars, in 1862, as reduced by Winnecke 
 and Stone, first led to a parallax of 8.92 to 8.94. But in 
 these investigations only a small portion of the observations 
 was used. When the great mass remaining was joined with 
 them, the result was 8’’.85. 
 
 The early determinations of the time required for light to 
 come from the sun were founded on the extremely uncertain 
 observations of eclipses of Jupiter’s satellites, and were five to 
 six seconds too small. The time, 493 seconds, being used in 
 some computations instead of 498 seconds, the distance of the 
 sun from the velocity of light was made too small. 
 
 In both of Leverrier’s methods some small errors of computa- 
 tion have been found, the effect of all of which is to make his 
 parallax too great. Correcting these, and making no change in 
 any of his data, the results are respectively 8.85 and 8.83. 
 
 § 5. Stellar Parallax. 
 
 It is probable that no one thing tended more strongly to 
 impress the minds of thoughtful men in former times with 
 
204 PRACTICAL ASTRONOMY. 
 
 the belief that the earth was immovable than did the absence 
 of stellar parallax. We may call to mind that the annual par- 
 allax of the fixed stars arises from the change in their direc- 
 tion produced by the motion of the earth from one side of 
 its orbit to the other. One of the earliest forms in which we 
 may suppose this parallax to have been looked for is shown 
 in Fig.58. Suppose AB to be the earth’s orbit with the sun, 
 
 R ee L 
 
 ~ 
 Pees 
 <a 
 ae 
 ~~ 
 een, 
 ~ 
 ~ 
 ee 
 a ace 
 
 Fig. 58.—Effect of stellar parallax. 
 
 S, near its centre, and FT’ two stars so situated as to be direct- 
 ly opposite each other when the earth is at A; that is, when 
 the direction of each star is 90° distant from that of the sun. 
 Then it is clear that, after six months, when the earth is at B, 
 the stars will no longer be opposite each other, the point U, 
 which is opposite A, making the angle 7’BU, with the direc- 
 tion of 7. The stars will all be displaced in the same direc- 
 tion that the sun is in from the earth. When it was found 
 that the most careful observations showed no such displace- 
 ment, the conclusion that the earth did not move seemed in- 
 evitable. We have seen how Tycho was led in this way to 
 reject the doctrine of the earth’s motion, and favor a system 
 in which the sun moved around it. In this Tycho was fol- 
 lowed by the ecclesiastical astronomers who lived during the 
 seventeenth century, and who, finding no parallax whatever to 
 any of the stars, were led to reject the Copernican system. 
 The telescope furnishing so powerful an auxiliary in meas- 
 uring small angles, it was natural that the defenders of the 
 Copernican system should be anxious to employ it in detect- 
 ing the annual parallax of the stars. But the earlier observ- 
 ers had very imperfect notions of the mechanical appliances 
 necessary to do‘this with success, and, in consequence, the in- 
 vention of the telescope did not result in any immediate im- 
 
STELLAR PARALLAX. 205 
 
 provement in the methods of celestial measurement. A step 
 was taken in 1669 by Hooke, of England, who was among the 
 first to see how the telescope was to be applied in the meas- 
 urement of the apparent distances of the stars from the ze- 
 nith. He fixed a telescope thirty-six feet long in his house, in 
 a vertical position, the object-glass being in 4n opening in the 
 roof, while the eye-piece was in one of the lower rooms. A 
 fine plumb-line hung down from the object-glass to a point 
 below, the eye-piece, which gave a truly vertical line from 
 which to measure. The star selected for observation was y 
 Draconis, because it was comparatively bright, and passed over 
 the zenith of London. His mode of observation was to meas- 
 ure the distance of the image of the star from, the plumb-line 
 from day to day at the moment of its passing the meridian. 
 He had made but four observations when his object-glass was 
 accidentally broken, and the attempt ended without leading 
 to any result whatever. 
 
 Between 1701 and 1704, Roemer, then of Copenhagen, at- 
 tempted to determine the sum of the double parallaxes of 
 Sirius and a Lyree by the principle shown in Fig.58. ‘These 
 stars lie somewhere near the opposite quarters of the celestial 
 sphere, and the angle between them will vary from spring to 
 autumn by nearly double the sum of their parallaxes. The 
 angle was measured by the transit instrument and the astro- 
 nomical clock, by noting the time which elapsed between the 
 transit of Sirius over the meridian, and that of a Lyre. This 
 time was found to be, on the average, 
 
 In drebruary) March; and A priliscisscce.s esse eee A 54th Or7 
 i mepiember and, OctOper......e:.0sse ene user esas 11 54 55.4 
 yi Trek ONG. verona cee net sce «os foewan crams cae 4.3 
 
 Here was a difference of four seconds of time, or a minute of 
 angle, which was then very naturally attributed to the motion 
 of the earth, and which was afterwards printed in a disserta- 
 tion entitled ‘Copernicus Triumphans.” It is now known that 
 there is no such parallax as this to either of these stars, and 
 
206 PRACTICAL ASTRONOMY. 
 
 Peters* has shown that the difference which was attributed 
 to parallax by the enthusiastic Danish astronomers really arose, 
 in great part, from the diurnal irregularity in the rate of their 
 clock, caused by the action of the diurnal change of tempera- 
 ture upon the uncompensated pendulums. In the spring the 
 interval of time measured elapsed during the night, Sirius 
 passing the meridian in the evening, and a Lyre in the morn- 
 ing. The cold of night made the clocks go too fast, and so 
 the measured interval came out too great. In the autumn 
 Sirius passed in the morning, and a Lyre in the evening; the 
 clock was going too slow on account of the heat of the day, 
 and the interval came out too small. 
 
 Among the numerous other vain efforts made by the astron- 
 omers of the last century to detect the stellar parallax, that of 
 Bradley is worthy of note, owing to the remarkable discovery 
 of the aberration of light to which it led. The principle of 
 his instrument was the same as that of Hooke, the zenith dis- 
 tance of the star y Draconis at the moment of its passing the 
 meridian being determined by the inclination of a telescope to 
 a fine plumb-line. The instrument thus used, which has be- 
 come so celebrated in the history of astronomy, has since been 
 known as Bradley’s zenith sector. In accuracy it was a long 
 step in advance of any which preceded it, so that by its means 
 Bradley was able to announce with certainty that the star in 
 question had no parallax approaching a single second. But 
 he found another annual oscillation of a very remarkable 
 character, arising from the progressive motion of light, which 
 will be described in the next chapter. It has frequently hap- 
 pened in the history of science that an investigation of some 
 cause has led to discoveries in a different direction of an en- 
 tirely unexpected character. 
 
 It would be tedious to describe in detail all the efforts 
 made by astronomers, during the last century and the early 
 part of the present one, to detect the stellar parallax. It will 
 
 * C. A. F. Peters, then of the Pulkowa Observatory, and now editor of the As- 
 tronomische Nachrichten. 
 
STELLAR PARALLAX. 207 
 
 be sufficient to say, in a general way, that they depended on 
 absolute measures; that is, the astronomer endeavored, gen- 
 erally by a divided circle, to determine from day to day the 
 zenith distance at which the star passed the meridian. The 
 position of the zenith was determined in various ways—some- 
 times by a fine plumb-line, sometimes by the level of quick- 
 silver. What is required is the angle between the plumb-line 
 and the line of sight from the observer to the star. The same 
 result can be obtained by observing the angle between a ray 
 coming directly from a star and the ray which, coming from 
 the star, strikes the surface of a basin of quicksilver, and is re- 
 flected upwards. Whatever method is used, a large angle has 
 to be measured, an operation which is always, affected by un- 
 certainty, owing to the influences of varying temperatures and 
 many other causes upon the instrument. The general result 
 of all the efforts made in this way was that while several of 
 the brighter stars seemed to some astronomers to have paral- 
 laxes, sometimes amounting to two or three seconds, though 
 generally not much exceeding a second, yet there was no such 
 agreement between the various results as was necessary to in- 
 spire confidence. As a matter of fact, we now know that 
 these results were entirely illusory, being due, not to parallax, 
 but to the unavoidable errors of the instruments used. 
 
 Struve was the first one to prove conclusively that the par- 
 allaxes even of the brighter stars were so small as to abso- 
 Iutely elude every mode of measurement before adopted. In 
 principle his method was that employed by Roemer, the sum 
 of the parallaxes of stars twelve hours distant in right ascen- 
 sion being determined by the annual change in the intervals 
 between their times of transit over the meridian. But he 
 made the great improvement of selecting stars which could 
 be observed as they passed the meridian below the pole, as 
 well as above it, so that a short time before or after observing 
 the transit of a star he could turn his transit instrument. be- 
 low the pole, and observe the transit of the opposite star from 
 west to east. Thus he was not under the necessity of depend- 
 ing on the rate of his clock for more than an hour or two, 
 
 15 
 
208 PRACTICAL ASTRONOMY. 
 
 while. Roemer had to depend on it for twelve hours. The re- 
 sult of Struve was that the average parallax of the twenty- 
 five brightest stars within 45° of the pole could not much, if 
 at all, exceed a single tenth of a second. 
 
 Such was the general state of things up to the year 1835. 
 It was then decided by Struve and Bessel, in leu of attempt- 
 ing to determine zenith distances, to adopt the method of 
 relative parallaxes. The idea of this method really dates al- 
 most from the invention of the telescope. It was considered 
 by Galileo and Huyghens that where a bright and a faint 
 star were seen side by side in the field of view of a telescope, 
 the latter was probably vastly more distant than the former, 
 and that consequently they would change their relative po- 
 sition as the earth moved from one side of the sun to the oth- 
 er. If, for instance, one star was three times the distance of 
 the other, its apparent motion produced by parallax would be 
 only a third that of the other, and there would remain a rel- 
 ative parallax equal to two-thirds that of the brighter star, 
 which could be detected by measuring the angular distance 
 of the two stars as seen in the telescope from day to day 
 throughout the year. The drawback to which this method is 
 subject is the impossibility of determining how many times 
 farther the one star is than the other; in fact, it may be that 
 the smaller star is really no farther than the large one. No 
 doubt it was this consideration which deterred the astrono- 
 mers of the last century from trying this very simple method. 
 
 The astronomers of the last generation found cases in 
 which there could be little doubt that a star was much near- 
 er to us than the small stars which surrounded it in the field 
 of the telescope. For instance, the star 61 Cygni, or rather 
 the pair of stars thus designated, are found not to occupy a 
 fixed position in the celestial sphere, like the surrounding 
 small stars, but to be moving forward in a straight line at the 
 rate of six seconds per year. ‘This amount of proper motion 
 was so unusual as to make it probable that the star must be 
 one of the nearest to us, although it was only of the sixth mag- 
 nitude. It was therefore selected by Bessel for the investi- 
 
STELLAR PARALLAX. 209 
 
 gation of its parallax relative to two other stars in its neigh- 
 borhood. The instrument used was the heliometer, an in- 
 strument which, as now made, admits of great precision, but 
 which was then liable to small uncertainties from various 
 causes. His early attempts to detect a parallax failed as 
 completely as had those of former observers. He recom- 
 menced them in August, 1837, his first series of measures be- 
 ing continued until October, 1838. The result of this series 
 was the detection of a parallax of about three-tenths of a sec- 
 ond (0’.3136). He then took down his instrument, made some 
 improvements in it, and commenced a second series, which he 
 continued until July, 1839; and his assistant, Schliter, until 
 March, 1840. The final value of the parallax deduced by 
 Bessel from all these observations was 0’.35. The reality of 
 this parallax has been well established by subsequent investi- 
 gators, only it has been found to be a little larger. From a 
 combination of all the results, Auwers, of Berlin, finds the 
 most probable parallax to be 0’.51. 
 
 The star selected by Struve for the measure of relative par- 
 allax was the bright one a Lyre. This has not only a sensible 
 proper motion, but is of the first magnitude; so that there is 
 every reason to believe it to be among those which are nearest 
 to us. The comparison was made with a single very small 
 star in the neighborhood, the instrument used being the nine- 
 inch telescope of the Dorpat Observatory. The observations 
 extended from November, 1835, to August, 1838. The result 
 was a relative parallax of a quarter of a second. Subsequent 
 investigations have reduced this parallax to two-tenths of a 
 second, so that although a Lyre is nearly a hundred times as 
 bright as either of the pair of stars 61 Cygni, it is more than 
 twice as far from us. 
 
 The star a Centauri in the southern hemisphere was long 
 supposed to have a parallax of nearly one second, and there- 
 fore to be the nearest of all the fixed stars. Its parallax was 
 first discovered by Henderson, the English Astronomer Royal 
 at the Cape of Good Hope, about the same time that Struve 
 and Bessel were making their first measures of parallax. In 
 
210 PRACTICAL ASTRONOMY. 
 
 former editions of this work the mean of the measures of 
 parallax was stated at 0’.93, corresponding to the distance 
 of 221,000 astronomical units.* This long accepted result has 
 recently been brought into great doubt by the researches of 
 Dr. William L. Elkin. He finds that corresponding observations 
 on other stars, made by the instrument with which the paral- 
 lax of a Centauri was fonnd, gave parallaxes for those stars 
 which it is highly improbable that they are affected with. <A 
 periodic error in the results of the instrument is thus suspect- 
 ed. Allowing for this error, the parallax of a Centauri will be 
 about 0.50, and therefore about the same as that of 61 Cygni. 
 
 A third star, having about the same parallax as these two, 
 has been discovered in Ursa Major. Professor Winnecket has 
 found its parallax to be 0°.501. 
 
 The most elaborate measures of stellar parallax made in 
 recent times are those by Dr. Briinnow, formerly director of 
 the observatory at Ann Arbor, Michigan. On his appointment 
 to the post of Astronomer Royal for Ireland, Dr. Briinnow 
 employed the equatorial telescope of the Dunsink Observa- 
 tory in such determinations with great success. The results 
 of his measures, with those of other astronomers, are given in 
 the Appendix to the present work. 
 
 The recent researches of various observers have resulted in 
 showing that there are about a dozen stars visible in our lati- 
 tudes of which the parallax ranges from a tenth to half a sec- 
 ond. Part of these are small stars, supposed to be near us 
 from their large proper motion, while others are stars of the 
 far brighter classes. It is, however, remarkable that, among 
 the thirteen stars of the first magnitude visible in our latitudes, 
 less than half have been found to have any measurable paral- 
 lax, even when the greatest refinements have been applied in 
 the observations. For the most part, the stars with a decided 
 parallax are not of a conspicuous magnitude. The general re- 
 
 * The astronomical unit is the distance of the earth from the sun, about 924 
 millions of miles. 
 
 + Dr. A. Winnecke, formerly assistant at the Pulkowa Observatory, and now 
 director of the observatory at Strasburg. 
 
STELLAR PARALLAX. OT 
 
 sult of measures of stellar parallax is, therefore, about as fol- 
 lows: the three stars, a Centauri, 61 Cygni, and Winnecke’s 
 star in Ursa Major have each a parallax so near to one-half a 
 second that it is impossible to say which is the nearest to our 
 system. About ten other stars have parallaxes ranging from 
 one to three tenths of a second. But these nearer stars are 
 not by any means of the first magnitude. We can, therefore, 
 make little more than a guess at the average parallax of the 
 brighter stars, which is generally estimated at one-tenth of a 
 second. ‘This gives a distance of more than two million radii 
 of the earth’s orbit. 
 
 In these measurements of the annual parallax of the fixed 
 stars, it sometimes happens that the astronomer finds his ob- 
 servations to give a negative parallax. To understand what 
 this means, we remark that a determination of the distance of 
 a star is made by determining its directions, as seen from op- 
 posite points of the earth’s orbit. If we draw a line from 
 each of these points, in the observed direction of the star, the 
 point in which the lines meet marks the position of the star. 
 A negative parallax shows that the two lines, instead of con- 
 verging to a point, actually diverge, so that there is no possible 
 position of the star to correspond to the observations. Such a- 
 paradoxical result can arise only from errors of observations. 
 
912 PRACTICAL ASTRONOMY. 
 
 CHAPTER IV. 
 THE MOTION OF LIGHT. 
 
 INTIMATELY connected with celestial measurements are the 
 curious phenomena growing out of the progressive move- 
 ment of light. It is now known that when we look at a star 
 we do not: see the star that now is, but the star that was sev- 
 eral years ago. Though the star should suddenly be blotted 
 out of existence, we should still see it shining for a number 
 of years before it would vanish from our sight. We should 
 see an event that was long past, perhaps one that was past 
 before we were born. ‘This non-coincidence of the time of 
 perception with that of occurrence is owing to the fact that 
 light requires time to travel. We can see an object only by 
 light which emanates from it and reaches our eye, and thus 
 our sight is behind time by the interval required for the light 
 to travel over the space which separates us from the object. 
 
 It was by observations of the satellites of Jupiter that it 
 was first found that celestial phenomena were thus seen be- 
 hind time. These bodies revolve round Jupiter much more 
 rapidly than our moon does around the earth, the inner satel- 
 lite making a complete revolution in eighteen hours. Owing 
 to the great magnitude of Jupiter and his shadow, this satel- 
 lite, as also the two next outside of it, are eclipsed at every, rev- 
 olution. The accuracy with which the times of disappearance 
 in the shadow could be observed, and the consequent value of 
 such observations for the determination of longitudes, led the 
 astronomers of the seventeenth century to make tables of the 
 times of occurrence of these eclipses. In attempting to im- 
 prove the tables of his predecessors, it was found by Roemer 
 (then of Paris, though a Dane by birth) that the times of the 
 
THE MOTION OF LIGHT. 213 
 
 eclipses could not be represented by an equable motion of 
 the satellites. He could easily represent the times of the 
 eclipses when Jupiter was in opposition to the sun, and there- 
 fore the earth nearest to Jupiter. But then, as the earth re- 
 ceded from Jupiter in its annual course round the sun, the 
 eclipses were constantly seen later, until, when it was at its 
 greatest distance from Jupiter, the fies appeared to be 22 
 minutes late. Such an inequality, Roemer concluded, could 
 not be real; he therefore attributed it to the fact that it must 
 take time for light to come from Jupiter to the earth, and 
 that this time is greater the more distant the earth is from 
 the planet. He therefore concluded that it took light 22 
 minutes to cross the orbit of the earth, and, consequently, 11 
 minutes to come from the sun to the earth. 
 
 The next great step in the theory of the progressive motion 
 of light was made by the celebrated Bradley, afterwards As- 
 tronomer Royal of England, to whose observations at Kew on 
 the star y Draconis with his zenith sector, in order to deter- 
 mine the parallax of the star, allusion has already been made. 
 The effect of parallax would have been to make the declina- 
 tion greatest in June and least in December; while in March 
 and September the star would occupy an intermediate or 
 mean position. But the actual result of the measures was 
 entirely different, and exhibited phenomena which Bradley 
 could not at first account for. The declinations of June and 
 December were the same, showing no effect of parallax. But, 
 instead of remaining the same the rest of the year, the decli- 
 nation was some forty seconds greater in September than in 
 March, when the effect of parallax should be the same. Thus, 
 the star had a regular annual oscillation; but instead of its 
 apparent motion in this little orbit being opposite to that of 
 the earth in its annual orbit, as required by the laws of rela- 
 tive motion, it was constantly at right angles to it. 
 
 After long consideration, Bradley saw the cause of the 
 phenomenon in the progressive motion of light combined 
 with the motion of the earth in its orbit. In Fig. 59 let S 
 be a star, and O7' a telescope pointed at it. Then, if the 
 
214 PRACTICAL ASTRONOMY. 
 
 telescope is not in motion, the ray SO7 emanating from the 
 star, and entering the centre of the object - glass, 
 will pass down near the right-hand edge of the eye- 
 piece, and the star will appear in the right of the 
 field of view. But, instead of being at rest, all our 
 telescopes are carried along with the earth in its 
 orbit round the sun at the rate of nearly nineteen 
 miles a second. Suppose this motion to be in the 
 direction of the arrow; then, while the ray is pass- 
 ing down the telescope, the latter moves a short dis- 
 tance, so that the ray no longer strikes the right- 
 hand edge of the eye-piece, but some point farther 
 to the left, as if the star were in the direction S’, 
 and the ray followed the course of the dotted line. 
 In order to see the star centrally, the eye end of the 
 telescope must be dropped a little behind, so that, 
 Fre. 59. instead of pointing in the direction 3S, it will really © 
 aa be pointing in the direction S’, shown by the dotted 
 
 ~ ray. This will then represent the apparent direc- 
 tion of the star, which will seem displaced in the direction in 
 which the earth is moving. 
 
 The phenomenon is quite similar to that presented by the 
 apparent direction of the wind on board a steamship in mo- 
 tion. If the wind is really at right angles to the course of the 
 ship, it will appear more nearly: ahead to those on board; and 
 if two ships are passing each other, they will appear to have 
 the wind in different directions. Indeed, it is said to have 
 been through noticing this very result of motion on board a 
 boat on the Thames, that the cause of the phenomenon he 
 had observed was suggested to Bradley. 
 
 The displacement of the stars which we have explained is 
 called the Aberration of Inight. Its amount depends on the ra- 
 tio of the velocity of the earth in its orbit to the velocity of 
 light. It can be determined by observing the declination of 
 a star at the proper seasons during a number of years, by 
 which the annual displacement will be shown. The value 
 now most generally received is that determined by Struve at 
 
 S 
 
 vi 
 i 
 | 
 | 
 | 
 | 
 ) 
 | 
 | 
 ! 
 | 
 | 
 | 
 ! 
 ! 
 | 
 I 
 | 
 I 
 I 
 | 
 | 
 | 
 | 
 ! 
 
 1 
 
 ap 
 
THE MOTION OF LIGHT. 215 
 
 the Pulkowa Observatory, and is 20.445. Though this is the 
 most reliable value yet found, the two last figures are both 
 uncertain. We can say little more than that the constant 
 probably hes between 20.43 and 20.48, and that, if outside 
 these limits at all, it is certainly very little ontside. 
 
 This amount of aberration of each star shows that light 
 travels 10,089 times as fast as the earth in its orbit. From _ 
 this we can determine the time light takes to travel from the 
 sun to the earth entirely independent of the satellites of Ju- 
 piter. The earth makes the circuit of its orbit in 8654 days. 
 Then light would make this same circuit in $$¢33 of a day, 
 which we find to be 52 minutes 84 seconds. ‘The diameter 
 of the earth’s orbit is found by dividing its circumference by 
 3.1416, and the mean distance of the sun is half this diameter. 
 We thus find from the above amount of aberration that light 
 passes from the sun to the earth in 8 minutes 18 seconds. 
 
 The question now arises, Does the same result follow from 
 the observations of the satellites of Jupiter? If it does, we 
 have a striking confirmation of the astronomical theory of the 
 propagation of light. If it does not, we have a discrepancy, 
 the cause of which must be investigated. We have said that 
 the first investigator of the subject found the time required 
 to be 11 minutes. This determination was, however, uncertain 
 by several minutes, owing to the very imperfect character 
 of the early observations on which Roemer had to depend. 
 Early in the present century, Delambre made a complete in- 
 vestigation from all the eclipses of the satellites which had 
 been observed between 1662 and 1802, more than a thousand 
 in number. His result was 8 minutes 13.2 seconds. 
 
 There is a discrepancy of five seconds between this result 
 of Delambre, obtained some seventy years ago, and the mod- 
 ern determinations of the aberrations of the fixed stars made 
 by Struve and others. What is its cause? Probably only the 
 errors of the observations used by Delambre. In this case, 
 there would be no real difference. But some physicists and 
 astronomers have endeavored to show that there is a real 
 cause for such a difference, which they hold to indicate an er- 
 
216 PRACTICAL ASTRONOMY. 
 
 ror in the value of the aberration derived from observation 
 arising in this way. It is known from experiment that light 
 passes through glass or any other refracting medium more 
 slowly than through a void. In observations with a telescope 
 the light has to pass through the objective, and the time lost 
 in doing so will make the aberration appear larger than it 
 really is, and the velocity of light will appear too small. But 
 the commonly received theory (that of Fresnel) is that this 
 loss of time is compensated by the objective partially drawing 
 the ray with it. Desirous of setting the question at rest, Pro- 
 fessor Airy, a few years ago, constructed a telescope, which 
 he filled with water, with which he observed the constant of 
 aberration. The aberration was found to be the same as with 
 ordinary telescopes, thus proving the theory of Fresnel to be 
 correct, because on the other theory the aberration ought to 
 have been much increased by the water. 
 
 Hence this explanation of the difference of the two results 
 fails, and renders it more probable that there is some error in 
 Delambre’s result. A reinvestigation of all the observations 
 of Jupiter’s satellites is very desirable; but so vast is the labor 
 that no one since Delambre has undertaken it. Mr. Glasenapp, 
 a young Russian astronomer, has, however, recently investi- 
 gated all the observations of Jupiter’s first satellite made dur- 
 ing the years 1848-1873, and found from these that the time 
 required for light to pass from the sun to the earth is 8 min- 
 utes 20 seconds. Instead of being smaller than Struve’s re- 
 sult, this is two seconds larger, and seven seconds larger than 
 that of Delambre. It is therefore concluded that the differ- 
 ence between the results of the two methods arises entirely 
 from the errors of the observations used by Delambre, and 
 that Struve’s time (498 seconds) is not a second in error. 
 
 Each of the two methods we have described gives us the 
 time required for light to pass from the sun to the earth; but 
 neither of them gives us any direct information respecting the 
 velocity of light. Before we can determine the latter from 
 the former, we must know what the distance of the sun is. 
 Dividing this distance in miles by 498, we shall have the dis- 
 
 a _—— 
 
THE MOTION OF LIGHT. GIT 
 
 tance which light travels in a second. Conversely, if we can 
 find experimentally how far light travels in a second, then by 
 multiplying this distance by 498 we shall have the distance of 
 the sun. But we need only reflect that the velocity of light 
 is about 180,000 miles per second to see that the problons of 
 determining it experimentally is a most difficult one. It is 
 seldom that objects on the surface of the earth are distinctly 
 seen at a greater distance than forty or fifty miles, and over 
 such a distance light travels in the forty-thousandth part of a 
 second. As might be expected, the earlier attempts to fix the 
 time occupied by light in passing over distances so short as 
 those on the surface of the earth were entire failures. * The 
 first of these is due to Galileo; and his method is worth men- 
 tioning, to show the principle on which such a determination 
 can be made. He stationed two observers a mile or two apart 
 by mght, each having a lantern which he could cover in a 
 moment. The one observer, A, was to cover his lantern, and 
 the distant one, B, as soon as he saw the light disappear, cov- 
 ered his also. In order that A might see the disappearance 
 of Bb’s lantern, it was necessary that the light should travel 
 from A to B, and back again. Jor instance, if it took one 
 second to travel between the two stations, B would continue 
 to see A’s light an entire second after it was really extinguish- 
 ed; and if he then covered his lantern instantly, A: would 
 still see it during another second, making two seconds in all 
 after he had extinguished his own, besides the time B might 
 have required to completely perform the movement of cover- 
 ing his. 
 
 Of course, by this rongh method Galileo found no inter- 
 val whatever. An occurrence which only required the hun- 
 dredth part of the thousandth of a second was necessarily in- 
 stantaneous. But we can readily elaborate his idea into the 
 more refined methods used in recent times. Its essential feat- 
 ure is that which must always be employed in making the de- 
 termination ; that is, it is necessary that the light shall be sent 
 from one station to another, and then returned to the first 
 one, where the double interval is timed. There is no possi- 
 
218 PRACTICAL ASTRONOMY. 
 
 bility of comparing the times at two distant stations with the 
 necessary precision. The first improvement we should make 
 on Galileo’s method would be to set up a mirror at the dis- 
 tant station, and dispense with the second lantern, the ob- 
 server A seeing his own lantern by reflection in the mirror. 
 Then, if he screened his lantern, he would continue to see it 
 by reflection in the mirror during the time the light required 
 to go and come. But this also would be a total failure, be- 
 cause the reflection would seem to vanish instantly. Our next 
 effort would be to try if we could not send ont a flash of 
 light from our lantern, and screen it off before it got back 
 agai. An attempt to screen off a single flash would also be 
 a failure. We should then try sending a rapid succession of 
 flashes through openings in a moving screen, and see wheth- 
 er they could be cut off by the sides of the openings before 
 their return. This would be 
 effected by the contrivance 
 shown in Fig. 60. We have 
 here a wheel with spokes ex- 
 tending from its circumfer- 
 ence, the distance between 
 them being equal to their 
 breadth. This wheel is placed 
 in front of the lantern, Z, so 
 that the light from the latter 
 Fra. 60.—Revolving wheel, for measuring the has to pass between the spokes 
 
 cat ene of the wheel in order to reach 
 the distant mirror. In the figure the reader is supposed to be 
 between the wheel and the reflecting mirror, facing the for- 
 mer, so that he sees the light of the lantern, and also the eye 
 of the observer, between the spokes. The latter, looking be- 
 tween the spokes, will see the light of the lantern reflected 
 from the mirror. Now, suppose he turns the wheel, still keep- 
 ing his eye at the same point. Then, each spoke cutting off the 
 light of the lantern as it passes, there will be a succession of 
 flashes of light which will pass through between the spokes, 
 travel to the mirror, and thence be reflected back again to the 
 
 a 
 
THE MOTION OF LIGHT. 219 
 
 wheel. Will they reach the eye of the observer behind the 
 wheel? Evidently they will, if they return so quickly that a 
 tooth has not had time to intervene. But suppose the wheel to 
 turn so rapidly that a tooth just intervenes as the flash gets 
 back to it. Then the observer will see no light in the mirror, 
 because each successive flash is caught by the following tooth 
 just before it reaches the observer’s eye. Suppose, next, that 
 he doubles the speed of his wheel. Then, while the flash is 
 travelling to the mirror and back, the tooth will have passed 
 clear across and out of the way of the flash, so that the latter 
 will now reach the observer’s eye through the opening next 
 following that which it passed through to leave the lantern. 
 Thus, the observer will see a succession of,flashes so rapid 
 that they will seem entirely continuous to the eye. If the 
 speed of the wheel be again increased, the return flash will be 
 caught on the second tooth, and the observer will see no light, 
 while a still further increase of velocity will enable him to 
 see the flashes as they return throngh the second interval be- 
 tween the spokes, and so on. 
 
 In principle, this is Fizeau’s method of measuring the ve- 
 locity of light. In place of spokes, he has exceedingly fine 
 teeth in a large wheel. He does not look between the teeth 
 with the naked eye, but employs a telescope so arranged that 
 the teeth pass exactly through its focus. An arrangement, is 
 made by which the light passes through the same focus with- 
 out reaching the observer’s eye except by reflection from the 
 distant mirror. ‘The latter is placed in the focus of a second 
 telescope, so that it can be easily adjusted to send the rays 
 back in the exact direction from which they come. To find 
 the time it takes the light to travel, it is necessary to know the 
 exact velocity of the wheel which will ent off the return light 
 entirely, and thence the number of teeth which pass in a sec- 
 ond. Suppose, for instance, that the wheel had a thousand 
 teeth, and the reflector was nine miles away, so that the light 
 had to travel eighteen miles to get back to the focus of the 
 telescope. Then it would be found that with a velocity of 
 about five turns of the wheel per second, the light would be 
 
220 PRACTICAL ASTRONOMY. 
 
 first cut off. Increasing the velocity, it would reappear, and 
 would grow brighter until the velocity reached ten turns per 
 second. It would then begin to fade away, and at fifteen 
 turns per second would be again occulted, and so on. With 
 the latter velocity, fifteen thousand teeth and fifteen thousand 
 intervals would pass in a second, while two teeth and one in- 
 terval passed during the time the light was performing its 
 journey. The latter would, therefore, be performed in the 
 ten-thousandth part of a second, showing the actual velocity 
 to be 180,000 miles per second. The most recent determina- 
 tion made in this way is by M. Cornu, of Paris, who has made 
 some improvements in the mode of applying it. His results 
 will be described presently. 
 
 Ingenious and beautiful as this method is; I do not think it 
 can be so accurate as another employed by Foucault, in which 
 it is not a toothed wheel which revolves, but a Wheatstone 
 mirror. To explain the details of the apparatus actually used 
 | would be tedious, 
 but the principle on 
 which the method 
 rests can be seen 
 quite readily. Sup- 
 pose AB, Fig. 61, to 
 represent a flat mir- 
 ror, seen edgewise, 
 revolving round an 
 ye axis at X,and Ca 
 Fic. 61.—Ilustrating Foucault’s method of measuring the fixed concave mir- 
 
 peice ty eas ror, so placed that 
 the centre of its concavity shall fall on X. Let O be a lumi- 
 nous point, from which emanates a single ray of light, OX. 
 This ray, meeting the mirror at X, is reflected to the concave 
 mirror, C, which it meets at a right angle, and is therefore re- 
 flected directly back on the line from which’ it came, first to 
 “X, and then through the point O, from which it emanated, so 
 that an eye stationed at / will see it returning exactly through 
 the point O. No matter how the observer may turn the mir- 
 
THE MOTION OF LIGHT. O07 
 
 ror AB, he cannot make the reflected ray deviate from this 
 line: he can only make it strike a different point of the mir- 
 ror@. If he turns AB so that after the ray is reflected from 
 it, it does not strike C at all, then he will see no return ray. 
 If the ray is reflected back at all, it will pass through O. This 
 result is founded on the supposition that the mirror AB re- 
 mains in the same position during the time the ray occupies 
 in passing from X to C and back. But suppose the mirror 
 AB to be revolving so rapidly that when the ray gets back 
 to X, the mirror has moved to the position of the dotted line 
 A’'B’. Then it will no longer be reflected back through O, 
 but will be sent in the direction 4’, the angle XH’ being 
 double that through which the mirror has moved during the 
 time the ray was on its passage. Knowing the velocity of 
 the mirror, and the angle HX LH’, this time is easily found. 
 Evidently the observer cannot see a continuous light at L’, 
 because a reflection can be sent back only when the revolving 
 mirror is in such a position as to send the ray to some point 
 of the concave mirror,C. What will really be seen, therefore, 
 is a succession of flashes, each flash appearing as the revolving 
 mirror is passing through the position AL. But when the 
 mirror revolves rapidly, these flashes will seem to the eye to 
 form a continuous light, which, however, will be fainter than 
 if the mirror were at rest,in the proportion which the arc of 
 the concave mirror, C, bears to an entire circle. Beyond the 
 enfeeblement of the light, this want of continuity is not pro- 
 ductive of any inconvenience. It was thus found by Fou- 
 cault that the velocity of light was 185,000 miles per second, a 
 result which is probably within a thousand miles of the truth. 
 The preceding explanation shows the principle of the meth- 
 od, but not the details necessary in applying it. It is not 
 practicable to isolate a single ray of light in the manner sup- 
 posed in the figure, and therefore, without other apparatus, 
 the light from O would be spread all over the space around # 
 . and #’. The desired result is obtained by placing a lens be- 
 tween the luminous point O and the revolving mirror in such 
 a position that all the light falling from O upon the lens shall, 
 
 * 
 
222 PRACTICAL ASTRONOMY. 
 
 after reflection, be brought to a focus upon the surface of the 
 concave mirror, C. Then when the mirror AB is made to re- 
 volve rapidly, the return rays passing back throngh the lens 
 on their return journey are brought to a focus at a point 
 along-side O, and distant from it by an amount which is pro- 
 portional to the time the light has required to pass from X to 
 Cand back again. 
 
 So delicate is this method, that the millionth of a second of 
 tine can be measured by it as accurately as a carpenter can 
 measure the breadth of a board with his rule. Its perfection 
 is the result of the combined genius of several men. The first 
 idea of employing a revolving mirror in the measurement of 
 a very minute interval of time is due to the late Sir Charles 
 Wheatstone, who thus measured the duration of the electric 
 spark. Then Arago showed that it conld be applied to de- 
 termine whether the velocity of light was greater in water 
 or in air. Fizeau and Foucault improved on Arago’s ideas 
 by the introduction of the concave mirror, having its centre 
 of curvature in the revolving mirror, and then this wonderful 
 piece of apparatus was substantially complete. The last de- 
 termination of the velocity of light with it was made by Fou- 
 cault, and communicated to the French Academy of Sciences 
 in 1862, with the statement that the velocity resulting from 
 all his experiments was 298,000 kilometres (185,200 miles) 
 per second. 
 
 The problem in question was next taken up by Cornu, of 
 Paris, whose result has already been alluded to. Notwith- 
 standing the supposed advantages of the Foucault-Wheat- 
 stone method, M. Cornu preferred that of Fizeau. His first 
 results, reached in 1872, accorded quite well with those of 
 Foucault just cited, indicating a small but somewhat uncer- 
 tain increase. His experiments were repeated in 1874, and 
 their results were communicated to the French Academy of 
 Sciences in December of that year. In this last series of 
 
 measurements his station was the observatory, and the distant . 
 
 mirror was placed on the tower of Montlhéry, at a distance of 
 
 about fourteen English miles. The telescope through which 
 ? 
 
 i a 
 
THE MOTION OF LIGHT. 223 
 
 the flashes of light were sent and received was twenty-nine 
 feet long and of fourteen inches aperture. The velocity of 
 the toothed wheel could be made to exceed 1600 turns a sec- 
 ond, and by the electro-chronograph, on which the revolutions 
 were recorded, the time could be determined within the thou- 
 sandth of a second. At Montlhéry, the telescope, in the focus 
 of which the reflecting mirror was placed, was six inches in 
 aperture, and was held by a large cast-iron tube set in the 
 masonry of the tower. At this distance M. Cornu was able, 
 with the highest velocity of his revolving wheel, to make 
 twenty of its teeth pass before the flashes of light got back, 
 and to catch them, on their return, on the twenty-first tooth. 
 
 All the determinations, however, were not made with the 
 wheel going at this rate, but with such different velocities that 
 the rays were caught sometimes on one tooth and sometimes 
 on another, from the fourth to the twenty-first. The follow- 
 ing table shows the velocity of light in kilometres per second 
 when the ray was caught on the fourth tooth, on the fifth, and 
 so on to the twenty-first : 
 
 PROG A aian csvacyotespcatcgvanernges s BOURT OUTMLOOtINE Ler arrtesseasuediycsca teasers 300,340 
 | ET SSAA AS Ate bE SOO, DSO Aa OO ONT Aap: 300,350 
 Soa lee tty ial, Oecd dee VAD BOOT AO Paves Varuna. eavibeie \sdalads.oxaays 300,290 
 vi. Tog Ore eee SOULS Tie mee WN LG te eee ek eck 300,620 
 A hated Ne re Ae a By PTE hs eS yc Rapala i EM eres tala a 300,000 
 9 (CO ll lipemia sci BOOT SU ROU Steet ee meee 300,150 
 SARL OM SHALL Ae SOOGLO PEM AIIOL “7.8, fe 299,550 
 Sell TV Jt, atin ed tic wtcuwaravd SOE H Os malta EOLA bea lrasee ghee Oth ass 
 2 OE a a SO ai pir nee SU: BO. |e Oe OL wale eter aa eee 300,060 
 
 M. Cornu hence concludes that the velocity of light in air 
 is 800,330, and in a vacuum 300,400 kilometres per second. 
 
 Quite recently Ensign A. Michelson, U.S.N., has made, at the 
 Naval Academy, Annapolis, a third determination, using the re- 
 volving mirror. His result, reduced to a vacuum, is 299,940 
 kilometres per second, and is for the present to be regarded as 
 the standard, the probable error being not more than 50 kilo- 
 metres, though an error as great as 200 kilometres may be re- 
 
 garded as possible. 
 16 
 
224. PRACTICAL ASTRONOMY. 
 
 CHAPTER V. 
 
 THE SPECTROSCOPE. 
 
 In one of Dr. Lardner’s popular lectures on astronomy, de- 
 livered some thirty years ago, he introduced the subject of 
 weighing the planets as one in which he could with difficulty 
 expect his statements to be received with credulity. That 
 men should measure the distances of the planets was a state- 
 ment he expected his hearers to receive with surprise; but the 
 step from measuring to weighing was so long a one, that it 
 seemed to the ordinary mind to extend beyond all the bounds 
 of possibility. 3 
 
 Had a hearer told the lecturer that men would also be able 
 to determine the chemical constituents of the sun and stars, 
 and to tell whether any of them did or did not contain iron, 
 hydrogen, and other chemical elements, the lecturer would 
 probably have replied that that statement quite exceeded the 
 limits of his own credulity; that, while he himself saw clearly 
 how the planets were measured and weighed, he looked upon 
 the idea of determining their chemical constitution as a mere 
 piece of pleasantry, or the play of an exuberant fancy. And 
 yet, this very thing has, to a certain extent, been done by the 
 aid of the spectroscope. The chemical constitution of matter 
 in the state of gas or vapor can be detected almost as readily 
 at the distance of the stars as if we had it in our laboratories. 
 The difficulties which stand in the way do not arise from the 
 distance, but from the fact that matter in the heavenly bodies 
 seems to exist in some state which we have not succeeded in 
 exactly reproducing in our laboratories. Like many other 
 wonders, spectrum analysis, as it is called, is not at all extraor- 
 dinary after we see how it is done. Indeed, the only wonder 
 
THE SPECTROSCOPE. 225 
 
 now is how the first half of this century could have passed 
 without physicists discovering it. The essential features of 
 the method are so simple that only a knowledge of the ele- 
 ments of natural philosophy is necessary to enable them to be 
 understood. We shall, therefore, briefly explain them. 
 
 It is familiarly known that if we pass the rays of the sun 
 which enter a room by a small opening through a prism, the 
 light is separated into a number of bright colors, which are 
 spread out on a certain scale, the one end being red and the 
 other violet, while a long range of intermediate colors is found 
 between them. This shows that common white light is really 
 a compound of every color of the spectrum. This compound 
 is not like chemical compounds, made up of two or three or 
 some limited number of simples, but is composed of an infini- 
 ty of different kinds of light, all running into each other by 
 insensible degrees ; the difference, however, being only in col- 
 or, or in the capacity of being refracted by the prism through 
 which it passes. This arrangement of colors, spread out to our 
 sight according to the refrangibility of the light which forms 
 them, is called the spectrum. By the spectrum of any object 
 is meant the combination of colors found in the hight which 
 emanates from that object. For instance, if we pass the light 
 from a candle through a prism, so as to separate it into its 
 component colors, and make the light thus separated fall on 
 a screen, the arrangement of colors on the screen would be 
 called the spectrum of the candle. If we look at a bright 
 star through a prism, the combination of colors which we see 
 is called the spectrum of the star, and so with any other object 
 we may choose to examine. 
 
 As the experiment of forming a spectrum is commonly 
 made, there is a slight mixing-up of light of the different col- 
 ors, because light of the same degree of refrangibility will 
 fall on different parts of the screen according to the part of 
 the prism it passes through. When the separation of the light 
 is thus incomplete, the spectrum is said to be impure. In or- 
 der to make any successful examination of the light which 
 emanates from an object, our spectrum must be pure; that is, 
 
226 PRACTICAL ASTRONOMY. 
 
 each point of the spectrum must be formed by light of one 
 degree of refrangibility. To effect this in the most perfect 
 way, the spectrum is not formed on a screen, but on the retina 
 of the observer’s eye. An instrument by which this is done 
 is called a spectroscope. 
 
 The most essential parts of a spectroscope consist of a small 
 telescope with a prism in front of the object-glass. The ob- 
 server must adjust his telescope so that, removing the prism, 
 and looking directly at the object, he shall obtain distinct vis- 
 ion of it. Then, putting the prism in its place, and turning 
 the telescope to such an angle that the light which comes from 
 the object shall, after being refracted by the prism, pass direct- 
 ly into the telescope, he looks into the latter. When the prop- 
 er adjustments are made, he will see a pure spectrum of the 
 object. In order that this experiment may succeed, it is es- 
 sential that the object, when viewed directly, shall present the 
 appearance of a point, like a star or planet. If it is an object 
 which has a measurable surface, like the sun or moon, he will 
 see either no spectrum at all or only a very impure one. 
 
 For this reason, a spectroscope which consists of nothing but 
 a telescope and prism is not fitted for any purpose but that of 
 trial and illustration. To fit it for general use, another ob- 
 ject-glass, with a slit in its focus, is added. Fig. 62 shows the 
 
 Fig. 62.—Course of rays through a spectroscope. 
 
 essential parts of a modern spectroscope. At the farther end 
 of the second telescope, where the light enters, is a narrow 
 slit, which can be opened or closed by means of a screw, and 
 
THE SPECTROSCOPE. 227 
 
 through which the light from the object is admitted. The 
 rays of light following the dotted lines are made parallel by 
 passing through the lens, Z. They then fall on the prism, P, 
 by which they are refracted, and from which they emerge par- 
 allel, except that the direction of the rays of different colors 
 is different, owing to the greater or less degree of refraction 
 produced by the prism. They then pass through the object- 
 glass of the telescope, 7, by which the rays of each color are 
 brought to a focus at a particular point in the field of view, 
 the red rays all coming together at the lower point, the violet 
 ones at the upper point, and those of each intermediate color 
 at their proper place along the line. ‘The observer, looking 
 into the telescope, sees the spectrum of whatever object is 
 throwing its light through the slit. 
 
 If the object of which the observer wishes to see the spec- 
 trum is a flame, he places it immediately in front of the slit ; 
 and if it is an object of sensible surface, like the sun or moon, 
 he points the collimator, C, directly at it, so that the light 
 which enters the slit shall fall on the lens, Z. But if it is a 
 star, he cannot get light enough in this way to see it, and he 
 must either remove his collimator entirely, or fasten his spec- 
 troscope to the end of a telescope, so that the slit shall be 
 exactly in the focus. The latter is the method universally 
 adopted in examining the spectrum of a star. 
 
 If, with this instrument, we examine the light which comes 
 from a candle, from the fire, or from a piece of white-hot 
 iron, we shall find it to be continuous; that is, there is no gap 
 in the series of colors from one end to the other. But if we 
 take the light from the sun, or from the moon, a planet, or 
 any object illuminated by the sun, we shall find the spectrum 
 to be crossed by a great number of fine dark lines, showing 
 that certain kinds of light are wanting. It is now known 
 that the particular kinds of light which originally belonged 
 in these dark lines have been culled out by the gases surround- 
 ing the sun through which the light has passed. This culling- 
 out is called Selective Absorption. It is found by experiment 
 that each kind of gas has its own liking for light of peculiar 
 
928 PRACTICAL ASTRONOMY. 
 
 degrees of refrangibility, and absorbs the light which belongs 
 in the corresponding parts of the spectrum, letting all the 
 other light pass. 
 
 Perhaps we may illustrate this process by a similar one 
 which we might imagine mankind to perform. Suppose Nat- 
 ure should loan us an immense collection of many millions 
 of gold pieces, out of which we were to select those which 
 would serve us for money, and return her the remainder. 
 The English rummage through the pile, and pick out all the 
 pieces which are of the proper weight for sovereigns and half- 
 sovereigns; the French pick out those which will make five, 
 ten, twenty, or fifty france pieces; the Americans the one, five, 
 ten, and twenty dollar pieces, and so on. After all the suit- 
 able pieces are thus selected, let the remaining mass be spread 
 out on the ground according to the respective weights of the 
 pieces, the smallest pieces being placed in a row, the next in 
 weight in an adjoining row, and so on. We shall then find a 
 number of rows missing: one which the French have taken 
 out for five-frane pieces; close to it another which the Amer- 
 icans have taken for dollars; afterwards a row which have 
 gone for half-sovereigns, and so on. By thus arranging the 
 pieces, one would be able to tell what nations had culled over 
 the pile, if he only knew of what weight each one made its 
 coins. The gaps in the places where the sovereigns and half- 
 sovereigns belonged would indicate the English, that in the 
 dollars and eagles the Americans, and so on. If, now, we re- 
 flect how utterly hopeless it would appear, from the mere ex- 
 amination of the miscellaneous pile of pieces which had been 
 left, to ascertain what people had been selecting coins from it, 
 and how easy the problem would appear when once some 
 genius should make the proposed arrangement of the pieces 
 in rows, we shall see in what the fundamental idea of spec- 
 trum analysis consists. The formation of the spectrum is the 
 separation and arrangement of the light which comes from an 
 object on the same system by which we have supposed the 
 gold pieces to be arranged. ‘The gaps we see in the spectrum 
 tell the tale of the atmosphere through which the light has 
 
THE SPECTROSCOPE. 929 
 
 passed, as in the case of the coins they would tell what nations 
 had sorted over the pile. 
 
 That the dark lines in the solar spectrum are picked out by 
 the gases of the sun’s atmosphere has long been surmised ; in- 
 deed, Sir John Herschel seems to have had a clear idea of 
 the possibility of spectrum analysis half a century ago. The 
 difficulty was to find what particular lines any particular sub- 
 stance selects; since, to exert any selective action, a vastly 
 greater thickness of gas is generally required than it is prac- 
 ticable to obtain experimentally. This difficulty was sur- 
 mounted by the capital discovery of Kirchhoff and Bunsen, 
 that a glowing gas gives out rays of the same degree of refrangibil- 
 uy which it absorbs when light passes through it... For example, 
 if we put some salt into the flame of a spirit-lamp, and ex- 
 amine the spectrum of the light, we shall find a pair of bright- 
 yellow lines, which correspond most accurately to a pair of 
 black lines in the solar spectrum. These lines are known to 
 be due to sodium, a component of common salt, and their ex- 
 istence in the solar spectrum shows that there is sodium 
 in the sun’s atmosphere. They are therefore called the sodi- 
 um lines. By vaporizing various substances in sufficiently hot 
 flames, the spectra of a great number of metals and gases 
 have been found. Sometimes there are only one or two bright 
 lines, while with iron the number is counted by hundreds. 
 The quantity of a substance necessary to form these bright 
 lines is so minute that the presence of some metals in a com- 
 pound have been detected with the spectroscope when it was 
 impossible to find a trace of them in any other way. Indeed, 
 two or three new metals, the existence of which was before en- 
 tirely unknown, first told their story through the spectroscope. 
 
 The general relations of the spectrum to the state of the 
 substance from which the light emanated may be condensed 
 into three rules, or laws, as follows: 
 
 1. The light from a glowing solid or liquid forms a contin- 
 uous spectrum, in which neither bright nor dark lines are 
 found. The spectrum is of the same nature, no matter how 
 finely the substance may be divided. 
 
230 PRACTICAL ASTRONOMY. 
 
 2. If the light from the glowing solid passes through a gas- 
 eous “atmosphere, the spectrum mil be crossed by dark 1 
 occupying those parts of the spectrum where the light culled 
 out by the atmosphere belongs. 
 
 3. A glowing gas sends out light of the same degrees of 
 refrangibility as belong to that which it absorbs, so that its 
 spectrum consists of a system of bright lines occupying the 
 same position as the dark lines it would produce by absorption. 
 
 If, then, on examining the spectrum of a star or other heav- 
 enly body, we find only bright lines with dark spaces between 
 them, we may conclude that the body consists of a glowing 
 gas, and we judge what the gas is by comparing the spectrum 
 with those of various substances on the earth. If, on the oth- 
 er hand, the spectrum is a continuous one, except where cross- 
 ed by fine dark lines, we conclude that it emanates from a 
 glowing body surrounded by an atmosphere which culls out 
 some of the rays of light. 
 
 It will be seen that the spectroscope gives us no definite in- . 
 formation respecting the nature or composition of bodies in 
 the solid state. If we heat any sort of metal white-hot, sup- 
 posing only that it will stand this heat without being vapor- 
 ized, we shall have a spectrum continuous from end to end, in 
 which there will be neither bright nor dark lines to give any 
 indications respecting the substance. In order, therefore, to 
 detect the presence of any chemical element with this instru- 
 ment, that element must be in the form of gas or vapor. Here 
 we have one limitation to the application of the spectroscope 
 to the celestial bodies. ‘The tendency of bodies in space is to’ 
 cool off, and when they have once become so cool._as to solidi- 
 fy, the instrument in question can give us no further definite 
 information respecting their constitution. 
 
 Even if the body be in the gaseous state, we cannot always 
 rely on the spectroscope informing us with certainty of the 
 nature of the gas. The light we analyze must either be emit- 
 ted by the gas, the latter being so hot as to shine by its own 
 light, or it must be transmitted through it. Thus, the appli- 
 cation of spectrum analysis is confined to glowing gases and 
 
THE SPECTROSCOPE. 2387 
 
 the atmospheres of the stars and planets, the application to the . 
 latter depending on the fact that the sunlight reflected from 
 the surface of the planet passes twice through its atmosphere. 
 Even in these cases the interpretation of its results is sometimes 
 rendered difficult in consequence of the varied spectrum of the 
 same gas at different temperatures and under different degrees 
 of pressure. Under some conditions so many new lines are 
 introduced into the spectrum of hydrogen that it can hardly 
 be recognized. As a general rule, the greater the pressure, the 
 greater the number of lines which appear; indeed, it has been 
 found by Lockyer and Frankland that as the pressure and den- 
 sity of a gas are increased, its spectrum tends to become con- 
 tinuous. We must therefore regard the third of the above 
 rules respecting spectrum analysis, or, rather, the general rule 
 that a glowing gas gives a spectrum of bright lines, as not uni- 
 versally true. If we could, by artificially varying the temper- 
 ature, pressure, and composition of gases, accurately reproduce 
 the spectrum of a celestial body, the changes of the spectrum 
 which we have mentioned would be a positive advantage; 
 since they would enable us to determine, not merely the com- 
 position of a gaseous body, but its temperature and pressure. 
 This is, however, a field in which success has not yet been 
 reached. 
 
 There is still another cireumstance which renders the spec- 
 tra of the heavenly bodies more complex than was at first sup- 
 posed, but which may, by this very complexity, enable us to 
 make great. advances in our knowledge of the physical consti- 
 tution of the sun and stars. It is that the two classes of spec- 
 tra just described—namely, (1) a continuous spectrum crossed 
 by dark lines, and (2) a spectrum composed wholly of bright 
 lines—are only two extreme cases, and that in many cases 
 they are combined in very different proportions. If a white- 
 hot body is composed of a glowing atmosphere, the hotter 
 substances of this atmosphere may show bright lines, while 
 the cooler substances may absorb dark lines from the light 
 emitted by the hot body below. Thus, we may have bright 
 lines, dark lines, and strips of continuous spectrum all mixed 
 
932 PRACTICAL ASTRONOMY. 
 
 up in such a way that it may be hard to interpret what is 
 seen. The difficulty is to know whether a narrow, dark space 
 is produced by the absorption of a gas, or whether it is simply 
 an interval between two bright gaseous lines; and whether a 
 narrow, bright space is produced by a glowing gas, or whether 
 it is a small strip of continnous spectrum from a glowing solid 
 between two absorption bands. We have a mixed-up spec- 
 trum of this kind in the Bessemer furnace. The difficulty is 
 increased by the fact that the dark portions culled out by the 
 absorption of the cooler gases are not always fine perfectly 
 dark lines, but in many eases are broad, grayish bands. It is, 
 indeed, possible that these bands may be made up of groups 
 of fine lines, too close to be separately seen; but so long as the 
 separate lines cannot be distinguished, this question must be 
 undecided. 
 
 Until very lately, it was always supposed that the spectrum 
 of the light of the sun, so far as it could be analyzed, was 
 continuous from end to end, except where dark absorption 
 lines crossed it. A remarkable addition to this theory has, 
 however, been made by Professor Henry Draper, of New 
 York, the main point of the addition being that the spectrum 
 is crossed by the bright lines and bands arising from glowing 
 gases, and that these lines admit of being recognized in cer- 
 tain parts of the spectrum if the proper steps are taken to 
 bring them out. That bright lines might well exist in the 
 spectrum no one would deny, because the gases of the chro- 
 mosphere must produce them. But it has always been sup- 
 posed that they must be so excessively faint as to be entirely 
 invisible when projected on the spectrum of the sun itself, and 
 so no one is known to have sought for them with especial 
 care. Dr. Draper’s course has been to photograph side by 
 side the solar spectrum between the lines G and H, and the 
 corresponding part of the spectrum of oxygen rendered lumi- 
 nous by the electric spark. The result is that out of thirteen 
 bright lines of oxygen, some of them double or treble, nearly 
 all have corresponding lines in the solar spectrum. The co- 
 incidence is so striking that it seems hardly possible to avoid 
 
THE SPECTROSCOPE. 233 
 
 the conclusion that a considerable part of the violet light of 
 the sun’s spectrum arises from glowing oxygen in the photo- 
 sphere. 
 
 What gives especial interest to this investigation by Dr. 
 Draper is that it affords the first evidence which science has 
 found of the existence of oxygen in the sun, the dark lines 
 which would be produced by that substance having been 
 looked for in vain. It would seem either that the capacity of 
 oxygen for absorbing light selectively is very small, or that it 
 exists in the sun only at a very high temperature. 
 
 The reason why these lines are brought out here when they 
 are not found in other parts of the spectrum is to be found 
 in the extreme faintness of the violet part of the continuous 
 spectrum, whereby the bright lines are not obscured by the 
 dazzling brilliancy of the background of continuous spectrum. 
 If it be asked why these bright lines have not been noticed 
 before, the answer is, that the dark lines are here so broad 
 and numerous as to cut up the continuous spectrum into very 
 narrow lines of very irregular brightness, besides which ab- 
 sorption bands or half shades are numerous. Again, the lines 
 of oxygen do not appear to be so narrow and sharply defined 
 as those of the metallic vapors, and this makes it more diffi- 
 cult to distinguish them from spaces between the dark bands. 
 
 The reader now understands that when the light from a ce- 
 lestial object is analyzed by the prism, and the component col- 
 ors are spread out singly as on a sheet, the dark and bright 
 lines which we see are the letters of the open book which we 
 are to interpret so as to learn what they tell us of the body 
 from which the light came, or the vapors through which it 
 passed. When we see a line or a set of lines which we rec- 
 ognize as produced by a known substance, we infer the pres- 
 ence of that substance. The question may now be asked, How 
 do we know but that the lines we observe may be produced 
 by other substances besides those which we find to produce 
 them in our laboratories? May not the same lines be pro- 
 duced by different substances? This question can be an- 
 swered only by an appeal to probabilities. The evidence in 
 
234 PRACTICAL ASTRONOMY. 
 
 the case is much the same as that by which, recognizing the 
 picture of a friend, we conclude that it is not the picture of 
 any one else. For anything we can prove to the contrary, 
 another person might have exactly the same features, and 
 might, therefore, make the very same picture. But, as a mat- 
 ter of fact, we know that practically no two men whom we 
 have ever seen do look exactly alike, and it is extremely im- 
 probable that they ever would look so. The case is the same 
 in spectrum analysis. Among the great number of substances 
 which have been examined with the spectroscope, no two give 
 the same lines. It is therefore extremely improbable that a 
 given system of bright lines could be produced by more than 
 one substance. At the same time, the evidence of the spec- 
 troscope is not necessarily conclusive in all cases. Should 
 only a single line of a substance be found in the spectrum of 
 a star or nebula, it would hardly be safe to conclude from that 
 alone that the line was really produced by the known sub- 
 stance. Collateral evidence might, however, come in. If the 
 same line were found both in the sunlight and in that of a 
 great number of stars, we should be justified in concluding 
 that the lines were all produced by the same substance. All 
 we can say in doubtful cases is, that our conclusions must be 
 drawn with care and discrimination, and must accord with the 
 probabilities of each special case. 
 
PART I1I.—THE SOLAR SYSTEM. 
 
 CHAPTER I. 
 
 GENERAL STRUCTURE OF THE SOLAR SYSTEM. 
 
 Havin, in the preceding parts, described the general struct- 
 ure of the universe, and the methods used by astronomers in 
 measuring the heavens and investigating the celestial motions, 
 we have next to consider in detail the separate bodies which 
 compose the universe, and to trace the conclusions respecting 
 the general order of creation to which this examination may 
 lead us. Our natural course will be to begin with a general 
 description of the solar system to which our earth belongs, 
 considering, first, the great central body of that system, then 
 the planets in their order, and, lastly, such irregular bodies as 
 comets and meteors. 
 
 We have shown in the first part that the solar system was 
 found by Copernicus, Kepler, and Newton to consist of the 
 sun, as the great central body, with a number of planets re- 
 volving around it in ellipses, having the sun in one of their 
 foci; the whole being bound together by the law of universal 
 gravitation. Modern science has added a great number of 
 bodies, and shown the system to be a much more complex one 
 than Newton supposed. As we now know them, the bodies 
 of the system may be classified as follows: 
 
 1. The sun, the great central body ; 
 
 2. A group of four inner planets— Mercury, Venus, the 
 Earth, and Mars; 
 
 3. A swarm of small planets or asteroids revolving outside 
 the orbit of Mars (about 220 of them are now known); 
 
236 THE SOLAR SYSTEM. 
 
 4. A group of four outer planets—Jupiter, Saturn, Uranus, 
 
 and Neptune ; 
 5. A number of satellites of the planets, 20 being now 
 known, of which all but three belong to the group of outer 
 
 planets ; 
 
 Jupiter Saturn -, Uranus » Neptune ‘Earth 
 
 Fia. 63.—Relative size of sun and planets. 
 
 6. An unknown number of comets and meteors, revolving 
 in very eccentric orbits. 
 
 The eight planets of groups 2 and 4 are called the major 
 planets, to distinguish them from all others, which are smaller 
 
 or less important. 
 
GENERAL STRUCTURE OF THE SOLAR SYSTEM. 237 
 
 The range of size, distance, and mass among the bodies of 
 the system is enormous. Neptune is eighty times as far from 
 the sun as Mercury, and Jupiter several thousand times as 
 heavy. It is, therefore, difficult to lay down a map of the 
 whole system on the same scale. If the orbit of Mercury were 
 represented with a diameter of one-fourth of an inch, that of 
 Neptune would have a diameter of 20 inches. 
 
 With the exception of Neptune, the distances of the eight 
 major planets proceed in a tolerably regular progression, the 
 group of small planets taking the place of a single planet in 
 the series. The progression is known as the law of Titius, 
 from its first proposer, and is as follows: Take the series of 
 numbers 0, 3, 6, 12, 24, 48, each one after the second being 
 formed by doubling the one which precedes it. Add 4 to 
 each of these numbers, and we shall have a series of numbers 
 giving very nearly the relative distances of the planets from 
 the sun. The following table shows the series of numbers thus 
 formed, together with the actual distances of the planets ex- 
 pressed on the same scale, the distance of the earth being 
 called 10: 
 
 Planet. 
 
 Minor planets 
 RPE DILOh etreasse sche ococres ss 
 Saturn 
 
 It will be seen that before the discovery of Neptune the 
 agreement was so close as to suggest the existence of an actual 
 law of the distances. But the discovery of this planet in 1846 
 completely disproved the supposed law; and there is now no 
 reason to believe that the proportions of the solar system are 
 the result of any exact and simple law whatever. It is true 
 that many ingenious people employ themselves from time to 
 time in working out numerical relations between the distances 
 of the planets, their masses, their times of rotation, and so on, 
 
238 THE SOLAR SYSTEM. 
 
 and will probably continue to do so; because the number of 
 such relations which can be made to come somewhere near to 
 exact numbers is very great. This, however, does not indicate 
 any law of nature. If we take forty or fifty numbers of any 
 kind—say the years in which a few persons were born; their 
 ages in years, months, and days at some particular event in 
 their lives; the numbers of the houses in which they live; and 
 ‘so on—we should find as many curious relations among the 
 numbers as have ever been found among those of the planet- 
 ary system. Indeed, such relations among the years of the lives 
 of great actors in the world’s history will be remembered by 
 many readers as occurring now and then in the public journals. 
 
 Range of Planetary Masses.—The great diversity of the size 
 and mass of the planets is shown by the curious fact, that, con- 
 sidering the sun and the eight planets, the mass of each of the 
 nine bodies exceeds the combined mass of all those which are 
 smaller than itself. This is shown in the following simple cal- 
 culation. Suppose the sun to be divided into a thousand mill- 
 ions of equal parts, one of which parts we take as the unit of 
 weight: then, according to the best determinations yet made, 
 the mass of each planet will be that used in the following cal- 
 culation, in which each mass is added to the masses of all the 
 planets which are smaller than itself, the planets being taken 
 in the order of their masses, beginning with the smallest : 
 
 Mass Of MGrcoryss ccucse sso ssutisienvasegusetastrcdss ter ate tsemeeneee 200 
 Mass of Mare. oie Acrcesbess eactomet cased onc nalat Chet cope nen 339 
 Combined mass of Mercury and Mars.............cesseceeeeeees 539 
 Mass of V enilis...cccny cud eee ceeneteeean one teer oe tel een ieee 2,353 
 Combined mass of Mercury, Venus, and Mars...............- 2,892 
 Mass of the: Harth..diveshsascsstsinrcnvascteees the corer ssionseer kt tye 3,060 
 Combined mass of the four inner planets. .............seeseeeee 5,952 
 Mass:-Of Dranus..).st oducecacageen acenty Sie ede WL ont Tt ont 44,250 
 Combined mass of five plavietss:. .t.5....cssssetesecsienspccassecds 50,202 
 Mass Of Neptutie: . .. cis. ferrctewsn ees e etna re ee recesses ests fue ee 51,600 
 Combined’ mass of six Planets i iiveesueectewecever essere cuseess 101,802 
 WAASAAGL SSALIEN jy sie o's wev:n «bain cu Pe oetatioe ope mea te COOH NINE TEES Oo uae Vdsicte be 285,580 
 Combined(mass of seven planats, jisearceshup senses sr oaseh«ocdnen 387,382 
 DEM e rele) PILOT o 450 sccbs secon vis rds 0 so Uen acl: MURR EE EES TSK se vases ts 954,305 
 Combined mass of all the planets...........cscesescsecsccsccccces 1,341,687 
 
 Maas Of SS BUI. hide cas ses ce te ‘tine beotheeNe Teens ets etd vere 1,000,000,000 
 
ASPECTS OF THE PLANETS. 239 
 
 It will be seen that the combined mass of all the planets is 
 less than 7$» that of the sun; that Jupiter is between two and 
 three times as heavy as the other seven planets together; Sat- 
 urn more than twice as heavy as the other six; and so on. 
 
 Aspects of the Planets—The apparent motions of the plan- 
 ets are described in the first chapter of this work; and in the 
 second chapter it is shown how these apparent motions result 
 from the real motions as laid down by Copernicus. The best 
 time to see one of the outer planets is when in opposition to 
 the sun. It then rises at sunset, and passes the meridian at 
 midnight. Between sunset and midnight it will be seen some- 
 _ where between east and south. During the three months fol- 
 lowing the day of opposition, the planet will rise from three 
 to six minutes earlier every day. A month after opposition, it 
 will be two to three hours high soon after sunset, and will pass 
 the meridian between nine and ten o’clock at night; while 
 three months after opposition, it will be on the meridian about 
 six In the evening. Hence, knowing when a planet is in op- 
 position, a spectator will know pretty nearly where to look for 
 it. His search will be facilitated by the use of a star map 
 showing the position of the ecliptic among the stars, because 
 the planets are always very near the ecliptic. Indeed, if any 
 bright star is not down on the map, he may feel sure that it is 
 a planet. 
 
 In describing the individual planets, we give the times when 
 they are in opposition, so that the reader may always be able 
 to recognize them at favorable seasons, if he wishes to do so. 
 
 The arrangement of the planets, with their satellites, is as 
 follows : 
 
 Mercury. 
 
 Venus. 
 
 Earth, with its moon. 
 Mars, with 2 moons. 
 
 INNER GROUP.... 
 
 The minor planets, or asteroids. 
 
 . ( Jupiter, with 4 moons. 
 
 Outer Group or } Saturn, with rings and 8 moons, 
 Great PLaneTs. | Uranus, with 4 moons. 
 ee with 1 moon. 
 
 ily 
 
240 THE SOLAR SYSTEM. 
 
 This arrangement is partly exhibited in the following plan 
 of the solar system, showing the relations of the planetary or- 
 bits from the earth outward. The scale is too small to show 
 the orbits of Mercury and Venus. 
 
 orbit of Neptune 
 
 orbit of Uranus 
 
 st, of Satury 
 os 
 
 Vernal Equinox 
 
 a a ee a a ee en ee = 
 
 Fig. 64.—Orbits of the planets from the earth outward, showing their relative distances 
 from the sun in the centre. The positions of the planets are near those which they oc- 
 cupy in 1877. 
 
THE PHOTOSPHERE. 241 
 
 CHAPTER II. 
 
 THE SUN. 
 
 Tue sun presents to our view the aspect of a brilliant globe 
 32’, or a little more than half a degree, in diameter. To give 
 precision to our language, the shining surface of this globe, 
 which we see with the eye or with the telescope, and which 
 forms the visible sun, is called the photosphere. Its light ex- 
 ceeds in intensity any that can be produced by artificial 
 means, the electric light between charcoal points being the 
 only one which does not look absolutely black against the un- 
 clouded sun. Our knowledge of the nature of this luminary 
 commences with the invention of the telescope, since without 
 this instrument it was impossible to form any conception of 
 its constitution. The ancients had a vague idea that it was a 
 globe of fire, and in this they were more nearly right than 
 some of the moderns; but there was so entire an absence of 
 all real foundation for their opinions that the latter are of lit- 
 tle interest to any one but the historian of philosophy. We 
 shall, therefore, commence our description of the sun with a 
 consideration of the telescopic researches of recent times. 
 
 § 1. The Photosphere. 
 
 To the naked eye the photosphere, or shining surface of the 
 sun, presents an aspect of such entire uniformity that any at- 
 tempt to gain an insight into its structure seems hopeless. 
 But when we apply a telescope, we generally find it diversified 
 with one or more groups of dark-looking spots; and if the vis- 
 ion is good, and we look carefully, we shall soon see that the 
 whole bright surface presents a mottled appearance, looking 
 like a fluid in which ill-defined rice-grains are suspended. er- 
 haps the most familiar idea of this appearance will be pre- 
 
242 THE SOLAR SYSTEM. 
 
 sented by saying that the sun looks like a plate of rice soup, 
 the grains of rice, however, being really hundreds of miles in 
 length. Some years ago Mr. Nasmyth, of England, examining 
 the sun with high telescopic powers, announced that this mot- 
 tled appearance seemed to him to be produced by the inter- 
 lacing of long, narrow objects shaped like willow leaves, which, 
 running and crossing in all directions, form a net-work, cover- 
 ing the entire photosphere. This view, though it has become 
 celebrated through the very great care which Mr. Nasinyth 
 devoted to his observations, has not been confirmed by subse- 
 quent observers. 
 
 Among the most careful and laborious telescopic studies of 
 the sun recently made are those of Professor Langley.* He 
 has a fine telescope at his command, in a situation where the 
 air seems to be less disturbed by the sun’s rays than is usual 
 in other localities. According to his observations, when the 
 sun is carefully examined, the mottling which we have de- 
 scribed is seen to be caused by an appearance like fleecy 
 clouds whose outlines are nearly indistinguishable. We may 
 also discern numerous faint dots on the white background. 
 Under high powers, used in favorable moments, the surface 
 of any one of the fleecy patches is resolved into a congeries 
 of small, intensely bright bodies, irregularly distributed, which 
 seem to be suspended in a comparatively dark medium, and 
 whose definiteness of size and outline, thongh not absolute, is 
 yet striking, by contrast with the vagueness of the cloud-like 
 forms seen before, and which we now perceive to be due to 
 their aggregation. The “dots” seen before are considerable 
 openings, caused by the absence of the white nodules at cer- 
 tain points, and the consequent exposure of the gray medium 
 which forms the general background. These openings have 
 been called pores. Their variety of size makes any rneasure- 
 ments nearly valueless, thongh we may estimate in a very 
 rough way the diameter of the more conspicuous at from 2” 
 to 4”, 
 
 * Professor S. P. Langley, Director of the Observatory at Allegheny, Pennsyl- 
 vania. 
 
 a 
 
 a ae oo 
 
THE PHOTOSPHERE. 2438 
 
 In moments when the definition is very fine, the bright nod- 
 ules or rice-grains are found to be made up of clusters of mi- 
 nute points of light or “ granules,” about one-third of a second 
 in diameter. These have also been seen around the edges of 
 the pores by Secchi, who estimated their magnitude as even 
 less than that assigned by Langley. The fact that these points 
 are aggregated into little clusters, which ordinarily present the 
 appearance of rice-grains, gives the latter a certain irregulari- 
 ty of outline which Hee pean remarked by Mr. Huggins. Thus, 
 there appear to be three orders of aggregation in the brighter 
 regions of the photosphere: cloud-like forms which can be 
 easily seen at any time; rice-grains or nodules, into which these 
 forms are resolved, and which can always be seen with a fair 
 telescope under good definition; and granules which make up 
 the rice-grains. There is, however, no sharp distinction to be 
 drawn between the epantes and 90 rice-grains: it might be 
 almost as near the truth to say that the rice-grains are “Ol va- 
 rious sizes, ranging from one-third of a second in diameter to 
 one second or more, and that the smaller ones are often col- 
 lected into minute clusters, which can hardly be distinguished 
 from grains of larger size. 
 
 Yet more recent are the studies of the sun’s surface made 
 by Janssen,* of France, with the aid of photography. This 
 method has a great advantage in the strength and perma- 
 nency of the photographic record, and the consequent power 
 of studying it at leisure. A disadvantage arises from the 
 great foe of astronomical observation which we have already 
 described — atmospheric undulations, which render the sun’s 
 image tremulous and confused except at occasional moments. 
 This difficulty may, however, be obviated by taking a great 
 number of photographs, and selecting those which show the 
 best images. 
 
 In applying this method, Janssen has taken his photographs 
 on a larger scale than has been attempted by his predecessors, 
 his largest pictures of the sun being from twelve to fifteen 
 
 * Prof. J. C. Janssen, director of the physical observatory at Meudon, France. 
 
944 THE SOLAR SYSTEM. 
 
 inches in diameter. The granulation is thus brought out with 
 remarkable distinctness, as may be seen from the following 
 figure, which is enlarged so that the whole sun, ou the same 
 scale, would be three feet in diameter. 
 
 gers 
 
 Fig. 64a. 
 
 — Aspect of the Sun’s Surface as Photographed by Jansseu at the Observatory 
 of Meudon. 
 
 M. Janssen finds that the granular elements are of very dif- 
 ferent sizes and brilliancy, the diameters ranging from a few 
 tenths of a second to three or four seconds. The form is gen- 
 erally slightly elliptic, but is subject to considerable variations. 
 The differences of brilliancy among the granules seem to arise 
 from their being situated at different depths in the photo- 
 sphere. But the most remarkable result of Janssen’s photo- 
 graphs is what he calls the photospherie net-work, “ réseau 
 photosphérique.” This is not a net-work of lines, as we might 
 understand it, but a subdivision of the photosphere into regions 
 in which the granules look hard and well defined, and regions 
 in which they look softened and indistinct. This appearance 
 is shown, though somewhat imperfectly, in the above figure, 
 
 _— 
 
THE PHOTOSPHERE. 245 
 
 which is taken from one of Janssen’s photographs. The boun- 
 daries of the regions of well and ill defined granulations are 
 necessarily somewhat indefinite, and sometimes appear straight 
 and sometimes curved. The dimensions of the regions of ill- 
 defined granulation are.very variable. Sometimes they attain 
 a diameter of one minute or more. Within them, the granules 
 sometimes disappear entirely, their place being occupied by 
 streams of matter. This disappearance seems to be due to 
 violent movements of the photospheric matter destroying the 
 granular elements. 
 
 When we call these shining objects “granules,” it must be 
 remembered that we speak of the appearance, not of the reali- 
 ty. To subtend an angle of one second, at the distance of the 
 sun, a line must be 450 miles long; consequently, from what 
 is said of the size of the granules, they must be from 100 to 
 500 miles in length and breadth. 
 
 If we carefully examine the sun with a very dark smoked 
 glass, we shall find that the disk is brightest at the centre, 
 shading off on all sides towards the limb. Careful compari- 
 sons of the intensity of radiation of different parts of the disk 
 show that this diminution near the limb is common to all the 
 rays, whether those of heat, of light, or of chemical action. 
 The most recent measures of the heat rays were made by 
 Langley by means of a thermo-electric pile, those of the light — 
 rays by Pickering,* and those of the chemical rays by Vogel.t+ 
 The intensities of these several radiations at different distances 
 from the centre of the disk as thus determined are shown in 
 the table on the following page. The intensity at the centre 
 is always supposed 100. The first column gives the distance 
 from the centre in fractions of the sun’s radius, which is sup- 
 posed unity. Thus, the first line of the table corresponds to 
 the centre; the last to the edge. Professor Langley’s meas- 
 ures do not, however, extend to the extreme edge. 
 
 * Professor E. C. Pickering, Director of the Harvard Observatory, Cambridge, 
 Massachusetts. 
 
 + Dr. Hermann C. Vogel, formerly astronomer at Bothkamp, now of the Solar 
 Observatory in Potsdam, Prussia. 
 
246 THE SOLAR SYSTEM. 
 
 Distance from Heat Rays Light Chemical Rays 
 Centre of the Sun. (Langley). (Pickering), (Vogel). 
 
 4 100 100 
 .125 Nae 99 100 
 
 125 99 97 98 
 B75 AP 94. 95 
 50 95 9] 90 
 625 af 86 81 
 75 86 79 66 
 .85 ve: 69 48 
 .95 a 55 25 iy th 
 96 62 oy 23 
 
 It will be seen that near the edge of the disk the chemical 
 rays fall off most rapidly, the light rays next, and the heat 
 rays least of all. oughly speaking, each square minute near 
 the limb of the sun gives about half as much heat as at the 
 centre, about one-third as much light, and less than one-seventh 
 as many photographic rays. Of the cause of this degradation 
 of light and heat towards the limb of the sun no doubt has 
 been entertained since it was first investigated. It is found in 
 the absorption of the rays by a solar atmosphere. The sun 
 being a globe surrounded by an. atmosphere, the rays which 
 emanate from the photosphere in a horizontal direction have 
 a greater thickness of atmosphere to pass through than those 
 which strike out vertically; while the former are those we 
 see near the edge of the disk, and the latter near the centre. 
 The different absorptions of different classes of rays corre- 
 spond exactly to this supposition, it being known that the 
 more refrangible or chemical rays are most absorbed by va- 
 pors, arid the heat rays the least. 
 
 From this it follows that we get but a fraction—perhaps a 
 small fraction—of the light and heat actually emitted by the 
 sun; and that if the latter had no atmosphere, it would be 
 much hotter, much brighter, and bluer in color, than it actually 
 is. The total amount of absorption has been very differently 
 estimated by different authorities, Laplace supposing it might 
 be as much as eleven-twelfths of the whole amount. The 
 smaller estimates are, however, more likely to be near the 
 
THE PHOTOSPHERE. Q47 
 
 truth, there being no good reason for holding that more than 
 half the rays are absorbed. ‘That is, if the sun had no atmos- 
 phere, it might be twice as bright and as hot as it actually is, 
 but would not be likely to be three or four times so. Profess- 
 or Langley suggests that the glacial epoch may have been due 
 to a greater absorption of the sun’s heat by its atmosphere in 
 some past geological age. 
 
 A very important physical and astronomical problem is that 
 of measuring the total amount of heat radiated by the sun to 
 the earth during any period of time —say a day or a year. 
 The question admits of a perfectly definite answer, but there 
 are two difficulties in the way of obtaining it; one, to distin- 
 guish between the heat coming from the sun itself, and that 
 coming from the atmosphere and surrounding objects; the 
 other, to allow for the absorption of the solar heat by our at- 
 mosphere, which must be done in order to determine the to- 
 tal quantity emanating from the sun. The most successful 
 experiments for this purpose are those of Pouillet and of 
 Sir John Herschel. The results obtained by the former may 
 be expressed thus: if the air were out of the way, and a sheet 
 of ice were so held that the sun’s rays should fall upon it per- 
 pendicularly, and be all absorbed, the ice would melt away at 
 the rate of 144 inches in 24 honrs. Since the sun is part of 
 the time below the horizon, and is not perpendicular to more 
 than a single point of the earth’s surface when above it, the 
 average amount of ice which would be melted over the whole 
 earth is only a fraction of this, namely, 3.62 inches per day, 
 or something more than 100 feet per year. 
 
 Attempts have been made to determine the temperature of 
 the sun from the amount of heat which it radiates, but the 
 estimates have varied very widely, owing to the uncertainty 
 respecting the law of radiation at high temperatures. By sup- 
 posing the radiation proportional to the temperature, Secchi* 
 finds the latter to be several million degrees, while, by taking 
 another law indicated by the experiments of Dulong and 
 
 * Father Angelo Secchi, Director of the Observatory at Rome. 
 
 M 
 
245 THE SOLAR SYSTEM. 
 
 Petit, others find a temperature not many times exceeding 
 that of a reverberatory furnace. For the temperature of the 
 photosphere, it seems likely that the lower estimates are more 
 nearly right, being founded on an experimental law; but the 
 temperature of the interior must be immensely higher. 
 
 § 2. The Solar Spots and Rotation. 
 
 Even the poor telescopes made by the contemporaries of 
 Galileo could hardly be directed to the sun many times with- 
 out one or more spots being seen on his surface. Whatever 
 credit may be due for a discovery which required neither in- 
 dustry nor skill should, by the rule of modern science already 
 referred to, be awarded to Fabritius for the discovery of the 
 solar spots. This observer, otherwise unknown in astronomy, 
 made known the existence of the solar spots early in 1611— 
 a year after Galileo began to scan the heavens with his tel- 
 escope. His discovery was followed up by Galileo and Schei- 
 ner, by whom the first knowledge of the nature of the spots 
 was acquired. 
 
 The first idea of Scheiner was that the spots were small 
 planets in the neighborhood of the sun; but this was speedily 
 disproved by Galileo, who showed that they must be on the 
 surface of the sun itself. The idea of the sun being affected 
 with any imperfection so gross as a dark spot was repugnant 
 to the ecclesiastical philosophy of the times, and it is not un- 
 likely that Scheiner’s explanation was suggested by the desire 
 to save the perfection of our central luminary. 
 
 A very little observation showed that the spots had a regu- 
 lar motion across the disk of the sun from east to west, occu- 
 pying abont 12 days in the transit. A spot. generally appeared 
 first on or near the east limb, and, after 12 or 14 days, disap- 
 peared at the west limb. At the end of another 14 days or 
 more it reappeared at the east limb, unless in the mean time 
 it had vanished from sight entirely. The spots were found 
 not to be permanent objects, but to come into existence from 
 time to time, and, after lasting a few days, weeks, or months, 
 to disappear. But so long as they lasted, they always ex- 
 
THE SOLAR SPOTS AND ROTATION. 249 
 
 hibited the motion just described, and it was thence inferred 
 that the sun rotated on his axis in about 25 days. 
 
 The astronomers of the seventeenth and eighteenth centuries 
 used a method of observing the sun which will often be found 
 convenient for seeing the spots when one has not a telescope 
 supplied with dark glasses at his disposal. Take an ordinary 
 good spy-glass, or, indeed, a telescope of any size, and point 
 
 Fie. 65. — Method of holding telescope, to show sun on screen. 
 
 it at the sun. To save the eyes, the right direction may be 
 found by holding a piece of paper closely in front of the eye- 
 piece: when the sun shines through the telescope on this pa- 
 per, the pointing is nearly right. The telescope should be at- 
 tached to some movable support, so that its pointing can be 
 changed to the different directions of the sun, and should pass 
 through a perforation in some sort of a screen, so that the 
 sun cannot shine in front of the telescope except by passing 
 
250 THE SOLAR SYSTEM. 
 
 through it. An opening in a window-shutter will answer a 
 good purpose, only the rays must not have to pass through the 
 glass of the window in order to reach the telescope. Draw 
 out the eye-piece of the instrument about the eighth of an 
 inch beyond the proper point for seeing a distant object. 
 Then, holding a piece of white paper before the eye-piece at 
 a distance of from 6 to 12 inches, an image of the sun will be 
 thrown upon it. The distance of the paper must be adjusted 
 to the distance the eye-piece is drawn out. The farther we 
 draw out the eye-piece, the nearer the best image will be 
 formed. Having adjusted everything so that the edge of the 
 sun’s image shall be sharply defined, one or more spots can 
 generally be seen. This method, or something similar to it, is 
 often used in observing eclipses and transits of Mercury, and 
 is very convenient when it is desired to show an enlarged im- 
 age of the sun to a number of spectators. 
 
 When powerful telescopes were applied to the sun, it was 
 found that the spots were not merely the dark patches which 
 they first appeared to be, but that they comprised two well- 
 
 Fig. 66.—Solar spot, after Secchi. 
 
 marked portions. The central part, called the wmbra or nu- 
 cleus, is the darkest, and is surrounded by a border, interme- 
 diate in tint between the darkness of the spot and the brill- 
 
THE SOLAR SPOTS AND ROTATION. Q51 
 
 iancy of the solar surface. This border is termed the penwm- 
 bra. Ordinarily it appears of a uniform gray tint. But when 
 carefully examined with a good telescope in a very steady at- 
 mosphere, it is found to be striated, looking, in fact, much lke 
 the bottom of a thatched roof, the separate-straws being di- 
 rected towards the interior of the spot. This appearance is 
 shown in the figure. 
 
 The spots are extremely irregular in form and unequal in 
 size. ‘They are very generally seen in groups — sometimes 
 two or more combined into a single one; and it frequently 
 happens that a large one breaks up into several smaller ones. 
 Their duration is also extremely variable, ranging from a few 
 days to periods of several months. 
 
 Until about a century ago, it was a question whether the 
 spots were not dark patches, like scoria, floating on the molten 
 surface of the photosphere. Wilson, a Scotch observer, how- 
 ever, found that they appeared like cavities in the photosphere, 
 the dark part being really lower than the bright surface around 
 it. As a spot approached the edge of the disk, he found that 
 the penumbra grew disproportionately narrow on the side 
 nearest to the sun’s centre, showing that this side of it was 
 seen at a smaller angle than the other. This effect of per- 
 spective is shown in Fig. 67, where, near the sun’s limb, the 
 side of the penumbra nearest us is hidden by the photosphere. 
 That the spots are cavities is also shown by the fact that 
 when a large spot is exactly on the edge of the disk a notch 
 is sometimes seen there. The shaded penumbra seems to 
 form the sides of the cavity, while the umbra is the invisible 
 bottom. 
 
 These observations gave rise to the celebrated theory of 
 Wilson, which is generally connected with the name of Her- 
 schel, who developed it more fully. The interior of the sun 
 is, by this theory, a cool, dark body, surrounded by two layers 
 of clouds. The outer layer is intensely brilliant, and forms 
 the visible photosphere, while the inner layer is darker, and 
 forms the umbra around the spots. The latter are simply 
 openings through these clouds, which form from time to 
 
25? THE SOLAR SYSTEM. 
 
 Fia. 67.—Chauges in the aspect of a solar spot as it crosses the sun’s disk, showing it to be 
 a cavity in the photosphere. 
 time, and through which we see the dark body in the interior. 
 Anxious that this body should serve some especial purpose in 
 the economy of creation, they peopled it with intelligent be- 
 ings, who were protected from the fierce radiation of the pho- 
 tosphere by the layer of cool clouds, but were denied every 
 view of the universe without, except such glimpses as they 
 might obtain through the occasional openings in the photo- 
 sphere, which we see as spots. . 
 Leaving out the fancy of living beings, this theory account- 
 ed very well for appearances. That the photosphere could not 
 be absolutely and wholly solid, liquid, or gaseous seemed evi- 
 dent from the nature of the spots. If it were solid, the latter 
 could not be in such a constant state of change as we see 
 
THE SOLAR SPOTS AND ROTATION. 253 
 
 them; while if it were liquid or gaseous, these cavities could 
 not continue for months, as they were sometimes seen to, be- 
 cause the liquid or gaseous matter would rush in from all 
 sides, and fill them up. The only hypothesis that seemed left 
 open to Herschel was that the photosphere consisted of clouds 
 floating in an atmosphere. As the sides of the cavities looked 
 comparatively dark, the conclusion seemed inevitable that the 
 brilliancy of the photosphere was only on and near the sur- 
 face; and as the bottom of the cavity looked entirely dark, 
 the conclusion that the sun had a dark interior seemed una- 
 voidable. 
 
 The discovery of the conservation of force, and of the mut- 
 ual convertibility of heat and force, was fatal to this theory. 
 Such a sun as that of Herschel would have cooled off entirely in 
 a few days, and then we should receive neither light nor heat 
 from it. A continuous flood of heat such as the sun has been 
 radiating for thousands of years can be kept up only by a con- 
 stant expenditure of force in some of its forms; but, on Her- 
 schel’s theory, the supply necessary to meet this expenditure 
 was impossible. Even if the heat of the photosphere could 
 be kept up by any agency, it would be constantly conveyed to 
 the interior by conduction and radiation ; so that in time the 
 whole sun would become as hot as the photosphere, and its 
 inhabitants would be destroyed. In the time of Herschel it 
 was not deemed necessary that the sun should be a very hot 
 body, the heat received from his rays being supposed by many 
 to be generated by their passage through our atmosphere. 
 The photosphere was, therefore, supposed to be simply phos- 
 phorescent, not hot. This idea is still entertained by many 
 educated men who have not made themselves acquainted with 
 the laws of heat discovered during the present century. We 
 may, therefore, remark that it is completely untenable. One 
 of the best established results of these laws is that the surface 
 of the sun is intensely hot, probably much hotter than any re- 
 verberatory furnace. The great question in the present state 
 of science is, how the supply of heat is maintained against 
 such immense loss by radiation. 
 
254 THE SOLAR SYSTEM. 
 
 § 3. Periodicity of the Spots. 
 
 The careful observations of the solar spots which have been 
 made during the last century seem to indicate a period of 
 about eleven years in the spot-producing activity of the sun. 
 During two or three years the spots are larger and more nu- 
 merous than on the average; they then begin to diminish, 
 and reach a minimum five or six years after the maximum. 
 Another six years brings the return of the maximum. The 
 intervals are, however, somewhat irregular, and further obser- 
 vations are required before the law of this period can be fixed 
 with certainty. An idea of the evidence in favor of the pe- 
 riod may be formed from some results of the observations of 
 Schwabe, a German astronomer, who systematically observed 
 the sun during a large part of a long life. One of his meas- 
 ures of the spot-producing power was the number of days on 
 which he saw the sun without spots in the course of each 
 year. The following are some of his results: 
 
 From 1828 to 1831, sun without spots on only 1 day. 
 6é 
 
 In 1833, a + 139 days. 
 From 18386 to 1840, ‘‘ ty che 3 days. 
 In 1843, ree + Be 147 days. 
 From 1847 to 1851, ‘* “A 43 2 days. 
 In 1856, a i ay 193 days. 
 From 1858 to 1861, ‘‘ - oe no day. 
 In 1867, “4 ~ ye 195 days. 
 
 We see that the sun was remarkably free from spots in the 
 years 1835, 1848, 1856, and 1867, about half the time no con- 
 siderable spot being visible. This recurrence of the period 
 has been traced back by Dr. Wolf, of Zurich, to the time of 
 Galileo, and its average length is about 11 years 1 month. 
 The years of fewest sun-spots during the present century were 
 1810, 1823, 1838, 1844, 1856, and 1867. Continuing the 
 series, we may expect very few spots in 1878, 1889, etc. The 
 years of greatest production of spots were 1804, 1816, 1829, 
 1837, 1848, 1860, and 1870, from which we may conclude 
 that 1882, 1893, ete., will be years of numerous sun-spots. 
 
PERIODICITY OF THE SPOTS. Q55 
 
 The observations of Schwabe and the researches of Wolf 
 seem to have placed the existence of this period beyond a 
 doubt; but no satisfactory explanation of its cause has yet 
 been given. When first noticed, its near approach to the pe- 
 riod of revolution of Jupiter naturally led to-the belief that 
 there was a connection between the two, and that the attrac- 
 tion of the largest planet of the system produced some disturb- 
 ance in the sun, which was greater in perihelion than in aphe- 
 lion. But this connection seems to be disproved by the fact 
 that the sun-spot period is at least six months, and perhaps a 
 year, shorter than the revolution of Jupiter. It is therefore 
 probable that the periodicity in question is not due to any ac- 
 tion outside the sun, but is a result of some law of solar action 
 of which we are as yet ignorant. 
 
 There are certain supposed connections of the sun-spot pe- 
 riod with terrestrial phenomena which are of interest. Sir 
 William Herschel collected quite a mass of statistics tending to 
 show that there was an intimate connection between the num- 
 ber of sun-spots and the price of corn, the latter being low 
 when there were few spots, and high when they were more 
 numerous. His conclusion was that the fewer the spots, the 
 more favorable the solar rays to the growth of the crops. 
 This theory has not been confirmed by subsequent observa- 
 tion. There is, however, some reason to believe, from the 
 researches of Professors Lovering and Loomis, that the fre- 
 quency of auroras and of magnetic disturbances is subject to 
 a period corresponding to that of sun-spots, these occurrences 
 being most frequent when the spots are most numerous. Pro- 
 fessor Loomis considers the coincidence to be pretty well 
 proved, while Professor Lovering is more cautious, and waits 
 for further research before coming to a positive conclusion. 
 The occurrence of great auroras in 1859 and 1870-71 was 
 strikingly accordant with the theory. 
 
 § 4. Law of Rotation of the Sun. 
 
 Between the years 1843 and 1861, a very careful series of 
 observations of the positions and motions of the solar spots 
 : 18 
 
256 THE SOLAR SYSTEM. 
 
 was made by Mr. Carrington, of England, with a view of de- 
 ducing the exact time in which the sun rotates on his axis. 
 These observations led to the remarkable result that the time 
 of rotation shown by the spots was not the same on all parts 
 of the sun, but that the equatorial regions seemed to perform 
 a revolution in less time than those nearer the poles. Near 
 the equator the period was about 25.3 days, while it was a 
 day longer in 380° latitude. Moreover, the period of rotation 
 seems to be different at different times, and to vary with the 
 frequency of the spots. But the laws of these variations are 
 not yet established. In consequence of their existence, we 
 cannot fix any definite time of rotation for the sun, as we can 
 for the earth and for some of the planets. It varies at dif- 
 ferent times, and under different circumstances, from 25 to 
 264 days. 
 
 The cause of these variations is a subject on which there is 
 yet no general agreement among those who have most care- 
 fully investigated the subject. Zodllner* and Wolf see in the 
 general motions of the spots traces of currents moving from 
 both poles of the sun towards the equator. The latter con- 
 siders that the eleven-year spot-period is associated with a 
 flood of liquid or gaseous matter thrown up at the poles of 
 the sun about once in eleven years, and gradually finding its 
 way to the equator. Zoéllner adopts the same theory, and has 
 submitted it to a mathematical analysis, the basis of which is 
 that the sun has a solid crust, over which runs the fluid in 
 which the spots are formed. The current springs up near 
 the poles, and, starting towards the equator without any rota- 
 tion, is acted on by the friction of the revolving crust. By 
 this friction the crust continually tends to carry the fluid with 
 it. The nearer the current approaches the equator, the more 
 rapid the rotation of the crust, owing to its greater distance 
 from the axis. The friction acts so slowly that the current 
 reaches the equator before it takes up the motion of the erust. 
 On this hypothesis, the crust of the sun really revolves in 
 
 * Dr. J. C. F. Zollner, Professor in the University of Leipsie. 
 
THE SUN’S SURROUNDINGS. 257 
 
 about 25 days; and the reason that the fluid which covers it 
 revolves more slowly at a distance from the sun’s equator is 
 that it has not yet taken up this normal velocity of rotation. 
 
 This explanation of the seeming paradox that the equatorial 
 regions of the sun perform their revolution in a shorter time 
 than those parts nearer the poles, cannot be regarded as an es- 
 tablished scientific theory. It is mentioned as being, so far as 
 the writer is aware, the most completely elaborated explana- 
 tion yet offered. It is possible that the spots have a proper 
 motion of their own on the solar surface, and that this is the 
 reason of the apparent difference in the time of rotation in 
 different latitudes. Yet another theory of the subject is that 
 of Faye,* who maintains that these differences in the rates of 
 rotation are due to ascending and descending currents, as will 
 be more fully explained in presenting his views. But we here 
 touch upon questions which science is as yet far from being 
 in a condition to answer. 
 
 8 5. The Sun's Surroundings. 
 
 If the sun had never been examined with any other instru- 
 ment than the telescope, nor been totally eclipsed by the inter- 
 vention of the moon, we should not have formed any idea of 
 the nature of the operations going on at his surface; but we 
 might have been better satisfied that we had a complete knowl- 
 edge of his constitution. Indeed, it is remarkable that mod- 
 ern science has shown us more mysteries in the sun than it has 
 explained ; so that we find ourselves farther than before from 
 a satisfactory explanation of solar phenomena. When the an- 
 cients supposed the sun to be a globe of molten iron, they had 
 an explanation which quite satisfied the requirements of the 
 science of their times. The spots were no mystery to Galileo 
 and Scheiner, being simply dark places in the photosphere. 
 Herschel’s explanation of them was quite in accord with the 
 science of his time, and he may be regarded as the latest man 
 who has held a theory of the physical constitution of the sun 
 
 “ Mr. H. E, Faye, member of the French Academy of Sciences. 
 
258 THE SOLAR SYSTEM. 
 
 which was really satisfactory at the time it was propounded. 
 We have shown how his theory was refuted by the discovery 
 of the conservation of force; we have now to see what per- 
 plexing phenomena have been revealed in recent times. 
 
 Phenomena during Total Eclipses. — If, during the progress 
 of a total eclipse, the gradually diminishing crescent of the 
 sun is watched, nothing remarkable is seen until very near the 
 moment of its total disappearance. But, as the last ray of sun- 
 light vanishes, a scene of unexampled beauty, grandeur, and im- 
 pressiveness breaks upon the view. The globe of the moon, 
 black as ink, is seen as if it were hanging in mid-air, surround- 
 ed by a crown of soft, silvery light, like that which the old 
 painters used to depict around the heads of saints. Besides 
 this “corona,” tongues of rose-colored flame of the most fan- 
 tastic forms shoot out from various points around the edge of 
 the lunar disk. Of these two appearances, the corona was no- 
 ticed at least as far back as the tine of Kepler; indeed, it was 
 not possible for a total eclipse to happen without the specta- 
 tors seeing it. But it is only within a century that the at- 
 tention of astronomers has been directed to the rose-colored 
 flames, althongh an observation of them was recorded in the 
 Philosophical Transactions nearly two centuries ago. They 
 are known by the several names of “ flames,” ‘‘ prominences,” 
 and “ protuberances.” 
 
 The descriptions which have been given of the corona, al- 
 though differing in many details, have a general resemblance. 
 Halley’s description of it, as seen during the total eclipse of 
 1715, is as follows: 
 
 ‘CA few seconds before the sun was all hid, there discovered 
 itself round the moon a luminous ring about a digit, or per- 
 haps a tenth part of the moon’s diameter, in breadth. It was 
 of a pale whiteness, or rather pearl-color, seeming to me a lit- 
 tle tinged with the colors of the iris, and to be concentric 
 with the moon.” 
 
 The more careful and elaborate observations of recent times 
 show that the corona has not the circular form which was for 
 merly ascribed to it, but that it is quite irregular in its out- 
 
THE SUN’S SURROUNDINGS. ea, 259 
 
 line. Sometimes its form is more nearly square than round, 
 the corners of the square being about 45° of solar latitude, 
 and the sides, therefore, corresponding to the poles and the 
 equator of the sun. This square appearance does not, how- 
 ever, arise from any regularity of form, but from the fact that 
 the corona seems brighter and higher half way between the 
 poles and the equator of the sun than it does near those points. 
 
 Fig. 68.—Total eclipse of the sun as seen at Des Moines, Iowa, August 7th, 1869. Drawn 
 by Professor J. R. Eastman. The letters, a, b, c, etc., mark the positions of the prom- 
 inences. 
 
 These prominent portions sometimes seem like rays shooting 
 ont from the sun. The corona is always brightest at its base, 
 gradually shading off toward the onter edge. It is impossi- 
 ble to say with certainty how far it extends, but there is no 
 doubt that it has been seen as far as one semidiameter from 
 the moon’s limb. 
 
260 THE SOLAR SYSTEM. 
 
 The corona was formerly supposed to be an atmosphere 
 either of the moon or of the sun. Thirty or forty years ago, 
 the most plausible theory was that it was a solar atmosphere, 
 and that the red protuberances were clouds floating in it. 
 That the corona could be a lunar atmosphere was completely 
 disproved by its irregular outline, for the atmosphere of a 
 body like the moon would necessarily spread itself around in 
 nearly uniform layers, and could not be piled up in some 
 quarters, as the matter of the corona is seen to be. We shall 
 soon see that there is no doubt about the corona being some- 
 thing surrounding the sun. 
 
 The question whether the red protuberances belong to the 
 moon or the sun was settled during the total eclipse of 1860, 
 which was observed in Spain. It was then proved by meas- 
 ures of their height above the limb of the moon that the lat- 
 ter did not carry them with her, but passed over them. This 
 proved that they were fixed relatively to the sun. 
 
 At the time of this eclipse the spectroscope was in its in- 
 fancy, and no one thought of applying it to the study of the 
 corona and protuberances. The next considerable eclipse oc- 
 curred eight years later, in July, 1868, and was visible in In- 
 dia and Siam. The spectroscope had, in the mean time, come 
 into very general use, and expeditions were despatched from 
 several European countries to India to make an examination 
 of the spectra of the objects in question. The most success- 
 ful observer was Janssen, of France, who took-an elevated 
 position in the interior, where the air was remarkably clear. 
 When, on the eventful day, the last ray of sunlight was cut 
 off by the advancing moon, an enormous protuberance showed 
 itself, rising to a height of many thousand miles above the sur- 
 face of the sun. The spectroscope was promptly turned upon 
 it, and the practised eye of the observer saw in a moment that 
 the spectrum consisted of the bright lines due to glowing hy- 
 drogen. The protuberance, therefore, did not consist of any 
 substance shining merely by reflected sunlight, but of an im- 
 mense mass of hydrogen gas, so hot as to shine by its own 
 light. The theory of the cloud-like nature of the protuber- 
 ances was overthrown in a moment. 
 
THE SUN’S SURROUNDINGS. 261 
 
 This observation marks the commencement of a new era in 
 solar physics, which, by a singular coincidence, was inaugu- 
 rated independently by another observer. As Janssen looked 
 at the lines which he was the first of men to see, it occurred 
 to him that they were bright enough to be seen after the total 
 phase of the eclipse had passed. He therefore determined to 
 watch them, and find how long he could follow them. He 
 kept sight of them, not only after the total phase had passed, 
 but after the eclipse was entirely over. In fact, he found that 
 with a sufliciently powerful spectroscope, he could see the 
 spectral lines of the protuberances at any time when the air 
 was perfectly clear, so that the varying forms of these remark- 
 able objects which had hitherto been seen only during the 
 rare moments of a total eclipse could be made a subject of 
 regular observation. 
 
 But this great discovery was made in England, independ- 
 ently of the eclipse, by Mr. J. Norman Lockyer. This gen- 
 tleman was an active student of the subject of spectroscopy ; 
 and it had occurred to him that the matter composing these 
 protuberances, being so near the surface of the sun, must be 
 hot enough, not only to shine by its own light, but to be quite 
 vaporized, and, if so, its spectrum might be seen by means of 
 the spectroscope. Finding that the instrument he possessed 
 would show nothing, he ordered a more powerful one. But 
 its construction was attended with so much delay that it was 
 not ready till October, 1868. On the 20th of that month, he 
 pointed it upon the margin of the sun, and found three bright 
 lines in the spectrum, two of which belonged to hydrogen. 
 Thus was realized an idea which he had formed two years be- 
 fore, but which he was prevented from carrying out by the 
 want of a suitable instrument. His success was immediately 
 communicated to the French Academy of Sciences, the news 
 reaching that body on the very day that word was received 
 from Janssen, in India, that he had also solved the same prob- 
 lem. 
 
 Following up his researches, Mr. Lockyer found that the 
 protuberances arose from a narrow envelope surrounding the 
 
262 THE SOLAR SYSTEM. 
 
 Fig. 69.—Specimens of solar protuberances, as drawn by Secchi. The bright base in each 
 p ’ eS 
 figure represents the chromosphere from which the red flames rise. 
 
 whole surface of the sun, being, in fact, merely elevated por- 
 tions of this envelope: that is to say, the sun is surrounded 
 by an atmosphere composed principally of hydrogen gas, por- 
 tions of which are here and there thrown up in the form of 
 
THE SUN’S SURROUNDINGS. 263 
 
 enormous tongues of flame, which, however, can never be seen 
 except with the spectroscope, or during total eclipses. To this 
 atmosphere Mr. Lockyer gave the name of the chromosphere. 
 This new method of research throws no light upon the con- 
 stitution of the corona, because the spectrum of this object is 
 too faint to be studied at any time, except during total eclipses. 
 There have been two in the United States within ten years, 
 during both of which the corona was carefully studied with 
 all the appliances of modern science. The first of these 
 eclipses occurred on August 7th, 1869, when the shadow of 
 the moon passed over Iowa, Illinois, Kentucky, South-western 
 Virginia, and North Carolina. The second was that of July 
 29th, 1878, when the shadow passed over Wyoming, Colora- 
 do, and Texas. One of the most curious results of the last 
 eclipse is derived from a study of the photographs taken by 
 parties sent out from the Naval Observatory. These show 
 that the corona is not a mass of foggy or milky light, as it 
 usually appears in small telescopes, but has a hairy structure, 
 like long tufts of flax. This structure was noticed by W. 8. 
 Gilman during the eclipse of 1869, but does not seem to have 
 been generally remarked. The most prominent feature of the 
 spectrum of the corona is a single bright line in the green 
 portion, discovered independently by Professors Harkness and 
 Young during the eclipse of 1869. It has not been identified 
 in the spectrum of any terrestrial substance. This would in- 
 dicate that the corona consisted in part of some gases un- 
 known on the earth. There is also a faint continuous spec- 
 trum, in which the dark lines of the solar spectrum can be 
 seen, but these lines are much more prominent during some 
 eclipses than during others. This portion of the spectrum 
 must be due to reflected sunlight. It would seem, therefore, 
 that the corona comprises a mixture of gaseous matter, shining 
 by its own light, and particles reflecting the light of the sun. 
 Continued observations of the spectra of the various gases 
 surrounding the sun show a much greater number of lines 
 than have ever been seen during total eclipses. Mr. Lockyer 
 himself, by diligent observation extending over several years, 
 
264 THE SOLAR SYSTEM. 
 
 found over a hundred. But the greatest advance in this re- 
 spect was made by Professor C. A. Young. In 1871 an astro- 
 nomical expedition was fitted out by the Coast Survey, for the 
 purpose of learning by actual trial whether any great advan- 
 tage would be gained by establishing an observatory on the 
 most elevated point crossed by the Pacific Railway. This 
 point was Sherman. The spectroscopic part of the expedition 
 was intrusted to Professor Young. Although there was a 
 great deal of cloudy weather, yet, when the air was clear, far 
 less light was reflected from the sky surrounding the sun than 
 at lower altitudes, which was a great advantage in the study 
 of the sun’s surroundings. Professor Young found no less 
 than 278 bright lines which he was able to identify with cer- 
 tainty. The presence of many known substances, especially 
 iron, magnesium, and titanium, is indicated by these lines; 
 but there are also many lines which are not known to pertain 
 to any terrestrial substance. 
 
 §$ 6. Physical Constitution of the Sun. 
 
 Respecting the physical constitution of the sun, there are 
 some points which may be established with more or less cer- 
 tainty, but the subject is, for the most part, involved in doubt 
 and obscurity. Since the properties of matter are the same 
 everywhere, the problem of the physical constitution of the 
 sun is solved only when we are able to explain all solar phe- 
 nomena by laws of physics which we see in operation around 
 us. The fact that the physical laws operative on the sun must 
 be at least in agreement with those in operation here, is not 
 always remembered by those who have speculated on the sub- 
 ject. In stating what is probable, and what is possible, in 
 the causes of solar phenomena, we shall begin on the outside, 
 and go inwards, because there is less doubt about the opera- 
 tions which go on outside the sun than about those on his sur- 
 face or in the interior. 
 
 As we approach the sun, the first material substance we 
 meet with is the corona, rising to heights of five or ten, per- 
 haps even fifteen, minutes above his surface, that is, to a height 
 
PHYSICAL CONSTITUTION OF THE SUN. 265 
 
 of from one to three hundred thousand miles. Of this ap- 
 pendage we may say with entire confidence that it cannot be 
 an atmosphere in the sense in which that word is commonly 
 used, that is, a continuous mass of elastic gas held up by its 
 own elasticity. Of the two reasons in favor of this denial, one 
 seems to me almost conclusive, the other entirely so. They 
 are as follows: 
 
 1. Gravitation on the sun is about 27 times as great as on 
 the earth, and any gas is there 27 times as heavy as here. In 
 an atmosphere each stratum is compressed by the weight of 
 all the strata above it. The result is, that as we go down by 
 successive equal steps, the density of the atmosphere increases 
 in geometrical progression. An atmosphere of the lightest 
 known gas—hydrogen—would double its density every five or 
 ten miles, though heated to as high a temperature as is likely 
 to exist at the height of a hundred thousand miles above the 
 sun’s surface. But there is no approximation to such a rapid 
 increase in the density of the corona as we go downwards. If 
 we suppose the corona to be such an atmosphere, we must 
 suppose it to be hundreds of times lighter than hydrogen. 
 
 2. The great comet of 1843 passed within three or four 
 minutes of the surface of the sun, and therefore directly 
 through the midst of the corona. At the time of nearest ap- 
 proach its velocity was 350 miles per second, and it went with 
 nearly this velocity through at least 300,000 miles of corona, 
 coming out without having suffered any visible damage or 
 retardation. To form an idea what would have become of 
 it had it encountered the rarest conceivable atmosphere, we 
 have only to reflect that shooting-stars are instantly and com- 
 pletely vaporized by the heat caused by their encounter with 
 our atmosphere at heights of from 50 to 100 miles; that is, at 
 a height where the atmosphere entirely ceases to reflect the 
 light of the sun. The velocity of shooting-stars is from 20 to 
 40 miles per second. Remembering, now, that resistance and 
 heat increase at least as the square of the velocity, what would 
 be the fate of a body, or a collection of bodies like a comet, 
 passing through several hundred thousand miles of the rarest 
 
266 THE SOLAR SYSTEM. 
 
 atmosphere at a rate of over 800 miles a second? And how 
 rare must such an atmosphere be when the comet passes not 
 only without destruction, but without losing any sensible ve- 
 locity! Certainly so rare as to be entirely invisible, and inca- 
 pable of producing any physical effect. | 
 
 What, then, is the corona? Probably detached particles 
 partially or wholly vaporized by the intense heat to which 
 they are exposed. A mere dust-particle in a cubic mile of 
 space would shine intensely when exposed to such a flood of 
 light as the sun pours out on every body in his neighborhood. 
 The difficult question which we meet.is, How are these parti- 
 cles held up? To this question only conjectural replies can 
 be given. That the particles are not permanently held in one 
 position is shown by the fact that the form of the corona is 
 subject to great variations. In the eclipse of 1869, Dr. Gould 
 thought he detected variations during the three minutes the 
 eclipse lasted. The three conjectures that have been formed 
 on the subject are: 
 
 1. That the matter of the corona is in what we may call a 
 state of projection, being constantly thrown up by the sun, 
 while each particle thus projected falls down again according 
 to the law of gravitation. The difficulty we encounter here is 
 that we must suppose velocities of projection rising as high as 
 200 miles per second constantly maintained in every region 
 of the solar globe. 
 
 2. That the particles thrown out by the sun are held up a 
 greater or less time by electrical repulsion. We know that at- 
 mospheric electricity plays an active part in terrestrial mete- 
 orology ; and if electric action at the surface of the sun is pro- 
 portional to those physical and chemical actions which we 
 find to give rise to electrical phenomena here on the earth, 
 the development of electricity there must be on an enormous 
 scale. 
 
 3. That the corona is due to clouds of minute meteors cir- 
 culating around the sun in the immediate vicinity of that lu- 
 minary. 
 
 As already intimated, none of these explanations is much 
 
PHYSICAL CONSTITUTION OF THE SUN. 267 
 
 better than a conjecture, though it is quite probable that the 
 facts of the case are divided somewhere among them. 
 
 Next inside the corona lies the chromosphere. Here we 
 reach the true atmosphere of the sun, rising in general a few 
 seconds above his surface, but now and then projected up- 
 wards in immense masses which we might call flame, if the 
 word were not entirely inadequate to convey any conception 
 
 Fig. 70.—The sun, with its chromosphere and red flames, on July 23d, 1871, as drawn by 
 Secchi. The figures mark the flames, 17 in number. 
 of the enormous seale on which thermal action is there car- 
 ried on. What we call fire and flame are results of burn- 
 ing; but the gases at the surface of the sun are already so 
 hot that burning is not possible. Hydrogen is the principal 
 material of the upper part of the chromosphere; but, as we 
 descend, we find the vapors of a great number of metals, in- 
 cluding iron and magnesium. At the base, where the metals 
 are most numerous, and the density the greatest, occurs the 
 absorption of the solar rays which causes the dark lines in the 
 
268 THE SOLAR SYSTEM. 
 
 spectrum already described (p. 225). This seems satisfactori- 
 ly proved by an observation of Professor Young’s during the 
 eclipse of 1870, in Spain. At the moment of disappearance 
 of the last rays of sunlight, when he had a glimpse of the 
 base of the chromosphere, he saw all the spectral lines re- 
 versed ; that is, they were bright lines on a dark ground. The 
 vapors which absorb certain rays of the light which passes 
 through them from the sun then emitted those same rays 
 when the sunlight was cut off. 
 
 The most astonishing phenomena connected with the chro- 
 mosphere are those outbursts of its matter which form the pro- 
 tuberances. The latter are of two classes—the cloud-like and 
 the eruptive. The first class presents the appearance of clouds 
 floating in an atmosphere; but as no atmosphere dense enough 
 to sustain anything can possibly exist there, we find the same 
 difficulty in accounting for them that we do in accounting for 
 the suspension of the matter of the corona. In fact, of the 
 three conjectural explanations of the corona, two are inadmis- 
 sible if applied to the protuberances, since these cloud-like 
 bodies sometimes remain at rest too long to be supposed moy- 
 ing under the influence of the sun’s gravitation. This leaves 
 the electrical explanation as the only adequate one yet brought 
 forward. The eruptive protuberances seem to be due to the 
 projection of hydrogen and magnesium vapor from the region 
 of the chromosphere with velocities which sometimes rise to 
 150 miles a second. The eruption may continue for hours, or 
 even days, the vapor spreading out into great masses thousands 
 of miles in extent, and then falling back on the chromosphere. 
 
 Is it possible to present in language any adequate idea of 
 the scale on which natural operations are here carried on? If 
 we call the chromosphere an ocean of fire, we must remember 
 that it is an ocean hotter than the fiercest furnace, and as deep 
 as the Atlantic is broad. If we call its movements hurricanes,. 
 we must remember that our hurricanes blow only about a hun- 
 dred miles an hour, while those of the chromosphere blow as 
 far in a single second. They are such hurricanes as, “ coming 
 down upon us from the north, would, in thirty seconds after 
 
PHYSICAL CONSTITUTION OF THE SUN. 269 
 
 they had crossed the St. Lawrence, be in the Gulf of Mexico, 
 carrying with them the whole surface of the continent in a 
 mass, not simply of ruin, but of glowing vapor, in which the 
 vapors arising from the Eeolntion of the materials composing 
 the cities of Boston, New York, and Chicago would be mixed 
 in a single distin aie eer plonds Wien we speak of erup- 
 tions, we call to mind Vesuvius burying the surrounding cities 
 in Java; but the solar eruptions, thrown fifty thousand miles 
 high, would ingulf the whole earth, and dissolve every organ- 
 ized being on its surface in a moment. When the medieval 
 
 poets sung, 
 ‘¢ Dies ire, dies illa 
 Solvet szeclum in favilla,” 
 
 they gave rein to their wildest imagination, without reaching 
 any conception of the magnitude or fierceness of the flames 
 around the sun. 
 
 Of the corona and chromosphere the telescope ordinarily 
 shows us nothing. They are visible only during total eclipses, 
 or by the aid of the spectroscope. All we see with the eye or 
 the telescope is the shining surface of the sun called the pho- 
 tosphere, on which the chromosphere rests. It is this which 
 radiates both the light and the heat which reach us. The 
 opinions of students respecting the constitution of the photo- 
 sphere are so different that it is hardly possible to express any 
 views that will not be challenged in some quarter. Although 
 a contrary opinion is held by many, we may venture to say 
 that the rays of light and heat seem to come, not from a 
 gas, but from solid matter. This is indicated by the fact that 
 their spectrum is continuous, and also by the intensity of the 
 light, which far exceeds any that a gas has ever been made 
 to give forth. It does not follow from this that the photo- 
 sphere is a continuous solid or crust, since floating particles of 
 solid matter will shine in the same way. The general opinion 
 has been that the photosphere is of a cloud-like nature; that 
 is, of minute particles floating in an atmosphere of heated gases. 
 That it is not continuously solid like our earth seemed to be 
 fully shown by the variations and motions of the spots, which 
 
270 THE SOLAR SYSTEM. 
 
 have every appearance of going on in a fluid or gas. Indeed, 
 of late, some of the most eminent physicists regard it as pure- 
 ly gaseous, the pressure making it shine like a solid. 
 
 But this theory is attended with a difficulty which has not 
 been sufficiently considered. The photosphere is in striking 
 contrast to the gaseous chromosphere, in being subject to no 
 sensible changes of level. If it were gaseous, as supposed, 
 the solid particles having no connection with eacn other, we 
 should expect those violent eruptions which throw up the pro- 
 tuberances to carry up portions of it,so that it would now and 
 then present an irregular and jagged outline, as the chromo- 
 sphere does. But the most retined observations have never 
 shown it to be subject to the slightest change of level, or devi- 
 ation from perfect rotundity, except in the region of the spots, 
 where its continuity seems to be broken by immense chasm- 
 like openings. 
 
 The serene immobility of the photosphere, under such vio- 
 lent actions around it as we have described, lends some color 
 to the supposition that it is a solid crust which forms around 
 the glowing interior of the sun, or, at least, that it is composed 
 of a comparatively dense fluid resting upon such a crust. The 
 latter is the view of Zollner, who considers some sort of an 
 envelope between the exterior and the interior of the sun ab- 
 solutely necessary to account for the eruptive protuberances. 
 He places this solid envelope three or four thousand miles be- 
 low the surface of the photosphere. 
 
 Inside the photosphere we have the enormous interior 
 globe, 860,000 miles in diameter. The best-sustained theory 
 of the interior is the startling one that it is neither solid nor 
 liquid, but gaseous; so that our great luminary is nothing 
 more than an immense bubble. The pressure upon the inte- 
 rior portions of this mass is such as to reduce it to nearly the 
 density of a liquid; while the temperature is so high as to 
 keep the substances in a state which is between the liquid and 
 the gaseous, and in which no chemical action is possible. The 
 strong point in support of this gaseous theory of the sun’s in- 
 terior is, that it is the only one which explains how the sun’s 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 271 
 
 light and heat are kept up. How it does this will be shown 
 in treating of the laws which govern the secular changes of 
 the universe at large. 
 
 § 7. Views of Distinguished Students of the Sun on the Subject of 
 its Physical Oonstitution. 
 
 The progress of our knowledge of the sun during the past 
 ten years has been so rapid that only those can completely fol- 
 low it who make it the principal business of their lives. For 
 the same reason, the views respecting the sun entertained by 
 those who are engaged in studying it must be modified and 
 extended from time to time. The interest which necessarily 
 attaches to the physical source of all life and motion on our 
 globe renders the author desirous of presenting these views to 
 his readers in their latest form; and, through the kindness of 
 several of the most eminent investigators of solar physics now 
 living, he is enabled to gratify that desire. The following 
 statements are presented in the language of their respective 
 authors, except that, in the case of Messrs. Secchi and Faye, 
 they are translated from the French for the convenience of 
 the English reader. It will be noticed that in some minor 
 points they differ from each other, as well as from those which 
 the author has expressed in the preceding section. Such dif- 
 ferences are unavoidable in the investigation of so difficult a 
 subject. 
 
 Views of the Rev. Father Secchi.—*‘ For me, as for every one 
 else, the sun is an incandescent body, raised to an enormous 
 temperature, in which the substances known to our chemists 
 and physicists, as well as several other substances still unknown, 
 are in a state of vapor, heated to such a degree that its spec- 
 trum is continuous, either on account of the pressure to which 
 the vapor is subjected, or of its high temperature. This incan- 
 descent mass is what constitutes the photosphere. Its limit is 
 defined, as in the case of incandescent gases in general, by the 
 temperature to which the exterior layer is reduced by its free 
 radiation in space, together with the force of gravity exert- 
 ed by the body. The photosphere presents itself as composed 
 
 N 
 
 e 
 
272 THE SOLAR SYSTEM. 
 
 of small, brilliant granulations, separated by a dark net-work. 
 These granulations are only the summits of the flames which 
 constitute them, and which rise above the lower absorbing 
 layer, which forms the net-work, as we shall soon more clearly 
 see. 
 
 ‘“‘ Above the photospheric layer lies an atmosphere of a very 
 complex nature. At its base are the heavy metallic vapors, 
 at a temperature which, being less elevated, no longer permits 
 the emission of light with a continuous spectrum, although it 
 is sufficient to give direct spectra with brilliant lines, which 
 may be observed, during total eclipses of the sun, at its limb. 
 This layer is extremely thin, having a depth of only one or 
 two seconds of arc. According to the law of absorption laid 
 down by Kirchhoff, these vapors absorb the rays of the spec- 
 trum from the light of the photosphere which passes through 
 them, thus giving rise to the breaks known as the Fraunhofer 
 dark lines of the solar spectrum. These vapors are mixed 
 with an enormous quantity of hydrogen. This gas is present 
 in such a quantity that it rises considerably above the other 
 layer, and forms an envelope rising to a height of from ten 
 to sixteen seconds, or even more, which constitutes what we 
 call the chromosphere. This hydrogen is always mixed with 
 another substance, provisionally called heliwm, which forms the 
 yellow line D, of the spectrum of the protuberances, and with 
 another still rarer substance, which gives the green line 1474 
 k. This last substance rises to a much greater elevation than 
 the hydrogen; but it is not so easily seen in the full sun as 
 the latter. Probably there is some other substance not yet 
 well determined. Thus, the substances which compose this 
 solar envelope appear to be arranged in the order of their 
 density; but still without any well-defined separation, the dif- 
 fusion of the gases producing a constant mixture. 
 
 “This atmosphere becomes visible in total eclipses in the 
 form of the corona. It is very difficult to fix its absolute 
 height. The eclipses prove that it may reach to a height 
 equal to the solar diameter in its highest portions. 
 
 “No doubt it extends yet farther, and it may well be con- 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 273 
 
 nected with the zodiacal light. The visible layer of this at- 
 mosphere is not spherical; it is higher in middle latitudes, 
 near forty-five degrees, than at the equator. It is still more 
 depressed at the poles. At the base of the chromosphere, 
 the hydrogen has the shape of small flames composed of very 
 thin, close filaments which seem to correspond to the granu- 
 lations of the photosphere. During periods of tranquillity 
 the direction of these filaments is perpendicular to the solar 
 surface ; but during periods of agitation they are generally 
 more or less inclined, and often directed systematically tow- 
 ards the poles. 
 
 “The body of the sun is never in a state of absolute repose. 
 The various substances coming together in the interior of the 
 body tend to combine, in consequence of their affinity, and 
 necessarily produce agitations and interior movements of every 
 kind and of great intensity. Hence the numerous crises which 
 show themselves at the surface through the elevation of the 
 lower strata of the atmosphere by eruptions, and often by act- 
 ual explosions. Then the lower metallic vapors are projected 
 to considerable heights, hydrogen especially, at an elevation 
 visible in the spectroscope (in full sunlight) of one-fourth the 
 solar diameter. These masses of hydrogen, leaving the pho- 
 tosphere at a temperature higher than that of the atmosphere, 
 rise to the superior regions of the latter, remaining suspend- 
 ed, diffusing themselves at considerable elevations, and form- 
 ing what are called the prominences or protuberances. The 
 structure of the hydrogenous protuberances is entirely simi- 
 lar to that of fluid veins raising themselves from denser layers, 
 and diffusing in the more rare ones: but their extreme varia- 
 bility, even at the base, and the rapid changes of the place of 
 exit and diffusion, prove that they do not pass through any 
 orifice in a solid resisting layer. 
 
 “These eruptions are often mixed with columns of metallic 
 vapors of greater density, which do not attain the elevation 
 of the hydrogen, and of which the nature can be recognized 
 by the aid of the spectroscope: occasionally we see them fall- 
 ing back on the sun in the form of parabolic jets. The most 
 
274 THE SOLAR SYSTEM. 
 
 common substances are sodium, magnesium, iron, calcium, ete. 
 —indeed, the same substances which are seen to form the low, 
 absorbing layer of the solar atmosphere, and which by their 
 aosorption produce the Fraunhofer lines. A rigorous and in- 
 evitable consequence of these conditions is the fact that when 
 the mass thus elevated is carried by the rotation of the sun 
 between the photosphere and the eye of the observer, the ab- 
 sorption becomes very sensible, and produces a dark spot on 
 the photosphere itself. The metallic absorption lines are 
 then really wider and more diffused in this region; and if 
 the elevated mass is high and dense enough, we can even see 
 the re-reversal of the lines already reversed; that is to say, 
 we can see the bright lines of the substance itself on the back- 
 ground of the spot. This often happens for hydrogen, which 
 rises to a great height, and also with sodium and magnesium, 
 which metals have the rarest vapors. Here, then, we have the 
 origin of the solar spots. They are formed by masses of ab- 
 sorbing vapors which, brought out from the interior of the sun, 
 and interposed between the photosphere and the eye of the ob- 
 server, prevent a large part of the light from reaching our eyes. 
 
 “ But these vapors are heavier than the surrounding mass 
 into which they have been thrown. They therefore fall by 
 their own weight, and, tending to sink into the photosphere, 
 produce in it a sort of cavity or basin filled with a darker and 
 more absorbing mass. Hence the aspect of a cavity recognized 
 in the spots. If the eruption is instantaneous, or of very short 
 duration, this vaporous mass, fallen back on the photosphere, 
 soon becomes incandescent, reheated, and dissolved, and the 
 spot rapidly disappears; but the interior crises of the body of 
 the sun may be continued a long time; and the eruption may 
 maintain itself in the same place during two or more rotations 
 of the sun. Hence the persistence of the spots; for the cloud 
 can continue to form so long and so fast as the photosphere 
 dissolves it, as happens with the jets of vapor from our vol- 
 canoes. The eruptions, when about to terminate, may be re- 
 vived and reproduced several times near the same place, and 
 give rise to spots very variable in form and position. 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 275 
 
 “The spots are formed of a central region, called the nu- 
 cleus, or umbra, and of a surrounding part less dark, called 
 the penumbra. The latter is really formed of thin dark veils, 
 and of filaments or currents of photospheric matter which 
 tend to encroach upon the dark mass. These currents have 
 the form of tongues, often composed of globular masses look- 
 ing like strings of beads or willow leaves, and evidently are 
 only the grains of the photosphere precipitating themselves 
 towards the centre of the spot, and sometimes crossing it like 
 a bridge. 
 
 Fig. 71.—Illustrating Secchi’s theory of solar spots. 
 
 “In each spot we must distinguish three periods of exist- 
 ence: the first, of formation; the second, of rest; the third, 
 of extinction. In the first, the photospheric mass is raised 
 and distorted by a great agitation, often in the nature of a 
 vortex, which elevates it all around the flowing streams, and 
 forms irregular elevations, either without penumbra or with a 
 very irregular one. These irregular movements defy descrip- 
 tion: their velocities are enormous, and the agitated region 
 
276 THE SOLAR SYSTEM. 
 
 extends itself over several square degrees; but this upturn- 
 ing soon comes to an end, and the agitation slowly subsides, 
 and is succeeded by calm. In the second period, the agi- 
 tated and elevated mass falls back again, and tends to com- 
 bine in masses more or less circular; and to sink by its weight 
 into the surface of the photosphere. Hence the depressed 
 form of the photosphere, resembling a funnel, and the numer- 
 ous currents which come from each point of the circumference 
 to rush upon this obscure mass; but at the same time the con- 
 trast between it and the substance issuing still persists. The 
 spot takes a nearly stable and circular form, a contrast which 
 may last a long time—so long, in fact, as the interior actions of 
 the solar globe furnish new materials. At length, the latter 
 ceasing, the eruptive action languishes and is exhausted, and 
 the absorbing mass invaded on all sides by the photosphere is 
 dissolved and absorbed, and the spot disappears. 
 
 “The existence of these three phases is established by the 
 comparative study of the spots and eruptions. When a spot 
 is on the sun’s border during its first period, although the 
 dark region is invisible, its position is indicated by eruptions 
 of metallic vapors, if the spot be considerable. On the dark- 
 est ones the vapors of sodium, iron, and magnesium are seen 
 in the greatest quantity, and raised to great heights. A calm 
 and circular spot is crowned by beautiful facule and jets of 
 hydrogen and metallic vapors, very low, though quite brilliant. 
 A. spot which is on the point of closing up has no metallic 
 jets, and at the utmost only a few small jets of hydrogen, and 
 a more agitated and elevated chromosphere. Besides, obser- 
 vation teaches that the eruptions in general accompany the 
 spots, and that they are deficient at times when the spots are 
 wanting. ‘Thus the solar activity is measured by the double 
 activity of eruptions and spots which have a common source, 
 and the spots are really only a secondary phenomenon, de- 
 pending upon the eruptions and the more or less absorbing 
 quality of the materials: if the erupted materials were not 
 absorbent, we could see no spots at all. 
 
 “The eruptions composed simply of hydrogen do not pro- 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 27% 
 
 duce spots; thus they are seen on all points of the disk, while 
 the spots are limited to the tropical zones, where alone the 
 metallic eruptions appear. The eruptions of simple hydrogen 
 give rise to the facule. The greater brilliancy of the faculz 
 is due to two causes: the first is, the elevation of the photo- 
 sphere above the absorbing stratum of vapor which is very _ 
 thin (only one or two seconds of arc, as we have before said); 
 this elevated region thus escapes the absorption of the lower 
 stratum, and appears more brilliant. The other cause may be 
 that the hydrogen, in coming out, displaces the absorbing 
 stratum, and, taking the place of the metallic vapors, permits 
 a better view of the light of the photosphere itself. 
 
 “Thus, in conclusion, the spots are a secondary. phenomenon, 
 but, nevertheless, inform us of the violent crises which pre- 
 vail in the interior of the radiant globe. The frequency of 
 the spots corresponding to the frequency of eruptions, the two 
 phenomena, taken in connection, are the mark of solar activ- 
 ity. The spots occupy the zones on each side of the solar 
 equator, and rarely pass beyond the parallel of thirty degrees. 
 One or two seen at forty-five degrees are exceptions. That 
 parallel is therefore the limit of greatest activity of the body. 
 It is remarkable that the parallels of thirty degrees divide the 
 hemispheres into two sectors of equal volume. Beyond these 
 parallels we see faculee, but not true spots—or, at most, only 
 veiled spots indicative of a very feeble metallic eruption. 
 
 “Such a fluid mass, in which the parts are exposed to very 
 different temperatures, could not subsist without an interior 
 circulation. We do not yet know its laws; but the following 
 facts are well enough established: the zones of spots are not 
 fixed, but have a progressive motion from the equator towards 
 the poles. The spots, arrived at a certain high latitude, cease 
 to appear, but after some time reappear at lower latitudes, 
 and afterwards go on anew. Letween these phases of dis- 
 placement there is commonly a minimum of spots. During 
 periods of activity the protuberances have a dominant direc- 
 tion towards the pole, as also the flames of the chromosphere. 
 This indicates a general movement of the photosphere from 
 
278 THE SOLAR SYSTEM. 
 
 the equator to the poles. This movement is supported by the 
 displacement of the zones of eruption and of the protuber- 
 ances, which always seem to move towards the poles. 
 
 “Besides this movement in latitude, the photosphere has 
 also a movement in longitude, which is greatest at the equa- 
 tor. Thus the time of rotation of the body is different upon 
 different parallels, the minimum being at the equator. These 
 phenomena lead to the conclusion that the entire mass is af- 
 fected with a vortical motion which sets from the equator 
 towards the poles, in a direction oblique to the meridians. 
 The theory of these movements is still to be elaborated, and 
 is, no doubt, connected with the primitive mode in which the 
 sun was formed. 
 
 “The activity of the body is subject to considerable fluctu- 
 ations: the best established period is one of eleven and one- 
 third years, but the activity increases more rapidly than it di- 
 minishes—it increases about four years, and diminishes about 
 seven. ‘This activity is connected with the phenomena of ter- 
 restrial magnetism, but we cannot say in what way. We may 
 suppose a direct electro-magnetic influence of the sun upon 
 our globe, or an indirect influence due to the thermal action 
 of the sun, which reacts upon its magnetism. It is, indeed, 
 very natural to suppose that the ethereal mass which fills the 
 spaces of our planetary system may be greatly altered and 
 modified by the activity of the central body. But, whatever 
 may be the cause of these changes of activity, we are com- 
 pletely ignorant of them. The action of the planets has been 
 proposed as plausible, but it is far from being satisfactory. 
 The true explanation is reserved for the science which shall 
 reveal the nature of the connection which unites heat to elec- 
 tricity, to magnetism, and to the cause of gravity. 
 
 “ Of the interior of the sun we have no certain information. 
 The superficial temperature is so great, notwithstanding the 
 continual loss of heat which it suffers, that we cannot suppose 
 it less in the interior; and, consequently, no solid layer can ex- 
 ist there, except perhaps at depths where the pressure due to 
 gravity equals or surpasses the molecular dilatation produced 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 2%9 
 
 by temperature. However it may be, the layer accessible to 
 the exploration of our instruments is, no doubt, fluid and gase- 
 ous, and we can thus explain the variations of the solar diam- 
 eter established by certain astronomers. Notwithstanding these 
 small fluctuations, the radiation of the body info its planetary 
 system is nearly constant during widely separated periods, and 
 especially is it so during the historic period. This constancy 
 is due to several causes: first, to the enormous mass of the 
 body, which can be cooled only very slowly, owing to its very 
 high temperature; second, to the contraction of the mass, 
 which accompanies the condensation consequent upon the loss 
 of heat; third, to the emission of the heat of dissociation due 
 to the production of chemical actions which may take place 
 in the total mass. 
 
 “The origin of this heat is to be found in the force of grav- 
 ity; for it is well proved that the solar mass, by contracting 
 from the limits of the planetary system to its present volume, 
 would produce, not only its actual temperature, but one sev- 
 eral times greater. As to the absolute value of this tempera- 
 ture, we cannot fix it with certainty. Science not yet having 
 determined the relation which exists between molecular liv- 
 ing force (ves viva) and the intensity of radiation to a distance 
 (which last is the only datum given by observation), we find 
 ourselves in a state of painful uncertainty. Nevertheless, this 
 temperature must be several million degrees of our thermom- 
 eter, and capable of maintaining all known substances in a 
 state of vapor. 
 
 ‘** Rome, February 11th, 1877.” 
 
 Views of M. Faye.—“ In studying without any prepossession 
 the movements of the spots, we find, with Mr. Carrington, that 
 there exists a simple relation between their latitude and their 
 angular velocity. Nevertheless, this law does not suffice to 
 represent the observations with the exactitude which they ad- 
 mit of. It is still necessary to take account by calculation of a 
 parallax of depth which I estimate at +4, of the radius of the 
 sun, and of certain oscillations of very small extent, and of 
 long period, which the spots undergo perpendicular to their 
 
280 THE SOLAR SYSTEM. 
 
 parallels. Then the observations are represented with great 
 precision, from which I conclude that we have to deal with a 
 quite simple mechanical phenomenon. The law in question 
 can be expressed by the formula, 
 w=a—b sin’ d; 
 
 w being the angular velocity of a spot at the latitude A, and a 
 and 6 being constants, having the same value (a=857’.6 and | 
 6=157’.8) over the whole surface of the sun. These constants 
 may vary slowly with the time, but I have not studied their 
 variations. 
 
 “Admitting, as we shall see farther on, that the velocity of 
 a spot is the same as the mean velocity of that zone of the 
 photosphere in which it is formed, we see: 
 
 “1. That the contiguous strips of the photosphere are ani- 
 mated with a velocity of rotation nearly constant for each fila- 
 ment, at least during a period of several months or years, but 
 varying with the latitude from one strip to another. 
 
 “9, That these strips move nearly parallel to the equator, 
 and never give indications of currents constantly directed tow- 
 ards either pole, as in the upper regions of our atmosphere. 
 
 “3. That the spots are hollow, or at least that the black nu- 
 cleus is perceptibly depressed in respect to the photosphere. 
 
 “The diminution in the rate of superficial rotation, more 
 and more marked towards the poles, and the absence of all 
 motion from the equator, can only proceed from the vertical 
 ascent of materials rising incessantly from a great depth tow- 
 ards all points of the surface. It is sufficient that this depth 
 goes on increasing from the equator towards the poles, follow- 
 ing a law analogous to that of the rotation, in order that it 
 may produce at the surface a retardation increasing with the 
 latitude. This retardation is about two days in each rotation 
 at forty-five degrees of latitude. The mass of the sun, being 
 formed principally of metallic vapors condensable at a certain 
 temperature, and that temperature being reached at a certain 
 level in consequence of the exterior cooling, there ought to be 
 established a double vertical movement of ascending vapors, 
 which go to form a cloud of condensed matter susceptible of 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. -281 
 
 intense radiation, and of condensed products which fall back 
 in the form of rain into the interior. The latter are stopped 
 at the depth at which they meet a temperature high enough 
 to vaporize them anew, and afterwards force them to reascend. 
 As almost the entire mass of the sun partakes'of this double 
 movement, the heat radiated by the cloud will be borrowed 
 from this mass, and not from a superficial layer, the tempera- 
 ture of which would.rapidly fall, and which would soon con- 
 dense into a complete crust. Hence the formation and sup- 
 port of the photosphere, and the constancy and long duration 
 of its radiation, which is also partly fed by the ae contrac- 
 tion of the w Wire mass of the sun. 
 
 “The contiguous bands of the photosphere ae animated 
 with different velocities, there results a multitude of circular 
 gyratory movements around a vertical axis extending to a 
 great depth, as in our rivers and in the great upper currents 
 of our atmosphere. These whirlpools, which tend to equalize 
 the differences of velocity just spoken of, follow the currents 
 of the photosphere in the same way that whirlpools, and the 
 whirlwinds, tornadoes, and cyclones of our atmosphere follow 
 the upper currents in which they originate. Like these, they 
 are descending, as I have proved (against the meteorologists) 
 by a special study of these terrestrial phenomena. They carry 
 down into the depths of the solar mass the cooler materials of 
 the upper layers, formed principally of hydrogen, and thus 
 produce in their centre a decided extinction of light and heat 
 as long as the gyratory movement continues. Finally, the 
 hydrogen set free at the base of the whirlpool becomes re- 
 heated at this great depth, and rises up tumultuonsly around 
 the whirlpool, forming irregular jets which appear above the 
 chromosphere. ‘These jets constitute the protuberances. 
 
 “The whirlpools of the sun, like those on the earth, are of 
 all dimensions, from the scarcely visible pores to the enormous 
 spots which we see from time to time. They have, like those 
 of the earth, a marked tendency first to increase, and then to 
 break up, and thus form a row of spots extending along the 
 same parallel. The penumbra is due to a portion of the photo- 
 
282 THE SOLAR SYSTEM. 
 
 sphere which forms around their conical surface at a lower 
 level, on account of the lowering of the temperature produced 
 by the whirlpool. Sometimes in this sort of luminous sheath we 
 see traces of the whirling movement going on in the interior. 
 
 “It is more difficult to account for the periodicity of the 
 spots. It seems to me that it must depend upon fluctuations in 
 the form of the interior layer, to which the condensed matter 
 of the photosphere falls in the form of rain. This flow of 
 materials from above must alter, little by little, the velocity 
 of rotation of this layer. If its compression is changed in the 
 course of time, and if it becomes rounder, the variations in 
 the superficial velocity of the photosphere, as well as the gyra- 
 tory movements, will diminish in intensity and frequency. 
 
 “A time will at length arrive when the vertical movements 
 which feed the photosphere will become more and more hin- 
 dered. The cooling will then be purely superficial, and the 
 surface of the sun will harden into a continuous crust. 
 
 ‘¢ Paris, February, 1877.” 
 
 Views of Professor Young.—“1. It seems to me almost dem- 
 onstrated, as a consequence of the low mean density of the 
 sun and its great force of gravity, that the central portions of 
 that body, and, in fact, all but a comparatively thin shell near 
 the surface, must be in a gaseous condition, and the gases at 
 so high a temperature as to remain for the most part dissoci- 
 ated from each other, and incapable of chemical interaction. 
 Under the influence of the great pressure and high tempera- 
 ture, however, their density and viscosity are probably such as 
 to render their mechanical behavior more like that of such 
 substances as tar or honey than that of air, as we are famil- 
 iar with it. 
 
 “9. The visible surface of the sun, the photosphere, is com- 
 posed of clouds formed by the condensation and combination 
 of such of the solar gases as are cooled sufficiently by their 
 radiation into space. ‘These clouds are suspended in the mass 
 of uncondensed gases like the clouds in our own atmosphere, 
 and probably have, for the most part, the form of approximate- 
 ly vertical columns, of irregular cross-section, and a length 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 283 
 
 many times exceeding their diameter. The liquid and solid 
 particles of which they are made up descend continually, their 
 places being constantly supplied by fresh condensation from 
 the ascending currents which rise between the cloud-columns. 
 From the under-surface of the photosphere there must be an 
 immense precipitation of what may be called solar ‘rain and 
 snow, which descends into the gaseous core, and by the inter- 
 nal heat is re-evaporated, decomposed, and restored to its origi- 
 nal gaseous condition; the heat lost by the surface radiation 
 being replaced mainly by the mechanical work due to the 
 gradual diminution of the sun’s bulk, and the thickening of 
 the photosphere. I do not know any means of determining 
 the thickness of the photospheric shell, but, from the phenom- 
 ena of the spots, judge that it can hardly be less than ten 
 thousand miles, and that it may be much more. 
 
 “3. The weight of the cloud-shell, and the resistance offered 
 to the descending products of condensation, act to produce on 
 the enclosed gaseous core a constricting pressure, which forces 
 the gases upwards through the intervals between the clouds 
 with great velocity; so that jets or blasts of heated gas con- 
 tinually ascend all over the sun’s surface, the same material 
 subsequently redescending in the clond-columns, partly con- 
 densed into solid or liquid particles, and partly uncondensed, 
 but greatly cooled. It seems also not unlikely that in the up- 
 per part of the channels through which the ascending currents 
 rush, there may often occur the mixture of different ‘gases 
 cooled by expansion to temperatures sufficiently below the 
 dissociation point to allow of their explosive combination. 
 
 “4. The ‘chromosphere’ is simply the layer of uncondensed 
 gases which overlies the photosphere, though separated from 
 it by no definite surface. The lower portion of the chromo- 
 sphere is rich in all the vapors and gases which enter into the 
 sun’s composition; but at a comparatively small height the 
 denser and less permanent gases disappear, leaving in the up- 
 per regions only hydrogen and some other substances not as 
 yet identified. The dark lines of the solar spectrum originate 
 mainly in the absorption produced by the denser gases which 
 
284 THE SOLAR SYSTEM. 
 
 bathe the photospheric clouds, and these metallic vapors are 
 only occasionally carried into the upper regions by ascending 
 jets of unusual violence. When this occurs, it is almost in- 
 variably in connection with a solar spot. The prominences 
 are merely heated masses of the hydrogen and other chromo- 
 spheric gases, carried to a considerable height by the ascend- 
 ing currents, and apparently floating in the ‘coronal atmos- 
 phere,’ which interpenetrates and overtops the chromosphere. 
 “5. I do not know what to make of the corona. Its spec- 
 trum proves that a considerable portion of its light comes 
 from some exceedingly rare form of gaseous matter, which 
 cannot be identified with anything known to terrestrial chem- 
 istry; and this gas, whatever it may be, exists at a height of 
 not less than a million of miles above the solar surface, con- 
 stituting the ‘coronal atmosphere. Another portion of its 
 light appears to be simply reflected sunshine. But by what 
 forces the peculiar radiated structure of the corona is deter- 
 mined, I have no definite idea. The analogies of comets’ tails 
 - and auroral streamers both appear suggestive; but, on the other 
 hand, the spectra of the corona, the aurora borealis, the com- 
 ets, and the nebule are all different—no two in the least alike. 
 “6. As to sun-spots, there can be no longer any doubt, I 
 think, that they are cavities in the upper surface of the photo- 
 sphere, and that their darkness is due simply to the absorbing 
 action of the gases and vapors which fill them. It is also cer- 
 tain that very commonly, if not invariably, there is a violent 
 uprush of hydrogen and metallic vapors all around the outer 
 edge of the penumbra, and a considerable depression of the 
 chromosphere over the centre of the spot; probably, also, there 
 is a descending current through its centre. As to the cause 
 of the spots, and the interpretation of their telescopic details, 
 I am unsatisfied. The theory of Faye appears to me, on the 
 whole, the most reasonable of all that have yet been proposed ; 
 but I cannot reconcile it with the want of systematic rotation 
 in the spots, or their peculiar forms. Still, it undoubtedly has 
 important elements of truth, and may perhaps be modified so 
 as to meet these difficulties. As to the periodicity of the spots, 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 285 
 
 I am unable to think it due in any way to planetary action ; 
 at least, the evidence appears to me wholly insufficient as yet; 
 but I have no hypothesis to offer. Nor have I any theory to 
 propose to account for the certain connection between disturb- 
 ances of the solar surface and of terrestrial magnetism. 
 
 “7. As to the temperature of the sun’s surface, I have no 
 settled opinion, except that I think it must be much higher 
 than that of the carbon points in the electric light. The esti- 
 mates of those who base their calculations on Newton’s law of 
 cooling, which is confessedly a mere approximation, seem to 
 me manifestly wrong and exaggerated; on the other hand, the 
 very low estimates of the French physicists, who base their 
 calculations on the equation of Dulong and Petityseem to me 
 hardly more trustworthy, since their whole result depends 
 upon the accuracy of a numerical exponent determined by ex- 
 periment at low temperatures and under circumstances differ- 
 ing widely from those of the sun’s surface. The process is an 
 unsafe extrapolation. The sensible constancy of the solar 
 radiation seems to be fairly accounted for on the hypothesis 
 of slow contraction of the sun’s diameter. 
 
 “8. I look upon the accelerated motion of the sun’s equator 
 as the most important of the unexplained facts in solar phys- 
 ics, and am persuaded that its satisfactory elucidation will carry 
 with it the solution of most of the other problems still pending. 
 
 “Such, in brief, are my ‘opinions; but many of them I 
 hold with little confidence and tenacity, and anxiously await 
 more light, especially as regards the theory of the sun’s rota- 
 tion, the cause and constitution of the spots, and the nature of 
 the corona. The only peculiarity in my views lies, I think, 
 in the importance I assign to the effects of the descending 
 products of condensation, which I conceive to form virtually 
 a sort of constricting skin, producing pressure upon the gas- 
 eous mass beneath, something as the film of a bubble com- 
 presses the enclosed air. To the pressure thus produced I 
 ascribe mainly the eruptive phenomena of the chromosphere 
 and prominencees. 
 
 ‘*¢ Dartmouth College, March, 1877.” 
 
286 THE SOLAR SYSTEM. 
 
 Views of Professor Langley.—“ It seems to me that we have 
 now evidence on which to pass final adverse judgment on 
 views which regard the photosphere as an incandescent liquid, 
 or the spots as analogous either to scoriac matter, on the one 
 hand, or to clouds above the luminous surface, on the other. 
 According to direct telescopic evidence, the photosphere is 
 purely vaporous, and I consider these upper vapors to be 
 lighter than the thinnest cirri-of our own sky. The obser- 
 vation of faculee allies them and the whole ‘ granular’ cloud 
 structure of the surface most intimately with chromospheric 
 forms, seen by the spectroscope, and associates both with the 
 idea of an everywhere-acting system of currents which trans- 
 mit the internal heat, generated by condensation, to the sur- 
 face, and take back the cold, absorbent matter. This vertical 
 circulation goes to a depth, I think, sensible even by compari- 
 son with the solar diameter. It coexists with approximately 
 horizontal movements observed in what may be called the 
 successive upper photospheric strata in the vicinity of spots. 
 The spots give evidence of cyclonic action such as could only 
 occur in a fluid. Their darkness is due to the presence, in 
 unusual depth, of the same obscuring atmosphere which forms 
 the gray medium in which the Inminous photospheric forms 
 seem suspended, and which we here look through, where it 
 fills openings in the photospheric stratum, down to regions 
 of the solar interior made visible by the dim light of clouds 
 of luminous vapor, precipitated in lower strata where the dew- 
 point has been altered by changed conditions of temperature 
 and pressure. All observation and all legitimate inference 
 go to show that the sun is gaseous thronghout its mass, though 
 by this it is not meant to deny the probable precipitation of 
 cooling photospheric vapors in something analogous to rain; 
 a condition perhaps necessary to the maintenance of the equi- 
 librinm of the interchange of cold and heated matter between 
 exterior and interior; nor is it meant that the conditions of a 
 perfect fluid are to be expected, where these are essentially 
 modified (if by no other cause) by the viscosity due to extreme 
 heat. The temperature of the sun is, in my view, necessarily 
 
 a 
 
VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 287 
 
 much greater than that assigned by the numerous physicists, 
 who maintain it to be comparable with that obtainable in the 
 laboratory furnace; but we cannot confidently assign any up- 
 per limit to it until physics has advanced beyond its present 
 merely empirical rules connecting emission and temperature ; 
 for this, and not the lack of accurate data from physical 
 astronomy, is the source of nearly all the obscurity now at- 
 
 Fie. 72.—Solar spot, after Langley. 
 
 tending this important question. No theory of the solar con- 
 stitution which is free from some objection has yet been pro- 
 posed; but if the master-key to the diverse problems it pre- 
 sents has not been found, it is still true, I think, that the one 
 which unlocks most is that of M. Faye. 
 
 “ Of the potential energy of the sun, we may say that we 
 believe it to be sufficient for a supply of the present heat dur- 
 
 ing periods to be counted by millions of years. But what im- 
 20 
 
288 THE SOLAR SYSTEM. 
 
 mediately concerns us is the constancy of the rate of conver- 
 sion of this potential into actual radiant energy, as we receive 
 it, for on this depends the uniformity of the conditions under 
 which we exist. Now, this uniformity in turn depends on 
 the equality of the above-mentioned interchanges between the 
 solar surface and the interior, an equality of whose constancy 
 we know nothing save by limited experience. The most im- 
 portant statement with reference to the sun, perhaps, which 
 we can make with certainty is even a negative one. It is 
 that we have no other than empirical grounds, in the present 
 state of knowledge, for believing in the uniformity of the 
 solar radiation in prehistoric periods and in the future. 
 
 “The above remarks, limited as they are, appear to me to 
 cover nearly all the points as to the sun’s physical constitu- 
 tion (outside of the positive testimony of the spectroscope) on 
 which we are entitled to speak with confidence, even at the 
 present time.” 
 
THE PLANET MERCURY. 989 
 
 CHAPTER IIT. 
 
 THE INNER GROUP OF PLANETS. 
 
 § 1. The Planet Mercury. 
 
 Mercury is the nearest known planet to the sun, and the 
 smallest of the eight large planets. Its mean distance from 
 
 the sun is 40 millions of ery: 
 aun 
 ot 
 
 miles, and its diameter about 
 one-third that of the earth. 
 It was well known to the an- 
 cients, being visible to the 
 naked eye at favorable times, 
 if the observer is not in too 
 high a latitude. The central 
 and northern regions of Eu- 
 rope are so unfavorably sit- 
 uated for seeing it that it is 
 said Copernicus died without 
 ever having been able to ob- 
 
 , 4 . .~, “ia. 73.—Orbits of the four inner planets, il- 
 tain a view of iter het dite lustrating the eccentricity of those of Mercu- 
 
 culty of seeing it arises from = *Y 70 M8" 
 
 its proximity to the sun, as it seldom sets more than an hour 
 and a half after the sun, or rises more than that length of 
 time before it. Hence, when the evening is sufficiently ad- 
 vanced to allow it to be seen, it is commonly so near the hori- 
 zon as to be lost in the vapors which are seen in that direction. 
 Still, by watching for favorable moments, it can be seen sev- 
 eral times in the course of the year in any part of the United 
 States. The following are favorable times for seeing it after 
 sunset : 
 1882, Ce.cmeneners February 6th, June 1st, September 28th. 
 
 18832. iseresedeeneer January 21st, May 16th, September 7th. 
 L884. iy seaene eas January 5th, April 26th, August 19th, December 19th. 
 
290 THE SOLAR SYSTEM. 
 
 The corresponding times in subsequent years may be found 
 by subtracting 18 days from the dates for each year; that is, 
 they will occur 18 days earlier in 1885 than in 1884; 18 days 
 earlier in 1886 than in 1885, and so on. It is not necessary 
 to look on the exact days we have given, as the planet is gen- 
 erally visible for fifteen or twenty days at a time. Each date 
 given is about the middle of the period of visibility, which ex- 
 tends a week or ten days on each side. The best time for look- 
 ing is in the evening twilight, abont three-quarters of an hour 
 after sunset, the spring is in this respect much more favorable 
 than autumn. 
 
 Aspect of Mercury.—Mercury shines with a brilliant white 
 light, brighter than that of any fixed star, except, perhaps, 
 Sirius. It does not seem so bright as Sirius, because it can 
 never be seen at night except very near the horizon. Owing 
 to the great eccentricity of its orbit and the great variations of 
 its distance from the earth, its brilliancy varies considerably ; 
 but the favorable times we have indicated are near those of 
 greatest brightness. 
 
 Viewed with a telescope under favorable conditions, Mer- 
 cury is seen to have phases like the moon. When beyond the 
 sun, if seems round and small, being only about 5” in diame- 
 ter. When seen to one side of the sun, near its greatest ap- 
 parent angular distance, it appears like a half-moon. When 
 nearly between the sun and earth, its diameter is between 10” 
 and 12”, but only a thin crescent is visible. The manner in 
 which these various phases are connected with the position of 
 the planet relative to the earth and sun is the same as in the 
 case of Venus, and will be shown in the next section. 
 
 fotation, Figure, Atmosphere, etec.—About the beginning of 
 the present century Schrodter, the celebrated astronomer of 
 Lilienthal, who made the telescopic study of the planets a 
 speciality, thought that at times, when Mercury presented the 
 aspect of a crescent, the south horn of this crescent seemed 
 blunted at certain intervals. He attributed this appearance to 
 the shadow of a lofty mountain, and by observing the times 
 of its return was led to the conclusion that the planet revolved 
 
 ee 
 
TRANSITS OF MERCURY. 291 
 
 on its axis in 24 hours 5 minutes. He also estimated the 
 height of the mountain at twelve miles. But the more power- 
 ful instruments of modern times have not confirmed these 
 conclusions, and they are now considered as quite doubtful, if 
 not entirely void of foundation. That is, we must regard the 
 time of rotation of Mercury on its axis, and, of course, the 
 position of that axis, as not known with certainty, but as per- 
 haps very nearly 24 hours. 
 
 The supposed atmosphere of Mercury, the deviation of its 
 body from a spherical form, and many other phenomena 
 which observers have described, must be received with the 
 same scepticism. No deviation from a spherical form can be 
 considered as proved, the discordance of the measures showing 
 that the supposed deviations are really due to errors of obser- 
 vation. So, also, the appearances which many observers have 
 attributed to an atmosphere are all to be regarded as optical 
 illusions, or as due to the imperfections of the telescope made 
 use of. From measures of its light at various phases Zéllner 
 has been led to the conclusion that Mercury, like our moon, 
 is devoid of any atmosphere sufliciently dense to reflect the 
 hight of the sun. If this doubt and uncertainty seems surpris- 
 ing, it must be remembered that the nearness of this planet to 
 the sun renders it a very difficult object to observe with accu- 
 racy. We must look at it either in the daytime, when the air 
 is disturbed by the sun’s rays, or in the early evening, when the 
 planet is very near the horizon, and therefore in an unfavorable 
 situation. 
 
 Transits of Mercury.—Transits of this planet across the face 
 of the sun are much more frequent than those of Venus, the 
 average interval between successive transits being less than ten 
 years, and the longest interval thirteen years. These transits 
 are always looked upon with great interest by astronomers, on 
 account of the questions to which they have given rise. from 
 the earliest ages in which it was known that Mercury moved 
 around the sun, it was evident that it must sometimes pass be- 
 tween the earth and the sun; but its diameter is too small to 
 admit of its being seen in this position with the naked eye. 
 
292 THE SOLAR SYSTEM. 
 
 The first actual observation of Mercury projected on the face 
 of the sun was made by Gassendi, on November 7th, 1631. 
 His mode of observation was that already described for viewing 
 the solar spots, the image of the sun being thrown on a screen 
 by means of a small telescope. He came near missing his ob- 
 servation, owing to his having expected that the planet would 
 look much larger than it did. The imperfect telescopes of 
 that time surrounded every brilliant object with a band of 
 diffused light which greatly increased its apparent magni- 
 tude, so that Gassendi had no idea how small the planet really 
 was. 
 
 Gassendi’s observation was hardly accurate enough to be of 
 any scientific value at the present time. It was not till 1677 
 that a really good observation was made. Halley, of England, 
 in that year was on the island of St. Helena, and, being pro- 
 vided with superior instruments, was fortunate enough to make 
 a complete observation of a transit of Mercury over the sun 
 which occurred on November 7th. We have already men- 
 tioned the great accuracy which he attributed to his observa- 
 tion, and the phenomenon of the black drop which he was the 
 first to see. 
 
 The following are the dates at which it has been calculated 
 that transits of Mercury will occur during the remainder of 
 the present century. The first transit will be visible over the 
 whole United States, and the second on the Pacific coast. 
 
 SN Drowedecn sess ep tate? May 6th. TO Sic eussesastontan November 10th. 
 RBS asc avtt sees steers November 7th. | LG01C esocanancatee ves November 4th, 
 BOUL dvccdsestecat« May 9th 
 
 § 2. The Supposed Intra-Mercurial Planets. 
 
 At the present time the greatest interest which attaches to 
 transits of Mercury arises from the conclusion which Lever- 
 rier has drawn from a profound comparison of transits ob- 
 served before 1848 with the motion of Mercury as determined 
 from the theory of gravitation. This comparison indicates, 
 according to Leverrier, that the perihelion of Mercury moves 
 more rapidly by 40” a century than it ought to from the grav- 
 
THE SUPPOSED INTRA-MERCURIAL PLANETS. 293 
 
 itation of all the known planets of the system. He accounted 
 for this motion by supposing a group of small planets between 
 Mercury and the sun, and the question whether such planets 
 exist, therefore, becomes important. 
 
 Apparent support to Leverrier’s theory is given by the fact 
 that various observers have within the past century recorded 
 the passage over the disk of the sun of dark bodies which had 
 the appearance of planets, and which went over too rapidly or 
 disappeared too suddenly to be spots. But when we examine 
 these observations, we find that they are not entitled to the 
 slightest confidence. There is a large class of recorded as- 
 tronomical phenomena which are seen only by unskilful ob- 
 servers, with imperfect instruments, or under unfavorable cir- 
 cumstances. The fact that they are not seen by practised ob- 
 servers with good instruments is sufficient proof that there is 
 something wrong about them. Now, the observations of in- 
 tra-Mercurial planets belong to this class. Wolf has collected 
 nineteen observations of unusual appearances on the sun, ex- 
 tending from 1761 to 1865, but, with two or three exceptions, 
 the observers are almost unknown as astronomers. In at least 
 one of these cases the observer did not profess to have seen 
 anything like a planet, but only a cloud-like appearance. On 
 the other hand, for fifty years past the sun has been constant- 
 ly and assiduously observed by such men as Schwabe, Carring- 
 ton, Secchi, and Spoerer, none of whom have ever recorded 
 anything of the sort. That planets in such numbers should 
 pass over the solar disk, and be seen. by amateur observers, 
 and yet escape all these skilled astronomers, is beyond all 
 moral probability. 
 
 In estimating this probability we must remember that a 
 real planet appearing on the sun would be far more likely to 
 be recognized by a practised than by an unpractised observer, 
 much as a new species of plant or animal is more likely to be 
 recognized by a naturalist than by one who is not such. One 
 not accustomed to the close study of the solar spots might 
 have some difficulty in distinguishing an unusually round spot 
 from a planet. He is also liable to be deceived in various 
 
294 THE SOLAR SYSTEM. 
 
 ways.* For instance, the sun, by his apparent diurnal motion, 
 presents different parts of the edge of his disk to the hori- 
 zon in the course of a day; he seems, in fact, in the north- 
 ern hemisphere to turn round in the same direction with the 
 hands of a watch. Hence, if a spot is seen near the edge of 
 his disk it will seem to be in motion, though really at rest. 
 On the other hand, should an experienced observer see a planet 
 projected on the sun’s face, he could hardly fail to recognize it 
 in a moment; and should any possible doubt exist, it would be 
 removed by a very brief scrutiny. 
 
 The strongest argument against these appearances being 
 planets is, that the transit of a planet in such a position could 
 not be a rare phenomenon, but would necessarily repeat itself 
 at certain intervals, depending on its distance from the sun 
 and the inclination of its orbit. For instance, supposing an 
 inclination of 10°, which is greater than that of any of the 
 principal planets, and a distance from the sun one-half that 
 of Mercury, the planet would pass over the face of the sun, 
 on the average, about once a year, and its successive transits 
 would occur either very near the same day of the year, or on 
 a certain day of the opposite season. The supposed transits 
 to which we have referred occur at all seasons, and if we sup- 
 pose them real, we must suppose, as a logical consequence, 
 that the transits of these several planets are repeated many 
 times a year, and yet constantly elude the scrutiny of all good 
 observers, though occasionally seen by unskilled ones. This is 
 a sufficient reductio ad absurdum of the theory of their reality. 
 
 It is therefore certain that if the motion of the perihelion 
 of Mercury is due to a group of planets, they are each so small 
 as to be invisible in transit across the sun. It is, however, pos- 
 
 * Some readers may recall Butler’s sarcastic poem of the ‘‘ Elephant in the 
 Moon,” as illustrative of the possibility of an observer being deceived by some pe- 
 culiarity of his telescope. In one instance, about thirty years since, a telescopic 
 observation of something which we now know must have been flights of distant 
 birds over the disk of the sun was recorded, and published in one of the leading 
 astronomical journals, as a wonderful transit of meteors. ‘The publication was 
 probably not seriously intended, the description being a close parallel to that of 
 the satirical poet. See Astronomische Nachrichten, No. 549. 
 
 . 
 
THE PLANET VENUS. 995 
 
 sible that they might be seen during total eclipses, either in- 
 dividually as small stars, or in the aggregate as a cloud-like 
 mass of light. During the total eclipse of July 29th, 1878, 
 Professor J. C. Watson observed two objects which he consid- 
 ered to be such planets, but there was a known star in the 
 neighborhood of each object, and it is considered by some as- 
 tronomers that his observations may have been really made on 
 these stars. It is certain that even if the objects seen by Pro- 
 fessor Watson are intramercurial planets, they are too small 
 to influence the motion of Mercury. A mass three or four 
 times that of the latter planet is required to produce the ob- 
 served effect. The smaller we suppose the bodies the more 
 numerous they must be, and since telescopic observations seem 
 to show that most of them must be below the sixth magni- 
 tude, their number must be counted by thousands, and _ prob- 
 ably tens of thousands. Now, the zodiacal hight must arise 
 from matter revolving around the sun, and the question arises 
 whether this matter can be that of which we are in search. 
 One difficulty is, that unless we suppose the hypothetical group 
 of planetoids to move nearly in the plane of the orbit of Mer- 
 cury, they must change the node of that planet as well as its 
 perihelion. But no motion of the node above that due to the 
 action of the known planets has been found. We thus reach 
 the enforced conclusion that if the motion of the perihelion is 
 due to the cause assigned by Leverrier, the planetoids which 
 cause it must, in the mean, move in nearly the same plane 
 with Mercury. But it has not yet been shown that the axis 
 of the zodiacal light deviates from the ecliptic by so great an 
 angle as the orbit of Mercury, namely 7°. 
 
 § 3. The Planet Venus. 
 
 The planet Venus is very nearly the size of the earth, its di- 
 ameter being only about 300 miles less than that of our globe. 
 Next to the sun and moon, it is the most brilliant object in 
 the heavens, sometimes casting a very distinct shadow. It 
 never recedes more than about 45° from the sun, and is, there- 
 
 O 
 
296 THE SOLAR SYSTEM. 
 
 fore, seen by night only in the western sky in the evening, or 
 the eastern sky in the morning, according as it is east or west 
 of the sun. There is, therefore, seldom any difficulty in rec- 
 ognizing it. When at its greatest brilliancy, it can be clearly 
 seen by the naked eye in the daytime, provided that one knows 
 exactly where to look for it. It was known to the ancients by 
 the names of Hesperus and Phosphorus, or the evening and 
 the morning star, the former name being given when the 
 planet, being east of the sun, was seen in the evening after 
 sunset, and the latter when, being to the west of the sun, it 
 was seen in the east before sunrise. It is said that before the 
 birth of exact astronomy [Hesperus and Phosphorus were sup- 
 posed to be two different bodies, and that it was not until 
 their motions were studied, and the one was seen to emerge 
 from the sun’s rays soon after the other was lost in them, that 
 their identity was established. : 
 
 Aspect of Venus.—To the unaided eye Venus presents the 
 appearance of a mere star, distinguishable from other stars 
 only by its intense brilliancy. But when Galileo examined 
 this planet with his telescope, he found it to exhibit phases 
 like those of the moon. Desiring to take time to assure him- 
 self of the reality of his discovery, without danger of losing 
 his claim to priority through some one else in the mean time 
 making it independently, he published the following anagram, 
 in which it was concealed: 
 
 ‘Hee immatura a me jam frustra leguntur o. y.” 
 (These unripe things are now vainly gathered by me). 
 
 By transposing the letters of this sentence he afterwards 
 showed that they could be made into the sentence, 
 
 **Cynthiz figuras emulatur mater amorum” 
 (The mother of the loves imitates the phases of Cynthia). 
 
 That the disk of Venus was not round was first noticed by 
 Galileo in September, 1610. A computation of its position 
 at that time shows that it must have been a little gibbous, 
 more than half of its face being illuminated; but after a 
 
THE PLANET VENUS. 297 
 
 few months it changed into a crescent. Therefore Galileo 
 could not have found it necessary to wait long before explain- 
 ing his anagram. 
 
 The variations of the aspect and apparent magnitude of 
 Venus are very great. When beyond the sun, it is at a dis- 
 tance of 160 millions of miles, and presents the appearance 
 of a small round disk 10” in diameter. When nearest the 
 earth, it is only 25 millions of miles distant; and if its whole 
 face were visible, it would be more than 60” in diameter. 
 
 .@) .e) 
 
 © 
 © 
 
 9 
 
 ®) 
 
 Fie. 74.—Phases of Venus, showing apparent figure and magnitude of the bright and dark 
 portions of the planet in various points of its orbit. 
 
 But, being then on the same side of the sun with us, its dark 
 hemisphere is turned towards us, except, perhaps, an extreme- 
 ly thin crescent of the illuminated hemisphere. Between 
 these two positions it goes throngh all the intermediate 
 phases, the universal rule of which is that the nearer it is 
 to the earth, the smaller the proportion of its apparent disk 
 which is illuminated ; but the larger that disk would appear 
 could the whole of it be seen. Its greatest brilliancy occurs 
 between the time of its greatest elongation from the sun and 
 its inferior conjunction. 
 
 Supposed Rotation of Venus.—The earlier telescopists natu- 
 rally scrutinized the planets very carefully, with a view of find- 
 ing whether there were any inequalities or markings on their 
 surfaces from which the time of rotation on their axes could 
 be determined. In April, 1667, Cassini saw, or thought he 
 saw,a bright spot on Venus, by tracing which for several suc- 
 cessive evenings he found that the planet revolved in between 
 23 and 24 hours.. Sixty years later Blanchini, an Italian as- 
 
298 THE SOLAR SYSTEM. 
 
 tronomer, whose telescope is shown on page 112, supposed that 
 he found seven spots on the planet, which he considered to be 
 seas. By watching them from night to night, he concluded 
 that it required more than 24 days for Venus to revolve on 
 its axis. This extraordinary result was criticised by the sec- 
 ond Cassini, who showed that Blanchini, only seeing the plan- 
 et a short time each evening, and finding the spots night after 
 night in nearly the same position, concluded that it had moved 
 very little from night to night; whereas, in fact, it had made 
 a complete revolution, and a little more. At the end of 24 
 days it would be seen in its original position, but would have 
 made 25 revolutions in the mean time, instead of one only; as 
 Blanchini supposed. This would make the time of rotation 
 23 hours 24 minutes, while Cassini found 28 hours 15 minutes 
 from his father’s observations. 
 
 Between 1788 and 1798 Schréter applied to Venus a mode 
 of observation similar to that he used to find the rotation of 
 Mercury. Watching the sharp horns when the planet appear- 
 ed as a crescent, he thought that one of them was blunted at 
 certain intervals. Attributing this appearance to a high moun- 
 tain, as in the case of Mercury, he found a time of rotation 
 of 23 hours 21 minutes. 
 
 On the other hand, Herschel was never able to see any per- 
 manent markings on Venus. He thought he saw occasional 
 spots, but they varied so much and disappeared so rapidly that 
 he could not gather any evidence of the rotation of the plan- 
 et. He therefore supposed that Venus was surrounded by an 
 atmosphere, and that whatever markings might be occasional- 
 ly seen were due to clouds or other varying atmospheric phe- 
 nomena. 
 
 In 1842, De Vico, of Rome, came to the rescue of the older 
 astronomers by publishing a series of observations tending to 
 show that he had rediscovered the markings found by Blan- 
 chini more than a century before. He deduced for the time 
 of rotation of the planet 23 hours 21 minutes 22 seconds. 
 
 The best-informed astronomers of the present day look with 
 suspicion on nearly all these observations, being disposed to 
 
THE PLANET VENUS. 299 
 
 sustain the view of Herschel, though on grounds entirely dif- 
 ferent from those on which he founded it. It is certain that 
 there are plenty of observers of the present day, with instru- 
 ments much better than those of their predecessors, who have 
 never been able to see any permanent spots. The close agree- 
 ment between the times of rotation found by the older ob- 
 servers is indeed striking, and might seem to render it certain 
 that they must have seen spots which lasted several days. It 
 must also be admitted in favor of these observers that a fine 
 steady atmosphere is as necessary for such observations as a 
 fine telescope, and it is possible that in this respect the Italian 
 astronomers may be better situated than those farther north. 
 But the circumstance that the deduced times of rotation in 
 the cases both of Mercury and Venus differ so little from that 
 of the earth is somewhat suspicious, because if the appearance 
 were due to any optical illusion, or imperfection of the tele- 
 scope, it might repeat itself several days in succession, and 
 thus give rise to the belief that the time of rotation was near- 
 ly one day. The case is one on which it is not at present pos- 
 sible to pronounce an authoritative decision; but the balance 
 of probabilities is largely in favor of the view that the rota- 
 tation of Venus on its axis has never been seen or determined 
 by any of the astronomers who have made this planet an ob- 
 ject of study.* 
 
 Atmosphere of Venus.—The appearance of Venus when near- 
 ly between us and the sun affords very strong evidence of the 
 existence of an atmosphere. The limb of the planet farthest 
 from the sun is then seen to be illuminated, so that it appears 
 as a complete circle of light. If only half the globe of the 
 planet were illuminated by the sun, this appearance could 
 never present itself, as it is impossible for an observer to see 
 more than half of a large sphere at one view. There is no 
 
 * The latest physical observations on Venus with which I am acquainted are 
 those of Dr. Vogel at Bothkamp, in Part II. of the ‘‘ Bothkamp Observations” 
 (Leipzig, Engelmann, 1873). The result to which these observations point is that 
 the atmosphere of Venus is filled with clouds so dense that the solid body of the 
 planet can not be seen, and no time of rotation can be determined. 
 
300 THE SOLAR SYSTEM. 
 
 known way in which the sun can illuminate so much more 
 than the half of Venus as to permit a complete circle of light 
 to be seen except by the refraction of an atmosphere. 
 
 The appearance to which we allude was first noticed by 
 David Rittenhouse, of Philadelphia, while observing the tran- 
 sit of Venus on June 3d, 1769. When Venus had entered 
 about half-way upon the sun’s disk, so as to cut out a notch of 
 the form of a half-circle, that part of the edge of the planet 
 which was off the disk appeared illuminated so that the out- 
 line of the entire planet could be seen. As this appearance 
 was not confirmed by other observers, it seems to have excit- 
 ed no attention. But it was found by Madler in 1849 that 
 when Venus was near inferior conjunction, the visible crescent 
 extended through more than a half-circle. This showed that 
 more than half the globe of Venus was illuminated by the 
 sun, and Midler, computing the refractive power of the atmos- 
 phere which would be necessary to produce this effect, found 
 that it would exceed that of our own atmosphere; the hori- 
 zontal refraction being 44’, whereas on the earth it is only 
 34’, He therefore concluded that Venus was surrounded by 
 an atmosphere a little more dense than that of the earth. 
 
 The next important observation of the kind was made by 
 Professor O. 8. Lyman, of Yale College. In December, 1866, 
 Venus was very near her node at inferior conjunction, and 
 passed unusually near the line drawn from the earth to the 
 sun. Examining the minute crescent of the planet with a 
 moderate-sized telescope, he found that he could see the entire 
 circle of the planet’s disk, an exceedingly thin thread of light 
 being stretched round the side farthest from the sun. So far 
 as known, this was the first time that the whole circle of Venus 
 had been seen in this way since the time of Rittenhouse. It 
 is remarkable that both observations should have been made 
 by isolated observers in America. 
 
 Notwithstanding the concurrent testimony of Rittenhouse, 
 Madler, and Lyman, the bearing of their observations on what 
 was to be expected during the transit of Venus in December, 
 1874, was entirely overlooked. Accordingly, many of the ob- 
 
THE PLANET VENUS. 301 
 
 servers were quite taken by surprise to find that when Venus 
 was partly on and partly off the sun, the outline of that part 
 of her disk outside the sun could be distinguished by a deli- 
 cate line of light extending around it. In some cases the 
 time of internal contact at egress of the planet was missed, 
 through the observer mistaking this line of light for the limb 
 of the sun. | 
 
 That no one but Rittenhouse saw this line of hght during 
 the transit of 1769 is to be attributed to the low altitude of 
 the planet at most of the stations, and to the imperfect char- 
 acter of many of the instruments used. It is also to be re- 
 marked that the observers of that time had an erroneous no- 
 tion of the appearance which would be presented*by an atmos- 
 phere of Venus. It was supposed that the atmosphere would 
 give the planet a nebulous border when on the sun, caused by 
 the partial absorption of the light in passing through it. Cap- 
 tain Cook, at Otaheite, made separate observations of the 
 contacts of the supposed atmosphere and of the planet with 
 the limb of the sun. In fact, however, it would not be possi- 
 ble to see any indications of an atmosphere under such cir- 
 cumstances, for the reason that the light passing through its 
 denser portions would be refracted entirely out of its course, 
 so as not to reach an observer on the earth at all. 
 
 The spectroscope shows no indication that the atmosphere 
 of Venus exerts any considerable selective absorption upon 
 the light which passes through it. No new and well-marked 
 spectral lines are found in the light reflected from the planet, 
 nor has the spectrum been certainly found to differ from the 
 regular solar spectrum, except, perhaps, that some of the lines 
 are a little stronger. This would indicate that the atmosphere 
 in question does not differ in any remarkable degree from our 
 own, or, at least, does not contain gases which exert a power- 
 ful selective absorption on light. 
 
 Supposed Visibility of the Dark Hemisphere of Venus.—Many 
 astronomers of high repute have seen the dark hemisphere of 
 Venus slightly illuminated, the planet presenting the appear- 
 ance known as “the old moon in the new moon’s arms,” which 
 
302 THE SOLAR SYSTEM. 
 
 may be seen on any clear evening three or four days after the 
 change of the moon. It is well known that in the ease of 
 the moon her dark hemisphere is thus rendered visible by the 
 light reflected from the earth. But in the case of Venus, 
 there is no earth or other body large enough to shed so much 
 light on the dark hemisphere as to make it visible. There 
 being no sufficient external source of light, it has been attrib- 
 uted to a phosphorescence of the surface of the planet. If 
 the phosphorescence were always visible under favorable cir- 
 cumstances, there would be no serious difficulty in accepting 
 this explanation. But, being only rarely seen, it is hard to 
 conceive how any merely occasional cause could act all at 
 once over the surface of a planet the size of our globe, so as 
 to make it shine. Indeed, one circumstance makes it ex- 
 tremely difficult to avoid the conclusion that the whole ap- 
 pearance is due to some unexplained optical illusion. The 
 appearance is nearly always seen in the daytime or during 
 bright twilight—rarely or never after dark. But such an il- 
 lumination would be far more easily seen by night than by 
 day, because during the day an appearance easily seen at 
 night might be effaced by the light of the sky. If, then, the 
 phenomenon is real, why is it not seen when the circumstances 
 are such that it should be most conspicuously visible? This 
 is a question to which no satisfactory answer has been given, 
 and until it is answered we are justified in considering the ap- 
 pearance to be purely optical. 
 
 Supposed Satellite of Venus.—No better illustration of the er- 
 rors to which observations with imperfect instruments are lia- 
 ble can be given than the supposed observations of a satellite 
 of Venus, made when the telescope was still in its infancy. 
 In 1672, and again in 1686, Cassini saw a faint object near 
 Venus which exhibited a phase similar to that of the planet. 
 But he never saw it except on these two occasions. A similar 
 object was reported by Short, of England, as seen by him on 
 October 23d,1740. ‘The diameter of the object was a third 
 of that of Venus, and it exhibited a similar phase. Several 
 other observers saw the same thing between 1760 and 1764. 
 
THE PLANET VENUS. 303 
 
 One astronomer went so far as to compute an orbit from all 
 the observations; but it was an orbit in which no satellite of 
 Venus could possibly revolve unless the mass of the planet were 
 ten times as great as it really is. A century has now elapsed 
 without the satellite having been seen, and the fact that dur- 
 ing this century the planet has been scrutinized with better 
 telescopes than any which were used in the observations re- 
 ferred to affords abundant proof that the object was entirely 
 mythical. 
 
 How the observers who thought they saw the object could 
 have been so deceived it is impossible, at this distance of 
 time, to say with certainty. Had they been inexperienced, 
 we could say with some confidence that they were misled by 
 the false images produced to some extent in every telescope 
 by the light reflected from the cornea of the eye against the 
 nearest surface of the eye-piece, and thence back again into 
 the eye. Similar images are sometimes produced by the re- 
 flection of ight between the surfaces of the various lenses of 
 the eye- piece. They are well known to astronomers under 
 the name of “ ehosts;’ and one of the first things a young ob- 
 server must learn is to distinguish them from real objects. 
 They may also arise from a slight maladjustment of the lenses 
 of the eye-piece, and if, proceeding from this cause, they are 
 produced only when the actual object is in the centre of the 
 field, they may, for the moment, deceive the most experienced 
 observer.* If, in an ordinary achromatic telescope, in which 
 the interior curvatures of the lenses are the same, the latter 
 are not exactly at the same distance all the way round, a ghost 
 will be seen along-side of every bright object in all positions. 
 It is probable that all the observations alluded to were the re- 
 sults of some sort of derangements in the telescope, producing 
 false images by reflection from the glasses. 
 
 * One of the eye-pieces of the great Washington telescope shows a beautiful 
 little satellite along-side the planet Uranus or Neptune when the image of the 
 planet is brought exactly in the centre of the field of view, but it disappears as 
 soon as the telescope is moved. The writer was deceived by this appearance on 
 two occasions while scrutinizing these planets for close satellites. 
 
 21 
 
S04: * THE SOLAR SYSTEM. 
 
 § 4. The Earth. 
 
 Our earth is the third planet in the order of distance from 
 the sun, and slightly the largest of the inner group of four. 
 Its mean distance from the sun is about 924 millions of miles ; 
 but it is a million and a half less than this mean on January 
 Ist of every year, and as much greater on July Ist. That 
 is, its actual distance varies from 91 to 94 millions of miles. 
 As already remarked, these numbers are uncertain by several 
 hundred thousand miles. 
 
 Much of what we may call the astronomy of the earth— 
 such as its figure and mass, the length of the year, the obliq- 
 uity of the ecliptic, the causes of the changes in the seasons 
 and in the length of the days—has already been treated in 
 the chapter on gravitation, so that we have little of a purely 
 astronomical character to add here. The features of its sur- 
 face and the phenomena of its atmosphere belong rather to 
 geography and meteorology than to astronomy. But its consti- 
 tution gives rise to several questions in the treatment of which 
 astronomical considerations come into play. Prominent among 
 these is that of the state of the great interior mass of our 
 globe, whether solid or liquid. It is well known that wher- 
 ever we descend into the solid portions of the earth, we find a 
 rise in temperature, going on uniformly with the depth, at a 
 rate which nowhere differs greatly from 1° Fahrenheit in 50 
 feet. This rise of temperature has no connection with the 
 sea-level, but is found at all points of the surface, no matter 
 how elevated they may be. Wherever a difference of temper- 
 ature like this exists, there is necessarily a constant transfer of 
 heat from the warmer to the cooler strata by conduction. In 
 this way, the inequality would soon disappear by the warmer 
 strata cooling off, if there were not a constant supply of heat 
 inside the earth. The rise of temperature, therefore, cannot 
 be something merely superficial, but must continue to a great 
 depth. If we trace to past times the conditions which must 
 have existed in order that the increase might show itself at the 
 present time, we shall find it almost certain that, a thousand 
 
THE EARTH. 305 
 
 years ago, the whole earth was red-hot at a distance of ten or 
 fifteen miles below its surface; because otherwise its interior 
 could not have furnished the supply of heat which now causes 
 the observed increase. This being the case, it is probably red- 
 hot still, since it would be absurd to expect a state of things 
 like this to be merely temporary. In a word, we have every 
 reason to believe that the increase of say 100° a mile contin- 
 ues many miles into the interior of the earth. Then we shall 
 have a red heat at a distance of 12 miles, while, at the 
 depth of 100 miles, the temperature will be so high as to 
 melt most of the materials which form the solid crust of the 
 globe. 
 
 We are thus led to the theory, very generally received by 
 geologists, that the earth is really a sphere of molten matter 
 surrounded by a comparatively thin solid crust, on which we 
 live. This crust floats, as it were, on the molten interior. It 
 must be confessed that geological facts are, on the whole, fa- 
 vorable to this view. Observations on the pendulum have 
 been supposed to show that the specific 
 gravity of the earth under the great 
 mountain chains is generally less than in White hot, 
 the adjoining plains, which is exactly the 
 result that would flow from the theory. 
 The heavier masses, pressing upon the in- 
 terior fluid, would tend to elevate the sur- 
 rounding lighter masses, and when the two Fre.75.—Showing thickness 
 were in equilibrium, the latter would be Hae a emaitdlen oe 
 the higher, as a floating block of pine ty of a molten interior. 
 
 : : : The circle is thicker in 
 wood will rise higher out of the water  j,oportion than the solid 
 than a block of oak. Boiling springs in °™st. 
 many parts of the globe show that there are numerous hot re- 
 gions in the earth’s interior, and this heat cannot be merely 
 local, because then it would soon be dissipated. But the geol- 
 ogist finds the strongest proof of the theory in volcanoes and 
 earthquakes. The torrents of lava which have been thrown 
 out of the former through thousands of years show that there 
 are great volumes of molten matter in the earth’s interior, 
 
 or Molten 
 
 Interior 
 
306 THE SOLAR SYSTEM. 
 
 while the latter show this interior to be subject to violent 
 changes which a solid could not exhibit. 
 
 But mathematicians have never been able entirely to rec- 
 oncile the theory in question with the observed phenomena of 
 precession, nutation, and tides. ‘To all appearance, the earth 
 resists the tide-producing action of the sun and moon exactly 
 as if it were solid from centre to circumference. Sir William 
 Thomson has shown that if the earth were less rigid than steel, 
 it would yield so much to this action that the tides would be 
 much smaller than on a perfectly rigid earth; that is, the at- 
 traction of the bodies in question would draw the earth itself 
 out into an ellipsoidal form, instead of drawing merely the 
 waters of the ocean. arth and ocean moving together, we 
 could see no tides at all. If the earth were only a thin shell 
 floating on a liquid interior, the tides would be produced in 
 the latter; the thin shell went bend in such a way that the 
 tides in the ocean would be nearly neutralized. Again, the 
 question has arisen whether the liquid interior would be af- 
 fected by precession ; whether, in fact, the crust would not slip 
 over it, so that in time the liquid would rotate in one direc- 
 tion, and the crust in another. Altogether, the doctrine of the 
 earth’s fluidity is so fraught with difficulty that, notwithstand- 
 ing the seeming strength of the evidence in its favor, it must 
 be regarded as at least very doubtful. It may be added that 
 no one denies that the interior of our planet is intensely hot— 
 hot enough, in fact, to melt the rocks at its surface — but it 
 is supposed that the enormous pressure of the outer portions 
 tends to keep the inner part from melting. Nor is it ques- 
 tioned by Sir William Thomson that there are great volumes 
 of melted matter in the earth’s interior from which volcanoes 
 are fed; but he maintains that, after all, these volumes are 
 small compared with that of the whole earth. 
 
 Refraction of the Atmosphere.—If a ray of light pass through 
 our atmosphere in any other than a vertical direction, it is 
 constantly curved downwards by the refractive power of that 
 medium. ‘The more nearly horizontal the course of the ray, 
 the greater the curvature. In consequence of this, all the 
 
THE EARTH. 307 
 
 heavenly bodies appear a little nearer the zenith, or a little 
 higher above the horizon, than they actually are. The dis- 
 placement is too small to be seen by the naked eye except 
 quite near the horizon, where it increases rapidly, amounting 
 to more than half a degree at the horizon itself. Consequent- 
 ly, at any point where we have a clear horizon, as on a prairie, 
 or the sea-shore, the whole disk of the sun will be seen above 
 the horizon when the true direction is below it. A slight in- 
 crease is thus given to the length of the day. The sun in our 
 latitudes always rises three or four minutes sooner, and sets 
 three or four minutes later, than he would if there were no. 
 atmosphere. At the time of the equinoxes, if we suppose the 
 day to begin and end when the centre of the sun is on the 
 horizon, it is not of the same length with the night, but is six 
 or eight minutes longer. If we suppose the day to begin with 
 the rising of the sun’s upper limb, and not to end till the same 
 limb has set, then we must add some three minutes more to 
 its length. 
 
 If, standing on a hill, we watch the sun rise or set over the 
 ocean, one effect of refraction will be quite clearly visible. 
 When his lower limb almost seems to touch the water, it will 
 be seen that the form of his disk is no longer round, but ellip- 
 tical, the horizontal diameter being greater than the vertical. 
 The reason of this is that the lower limb is more elevated by 
 refraction than the upper one, and thus the vertical diameter 
 is diminished. 
 
 In practical astronomy, all observations of the altitude of 
 the heavenly bodies above the horizon must be corrected for 
 refraction, the true altitude being always less than that ob- 
 served. Very near the zenith the refraction is about 1” for 
 every degree, or 5,455 part the distance from the zenith. But 
 it increases at first in the proportion of the tangent of the ze- 
 nith distance, so that at 45°, or half-way between the zenith 
 and the horizon, it amounts to 60’; at the horizon it is 34’. 
 
 The Aurora Borealis—This phenomenon, though so well 
 known, is one of which great difficulty has been found in giv- 
 ing a satisfactory explanation. That it is in some way con- 
 
308 THE SOLAR SYSTEM. 
 
 d 
 
 Fie. 76.—Distribution of auroras, after Loomis. The darker the color, the more frequently 
 auroras are seen. 
 
 nected with the pole of the earth is shown by the fact that 
 its frequency depends on the latitude. In the equatorial re- 
 gions of our globe it is quite rare, and increases in frequency 
 as we go north. But the region of greatest frequency seems 
 
THE EARTH. | 309 
 
 to be, not the poles, but the neighborhood of the Arctic Cir- 
 cle, from which it diminishes towards both the north and the 
 south. This is shown more exactly in Professor Loomis’s 
 auroral map, of which we give a copy on the preceding page. 
 A close study of the aurora indicates that its connection is 
 not with the geographical, but with the magnetic pole. Two 
 distinct kinds of light are seen in the aurora; or we might 
 say that the light assumes two distinct forms, of which some- 
 times the one and sometimes the other preponderates. They 
 are as follows: ' 
 
 1. The cloud-like form. This consists of a large irregular 
 patch of light, frequently of a red or purple tinge. It is seen 
 in every direction, but more frequently in or near the northern 
 horizon, where it assumes the form of an arch or crown of 
 light. The two ends of the arch rest on the horizon, one on 
 each side of the north point. The middle of the arch rises a 
 few degrees above the horizon. 
 
 m | | 
 
 A ae i la ak 
 1 A | 
 
 Kaa: 
 
 9. The streamer or pillar form. This form consists of long 
 streamers or pillars, which extend in the direction of the dip- 
 ping magnetic needle. They look curved or arched, like the 
 celestial sphere on which they are projected, but they are re- 
 ally straight. They are in a state of constant motion. Some- 
 
310 THE SOLAR SYSTEM. 
 
 times they are spread out in the form of an immense flag 
 with numerous folds, dancing, quivering, and undulating, as 
 if moved by the wind. 
 
 Electric Nature of the Aurora.—There is abundant evidence 
 that the aurora is intimately connected with the electricity 
 and magnetism of the earth. During a brilliant aurora such 
 strong and irregular currents of electricity pass through the 
 telegraph wires that it is difficult to send a despatch. Some- 
 times the current runs with such force that a message may 
 be sent without a battery. The magnetic needle is also in a 
 state of great agitation. Before the spectroscope came into 
 use, these electric phenomena gave rise to the opinion that 
 the aurora was due entirely to currents of electricity passing 
 
 through the upper regions of the atmosphere from one pole to - 
 
 the other. But recent researches seem to show that, though 
 this view may be partly true, it is far from the whole truth, 
 and does not afford a complete explanation. The great height 
 of the aurora and the nature of its spectrum both militate 
 against it. 
 
 Height of the Aurora.—Several attempts have been made in 
 recent times to determine the height of the aurora above the 
 surface of the earth, by simultaneous observations of some 
 prominent streamer or patch of light from several far-distant 
 stations. The general result is that it extends to the height of 
 from 400 to 600 miles. But the evidence of shooting-stars 
 and meteors seems to indicate that the limit of the atmosphere 
 is between 100 and 110 miles in height. If it extends above 
 this, it must be too rare to condnet electricity long before it 
 reaches the greatest height of the aurora; indeed, it is doubt- 
 ful whether it does not attain this rarity at a height. of 40 or 
 50 miles. If, then, the aurora really extends to the great 
 height we have mentioned, and still exists in a gaseous medi- 
 um, it seems difficult to avoid the conclusion that this medium 
 is something far more ethereal than the gases which form our 
 atmosphere. It would, however, be unphilosophical to assume 
 the existence of such a medium without some other evidence 
 in its favor than that afforded by the aurora. We must in- 
 
 = 
 
THE EARTH. 311 
 
 clude the aurora among those things in which modern ob- 
 servations have opened up more difficulties than modern theo- 
 ries have explained. 
 
 Spectrum of the Aurora.—The spectrum of the aurora is so 
 far from uniform as to be quite puzzling. There is-one char- 
 acteristic bright line in the green part of the spectrum, known 
 as Angstrom’s line, from its first discoverer. This was the 
 only line Angstrom could see: he therefore pronounced the 
 light of the aurora to be entirely of one color. Subsequent 
 observers, however, saw many additional lines, but they were 
 different in different auroras. Among those who have made 
 careful studies of the aurora with the spectroscope are the 
 late Professor Winlock, of Harvard University; Professor 
 Barker, of Philadelphia; and Dr. H. C. Vogel, formerly of 
 Bothkamp. 
 
 Cc D E 6 F 
 Fie. 78.—Spectrum of two of the great auroras of 1871, after Dr. H. C. Vogel. 
 
 Fig. 78 shows the spectra of two auroras, as drawn by Dr. 
 Vogel. It will be seen that there is one fine bright line be- 
 tween PD and /£, which would fall in the yellowish-green part 
 of the spectrum, while the others are all broad, ill-defined 
 bands. Dr. Vogel notices a remarkable connection between 
 these lines and several groups of lines produced by the vapor 
 of iron, and inquires whether this vapor can possibly exist in 
 the upper regions of our atmosphere. A more complete study 
 of the spectra of vapors at different pressures and tempera- 
 tures is necessary before we can form a decided opinion as to 
 what the aurora really is. | 
 
312 THE SOLAR SYSTEM. 
 
 Of the supposed periodicity of the aurora, and its connection 
 with sun-spots, we have already spoken. Granting the reality 
 of this connection, we may expect that auroras will be very 
 frequent between the years 1880 and 1884; and if this ex- 
 pectation is realized, little doubt of the connection will remain. 
 
 § 5. The Moon. 
 
 The moon is much the nearest to us of all the heavenly 
 bodies; no other, except possibly a comet, ever coming nearer 
 than a hundred times her distance. Her mean distance is, in 
 round numbers, 240,000 miles. Owing to the ellipticity of her 
 orbit and the attractive force of the sun, it varies from ten to 
 twenty thousand miles on each side of this mean in the course 
 of each monthly revolution. The least possible distance is 
 221,000 miles; the greatest is 259,600 miles. It very rarely 
 approaches either of these limits, the usual oscillation being 
 about 13,000 miles on each side of the mean distance of 
 240,300. The diameter of the moon is 2160 miles, or some- 
 what less than two-sevenths that of the earth. Her volume is 
 about one-fiftieth that of the earth, and if she were as dense 
 as the latter, her mass would be in the same proportion. 
 
 Fig. 79.—Relative size of earth and moon, 
 But her actual mass is only about one-eightieth that of the 
 
 earth, showing that her density, or the specific gravity of the 
 material of which she is composed, is little more than half that 
 
THE MOON. 313 
 
 of our globe. Her weight is, in fact, about 34 times that of 
 her bulk of water. 
 
 The most remarkable feature of the motion of the moon is, 
 that she makes one revolution on her axis in the same time 
 that she revolves around the earth, and so always presents the 
 same face to us. In consequence, the other side of the moon 
 must remain forever invisible to human eyes. The reason of 
 this peculiarity is to be found in the ellipticity of her globe. 
 That she should originally have been set in revolution on her 
 axis with precisely the same velocity with which she revolved 
 around the earth, so that not the slightest variation in the re- 
 lation of the two motions should ever occur in the course of 
 ages, is highly improbable. If such had been the state of 
 things, the correspondence of the two motions could not have 
 been kept up without her axial rotation varying; because, 
 owing to the secular acceleration already described, the moon, 
 in the course of ages, varies her time of revolution, and so 
 the two motions would cease to correspond. But the effect of 
 the attraction of the earth upon the slightly elongated lunar 
 globe is such that if the two motions are, in the beginning, 
 very near together, not only will the axial rotation accommo- 
 date itself to the orbital revolution around the earth, but as 
 the latter varies, the former will vary with it, and thus the 
 correspondence will be kept up. 
 
 Figure, Rotation, and Lnbration of the Moon.—Supposing the 
 shape of the moon to be the same as if it were a fluid mass, 
 or covered by an ocean, it will be an ellipsoid with three un- 
 equal axes. ‘The shortest axis will be that around which it 
 revolves, which is not very far from being perpendicular to 
 the ecliptic. The next longest is that which lies in the direc- 
 tion in which the moon moves; while the longest of all is 
 that which points towards the earth. The reason that the 
 polar axis is the shortest is the same which makes the polar 
 axis of the earth the shortest, that is, the centrifugal force 
 generated by the revolution round that axis. If we consid- 
 ered only the action of this force, we should conclude that the 
 moon, like the earth, was an oblate spheroid, the equator be- 
 
314 THE SOLAR SYSTEM. 
 
 ing a perfect circle. But the attraction of the earth upon the 
 moon tends to elongate it in the direction of the line joining 
 the two bodies, in the same way that the attraction of the moon 
 upon the earth generates a tide-producing force which we have 
 already explained. At the centre of the moon the attraction 
 of the earth and the centrifugal force of the moon in its or- 
 bit exactly balance each other. But if we go to the farther 
 side of the moon, the centrifugal force will be greater, owing 
 to the larger orbit which that part of the moon has to de- 
 scribe, while the attraction of the earth will be less owing to 
 the greater distance of the particles it attracts. Hence, that 
 part of the moon tends to fly off from the centre and from the 
 earth. On this side of the moon the case is reversed, the at- 
 tractive force of the earth exceeding the centrifugal force of 
 those parts of the moon, whence those parts are impelled by a 
 force tending to draw them to the earth. The effect would 
 be much the same as if a rope were fastened to this side of 
 the moon, and constantly pulled towards the earth, while an- 
 other were fastened to the opposite side, and as constantly 
 pulled from the earth. Supposing the moon to be a liquid, 
 so as to yield freely, it is clear that the effect of these forces 
 would be to elongate her in the direction of the earth. 
 
 The deviations from a spherical form produced by these 
 causes are very minute. Taking the results of Lagrange and 
 Newton, the mean axis would be 463 feet longer than the 
 shortest one, and the longest 186 feet longer than the mean 
 one, or 2824 feet longer than the shortest one.* These differ- 
 ences are so much smaller than the average height of the 
 lunar mountains that the irregularities produced by the latter 
 might entirely overpower them; but the correspondence be- 
 tween the motions of rotation and revolution of the moon 
 shows that there must be, on the average, a real elongation in 
 
 * These numbers are, perhaps, not strictly correct. The extension of 186 feet 
 was deduced by Newton from a comparison of the distorting powers of the centrif- 
 ugal force of the earth with that of the force we have just described. He seems 
 to have overlooked the fact that the small density of the moon will cause the 
 elongation to be greater. 
 
 EE —— 
 
 CES ~ 
 
THE MOON. 315 
 
 the direction of the earth. This correspondence is kept up by 
 the slight additional attraction of the earth upon this extension 
 of the moon towards the earth, combined with the additional 
 centrifugal force of the extension on the other side. Although 
 these forces are not by any means the same as the distorting 
 forces already described, they may be represented in the same 
 way by two ropes, one of which pulls the protuberance on this 
 side towards the earth, while the other pulls the protuberance 
 on the other side from it. If the two protuberances do not 
 point exactly towards the earth, the effect of these two minute 
 forces will be to draw them very slowly into line. Conse- 
 quently, notwithstanding the slow variations to which the mo- 
 tion of the moon around the earth is subject in the course 
 of ages, the attraction of the earth will always keep this pro- 
 tuberant face turned towards us. Human eyes will never be- 
 hold the other side of the moon, unless some external force 
 acts upon her so as to overcome the slight balancing force 
 just described, and set her in more or less rapid motion on 
 her axis. If it is disappointing to reflect that we are for- 
 ever deprived of the view of the other side of our satellite, we 
 may console ourselves with the reflection that there is not the 
 slightest reason to believe that it differs in any respect from 
 this side. The atmosphere with which it has been covered, 
 and the inhabitants with which it has been peopled, are no 
 better than the products of a poetic imagination. 
 
 The forces we have just described as tending to keep the 
 same face of the moon pointed towards us would not produce 
 this effect unless the adjustment of the two motions—that 
 around the earth, and that on her axis—were almost perfect 
 in the beginning. If her axial rotation were accelerated by so 
 small an amount as one revolution in two or three years, there 
 is every reason to believe that she would keep on revolving at 
 the new rate, notwithstanding the force in question. The case 
 is much like that of a very easy-turning fly-wheel, which is 
 slightly weighted on one side. If we give the wheel a gentle 
 motion in one direction or another, the weight will cause the 
 wheel to turn till the heavy side is the lowest, and the wheel 
 
316 THE SOLAR SYSTEM. 
 
 will then vibrate very slowly on one side and the other of this 
 point. But if we give the wheel a motion rapid enough to 
 carry its heavy side over the highest point, then the weight 
 will accelerate the wheel while it is falling as much as it will 
 retard it while rising; and if there were no friction, the wheel 
 would keep on turning indefinitely. The question now arises, 
 How does it happen that these two motions are so exactly ad- 
 justed to each other that not only is the longer axis of the 
 _ moon pointed exactly towards the earth, but not the slightest 
 swing on one side or the other can be detected? That this 
 adjustment should be a mere matter of chance, without any 
 physical cause to produce it, is almost infinitely improbable, 
 while to suppose it to result from the mere arbitrary will of 
 the Creator is contrary to all scientific philosophy. But if the 
 moon were once in a partially fluid state, and rotated on her 
 axis in a period different from her present one, then the enor- 
 mous tides produced by the attraction of the earth, combmed 
 with the centrifugal force, would be accompanied by a fric- 
 tion which would gradually retard the rate of rotation, until 
 it was reduced to the point of exact coincidence with the rate 
 of revolution round the earth, as we now find it. We there- 
 fore see in the present state of things a certain amount of 
 probable evidence that the moon was once in a state of par- 
 tial fluidity. 
 
 The force we have just described as drawing the protuber- 
 aut portion of the moon towards the earth is so excessively 
 minute that it takes it a long time to produce any sensible ef- 
 fect; consequently, although the moon moves more rapidly in 
 some points of her orbit than in others, the force in question 
 produces no corresponding change in the moon’s rotation. 
 The protuberance does not, therefore, always point exactly at 
 the earth, but sometimes a little one side, and sometimes a lit- 
 tle the other, according as the moon is ahead of or behind her 
 mean place in the orbit. The result is, that the face which 
 the moon presents to us is not always exactly the same, there 
 being a slight apparent (not real) oscillation, due to the real 
 inequality in her orbital motion. This apparent swaying is 
 
THE MOON. ali 
 
 called libration, and in consequence of it there is nearly six- 
 tenths of the lunar surface which may, at one time or another, 
 come into view from the earth. 
 
 The Lunar Day.—In consequence of the peculiarity in the 
 moon’s rotation which we have described, the lunar day is 293 
 times as long as the terrestrial day. Near the moon’s equator 
 the sun shines without intermission nearly fifteen of our days, 
 and is absent for the same length of time. In consequence, 
 the vicissitudes of temperature to which the surface is exposed 
 must be very great. During the long lunar night the temper- 
 ature of a body on the moon’s surface would probably fall 
 below any degree of cold that we ever experience on the earth, 
 while during the day it must become hotter than anywhere 
 on our globe. 
 
 Astronomical phenomena, to an observer on the moon, would 
 exhibit some peculiarities. The earth would be an immense 
 moon, going throngh the same phases that the moon does to 
 us; but instead of rising and setting, it would only oscillate 
 back and forth through a few degrees. On the other side of 
 the moon it would never be seen at all. The diurnal motion 
 of the stars would take place in twenty-seven of our days, 
 much as they do here every day, while, as we have said, the 
 sun would rise and set in 294 of our days. 
 
 Geography of the Moon.— With the naked eye it is quite 
 readily seen that the brilliancy of the moon is far from uni- 
 form, her disk being variegated with irregular dark patches, 
 which have been supposed to bear a rude resemblance to a 
 human face. It is said to have been a fancy of some of the 
 ancient philosophers that the light and dark portions were 
 caused by the reflection of the seas and continents of the ter- 
 restrial globe, though it is hard to conceive of such an opin- 
 ion being seriously entertained. The first rude idea of the 
 real nature of the lunar surface was gained by Galileo with 
 his telescope. He saw that the brighter portions of the disk 
 were broken up with inequalities of the nature of mountains 
 and craters, while the dark parts were, for the most part, 
 smooth and uniform. Here he saw a striking resemblance to 
 
318 THE SOLAR SYSTEM. 
 
 the geographical features of our globe, and is said to have sng- 
 gested that the brighter and rougher portions might be conti- 
 nents, and the dark, smooth portions oceans. This view of the 
 resemblance to terrestrial scenery is commemorated in Mil- 
 ton’s description of Satan’s shield : 
 ‘¢ Like the moon, whose orb 
 Through optic glass the Tuscan artist views 
 At evening, from the top of Fesolé, 
 
 Or in Valdarno, to descry new lands, 
 Rivers, or mountains in her spotty globe.” 
 
 The opinion that the dark portions of the lunar disk were 
 seas was shared by Kepler, Hevelius, and Ricciolus. The last 
 two made maps of the moon in which they gave names to the 
 supposed seas, which names the regions still bear, though they 
 are strikingly fanciful. Among them are Oceanus Procella- 
 rum (the Ocean of Storms), Mare Tranquillitatis (Sea of Tran- 
 quillity), Mare Imbriwm (Rainy Sea), etc. The names of great 
 philosophers and astronomers were given to prominent feat- 
 ures, craters, etc. 
 
 If this resemblance between the earth and moon had been 
 established ; if it had been found that our satellite really had 
 seas and atmosphere, and was fitted for the support of or- 
 ganic life; still more, if any evidence of the existence of in- 
 telligent beings had been found, our interest in lunar geogra- 
 phy would have been immensely heightened. But the more 
 the telescope was improved, the more clearly it was seen that 
 there was no similarity between lunar and terrestrial scenery. 
 A very slight increase of telescopic power showed that there 
 was no more real smoothness in the regions of the supposed 
 seas than elsewhere. The inequalities were smaller and hard- 
 er to see on account of the darkness of color; but that was 
 all. ‘The sun would have been brilliantly imaged back from 
 the surfaces of the oceans in certain positions of the moon; 
 but nothing of the kind was ever seen. The polariscope 
 showed that the sun’s rays did not pass through any liquid at 
 the moon’s surface. Positive evidence of an atmosphere was 
 sought in vain. Supposed volcanoes were traced to bright 
 
THE MOON. 3819 
 
 spots, illuminated by light from the earth. Inequalities of 
 surface there were; but in form they were wholly different 
 from the mountains of the earth. So the beautiful fancies of 
 
 Fig. $0.—View of moon near the third quarter. From a photograph by Pio teReok Henry 
 Draper. 
 the earlier astronomers all faded away, leaving our satellite as 
 lifeless as an arid rock. 
 As the moon is now seen and mapped, the difference be- 
 tween the light and dark portions is due merely to a differ- 
 
 ence in the color of the material, much of which seems to be 
 Ue: 92 
 
320 THE SOLAR SYSTEM. 
 
 darker than the average of terrestrial objects. The mountains 
 consist, for the most part, of round saucer-shaped elevations, 
 the interior being flat, with small conical mounds rising here 
 and there. Sometimes there is a single mound in the centre. 
 It is very curious that the figures of these inequalities in the 
 lunar surface can be closely imitated by throwing pebbles 
 upon the surface of some smooth plastic mass, as mud or 
 mortar. They may be well seen during an eclipse of the sun, 
 when the contrast between the smoothness of the sun’s limb 
 and the roughness of that of the moon cannot escape notice. 
 Their appearance is most striking when the eclipse is annular 
 or total. In the latter case, as the last streak of sunlight is 
 disappearing, it is broken up into a number of points, which 
 have been known as “ Baily’s beads,” from the observer who 
 first described them, and which are caused by the sun shining 
 through the depressions between the lunar mountains. 
 
 To give the reader an idea what the formation of the lunar 
 surface is, we present a view of the spot or crater “ Coper- 
 nicus,” by Secchi, taken from the “ Memoirs of the Royal As- 
 tronomical Society,” vol. xxxii. The diameter of the central 
 portion, so much like a fort, is about 45 or 50 miles. 
 
 Among the most curious and inexplicable features of the 
 moon’s surface are the long narrow streaks of white material 
 which radiate from certain points, especially from the great 
 crater Tycho. Some of these can be traced more than a 
 thousand miles. The only way in which their formation has 
 been accounted for is by supposing that in some former age 
 immense fissures were formed in the lunar surface which were 
 subsequently filled by an eruption of this white matter which 
 forms the streaks. 
 
 Has the Moon an Atmosphere ?—This question may be an- 
 swered by saying that no evidence of a lunar atmosphere 
 entitled to any weight has ever been gathered, and that if 
 there is such an atmosphere, it is certainly not <j, part the 
 density of the earth’s atmosphere. The most delicate known 
 test of an atmosphere is afforded by the behavior of a star 
 when in apparent contact with the limb of the moon. In this 
 
THE MOON. $21 
 
 Fie. 81.—Lunar crater ‘‘ Copernicus,” after Secchi. 
 
 position the rays of light coming from the star would pass 
 through the lunar atmosphere, and be refracted by twice the 
 horizontal refraction of that atmosphere. The star would 
 then be apparently thrown out of its true position in the di- 
 rection from the moon’s centre by the amount of this double 
 refraction. But observations of stars in this position, at the 
 moment when the limb of the moon passes over them, have 
 never indicated the slightest displacement. It is certain that, 
 had the displacement been decidedly in excess of half a sec- 
 ond, it would have been detected; therefore, the double hori- 
 zontal refraction of the lunar atmosphere, if any exist, must 
 be as small as half a second.* The corresponding refraction 
 of the earth’s atmosphere is 4000 seconds. Therefore, the re- 
 
 * A similar test is afforded by the occultation of a planet, especially Saturn or 
 Venus, the limb of which would be a little flattened as it touched the moon. The 
 writer looked very carefully for this appearance during an unusually favorable oc- 
 cultation of Saturn which occurred on Aug. 6th, 1876, without seeing a trace of it. 
 
322 THE SOLAR SYSTEM. 
 
 fractive power of the lunar atmosphere cannot be much in ex- 
 cess of gyby that of the earth’s, and certainly falls below zy4o5. 
 
 Without an atmosphere no water or other volatile fluid can 
 exist on the moon, because it would gradually evaporate and 
 form an atmosphere of its own vapor.. The evaporation would 
 not cease till the pressure of the vapor became equal to its 
 elastic force at the mean temperature of the moon. If this 
 temperature were as low as the freezing-point, the pressure of 
 an atmosphere of water vapor would be +$> that of our at- 
 mosphere. So dense an envelope could not fail of detection 
 with our present means of observation. 
 
 The question whether any change is taking place on the 
 surface of the moon is one of interest. Hitherto, the pre- 
 ponderance of evidence has been against the idea of any 
 change. It is true that a few years ago there was a great 
 discussion in the astronomical world about a supposed change 
 in the aspect of the spot Linneeus, which was found not to 
 present the same appearance as on Beer and Miidler’s map. 
 But careful scrutiny showed that, owing to some peculiarity 
 of its surface, this spot varied its aspect according to the 
 manner in which it was illuminated by the sun, and these 
 variations appear to be sufficient to account for the supposed 
 change. To whatever geological convulsions the moon may 
 have been subjected in ages past, it seems as if she had now 
 reached a state in which no further change was to take place, 
 unless by the action of some new cause. This will not seem 
 surprising if we reflect what an important part the atmosphere 
 plays in the changes which are going on on the surface of the 
 earth. The growth of forests, the formation of deltas, the 
 washing-away of mountains, the disintegration and blacken- 
 ing of rocks, and the decay of buildings, are all due to the 
 action of air and water, the latter acting in the form of rain. 
 Changes of temperature powerfully re-enforce the action of 
 these causes, but are not of themselves sufficient to produce 
 any effect. Now, on the moon, there being neither air, wa- 
 ter, rain, frost, nor organic matter, the causes of disintegra- 
 tion and decay are all absent. A marble building erected 
 
THE MOON. 3823 
 
 upon the surface of the moon would remain century after 
 century just as it was left. It is true that there might be 
 bodies so friable that the expansions and contractions due to 
 the great changes of temperature to which the surface of the 
 moon is exposed would cause them to crumble. But whatev- 
 er crumbling might thus be caused would soon be done with, ° 
 and then no further change would occur. 
 
 Laght and Heat of the Moon.—That the sun is many times 
 brighter than the moon is evident to the eye; but no one 
 judging by the unaided eye would suppose the disparity to be 
 so great as it really is. It is found by actual trial that the 
 hight of the sun must be diminished several hundred thousand 
 times before it becomes as faint as the full moon. The results 
 of various experiments range between 300,000 and 800,000. 
 Professor G. B. Bond, of Cambridge, found the ratio to be 
 470,000. The most careful determination yet made is by 
 Zollner, who finds the sun to give 619,000 times as much 
 light as the full moon. This result is probably quite near 
 the truth. 
 
 The moon does not shine by sunlight alone. Whenever 
 the narrow crescent of the new moon is seen through a clear 
 atmosphere, her whole surface may be plainly seen faintly il- 
 Iuminated. This appearance is known as “the old moon in 
 the new moon’s arms.” The faint light thus shed upon the 
 dark parts of the moon is reflected from the earth. An ob- 
 server on the moon would see the earth in his sky as a large 
 moon, much larger than the moon is seen by us. When it is 
 new moon with us, it would be full earth, if we may be allowed 
 the term, to an observer on this side of the moon. Hence, 
 under those circumstances, most of the lunar hemisphere hid- 
 den by the sun is illuminated by earth-light, or by sunlight re- 
 flected by the earth, and is thus rendered visible. The case 
 is the same as if an observer on the moon should see the dark 
 hemisphere of the earth by the light of the full moon. 
 
 As the moon reflects the light of the sun, so also must she 
 reflect his heat. Besides, she must radiate off whatever heat 
 she absorbs from the sun. Hence, we must receive some heat 
 
324 THE SOLAR SYSTEM. 
 
 from the moon, though calculation will show the quantity to 
 be so small as to defy detection with the most delicate ther- 
 mometer, the average quantity being only sgo'so part of that 
 received from the sun. As the direct rays of the sun will not 
 raise the black-bulb thermometer more than 50 or 60 degrees 
 above the temperature of the air, those of the moon cannot 
 raise it more than zjy55 of a degree. By concentrating the 
 rays in the focus of a telescope of large aperture and compar- 
 atively short focal length, the temperature might be increased 
 a hundred times or more; but even then we should only have 
 an increase of = of a degree. Even this increase might be 
 unattainable, for the reason that the heat radiated by the 
 moon would not pass through glass. It is, therefore, only 
 since the discovery of thermo-electricity and the invention of 
 the thermo-electric pile that the detection of the heat from 
 the moon has been possible. The detection is facilitated by 
 using a reflecting telescope to concentrate the lunar rays, 
 because the moon is not hot enough to radiate such heat as 
 will penetrate glass. Lord Rosse and M. Marie- Davy, of 
 Paris, have thus succeeded in measuring the heat emanating 
 from the moon. The former sought not merely to determine 
 the total amount of heat, but how much it varied from one 
 phase of the moon to the other, and what portion of it was 
 the reflected heat of the sun, and what portion was radiated 
 by the moon herself, as if she were a hot body. He found 
 that from new to full moon, and thence round to new moon 
 again, the quantity of heat received varied in the same way 
 with the quantity of light; that is, there was most at full- 
 moon, and scarcely any when the moon was a thin crescent. 
 That only a small proportion of the total heat emitted was the 
 reflected heat of the sun, was shown by the fact that while 86 
 per cent. of solar heat passes through glass, only 12 per cent. 
 of lunar heat does so. This absorption by glass is well known 
 to be a property of the heat radiated by a body which is not 
 itself at a high temperature. The same result was indicated 
 in another way, namely, that while the sun is found by Zoll- 
 ner to give 618,000 times as much light as the moon, it only 
 
THE MOON. 325 
 
 gives 82,600 times as much heat. Thus both the ratio of solar 
 to lunar heat,and the proportion of the latter which is ab- 
 sorbed by glass, agree in indicating that about six-sevenths of 
 the heat receiv ed from the moon is radiated by the latter, 
 owing to the veneer of her surface produced by the ab- 
 sorption of the sun’s rays. 
 
 Lord Rosse was thus enabled to estimate the change of 
 temperature of the moon’s surface according as it was are 
 towards or from the sun, and found it to be more than 500° 
 Fahrenheit. But there was no way of determining the tem- 
 peratures themselves with exactness. Probably when the sun 
 does not shine the temperature is two or three hundred de- 
 grees below zero, and therefore below any ever, known on the 
 earth; while under the vertical sun it is as much above zero, 
 and therefore hotter than boiling water. 
 
 Liffect of the Moon on the Harth.—We have already explained, 
 in treating of gravitation, how the attraction of the moon 
 causes tides in the ocean. This is one of the best-known ef- 
 fects of lunar attraction. It is known from theory that a sim- 
 ilar tide is produced in the air, affecting the height of the ba- 
 rometer; but it is so minute as to be entirely masked by the 
 changes constantly going on in the atmospheric pressure from 
 other causes. There is also reason to believe that the occur- 
 rence of earthquakes may be affected by the attraction of the 
 moon; but this is a subject which needs further investiga- 
 tion before we can pronounce with certainty on a law of con- 
 nection. 
 
 Thus far there is no evidence that the moon directly affects 
 the earth or its inhabitants in any other way than by her at- 
 traction, which is so minute as to be entirely insensible except 
 in the ways we have described. A striking illustration of the 
 fallibility of the human judgment when not disciplined by sci- 
 entific training is afforded by the opinions which have at vari- 
 ous times obtained currency respecting a supposed influence 
 of the moon on the weather. Neither in the reason of the 
 case nor in observations do we find any real support for such 
 a theory. It must, however, be admitted that opinions of this 
 
326 THE SOLAR SYSTEM. 
 
 character are not confined to the uneducated. In scientific 
 literature several papers are found in which long series of me- 
 teorological observations are collated, which indicate that the 
 mean temperature or the amount of rain had been subject to 
 a slight variation depending on the age of the moon. But 
 there was no reason to believe that these changes arose from 
 any other cause than the accidental vicissitudes to which the 
 weather is at all times subject. There is, perhaps, higher au- 
 thority for the opinion that the rays of the full moon clear 
 away clouds; but if we reflect that the effect of the sun it- 
 self in this respect is not very noticeable, and that the full 
 moon gives only zotoo Of the heat of the sun, this opinion 
 will appear extremely improbable. 
 
 § 6. The Planet Mars. 
 
 The fourth planet in the order of distance from the sun, 
 and the next one outside the orbit of the earth, is Mars. Its 
 mean distance from the sun is about 141 millions of miles. 
 The eccentricity of its orbit is such that at perihelion it is only 
 128 millions of miles from the sun, while in aphelion it is 154 
 millions distant. It is, next to Mercury, the smallest of the 
 primary planets, its diameter being little more than 4000 
 miles. It makes one revolution in its orbit in less than two 
 years (more nearly in 687 days, or 4384 days short of two Ju- 
 lian years). If the period were exactly two years, it would 
 make one revolution while the earth made two, and the oppo- 
 sitions would occur at intervals of two years. But, going a 
 little faster than this, it takes the earth, on the average, fifty 
 days over the two years to catch up to it. The times of oppo- 
 sition are shown in the following table: 
 
 1875....June 20th. 1879....November 12th. | 1884.... January 31st. 
 1877....September 5th. | 1881....December 26th. | 1886.... March 6th. 
 
 The times of several subsequent oppositions may be found 
 with sufficient exactness for the identification of the planet by 
 adding two years and two months for every opposition, except 
 during the spring months, when only one month is to be 
 
THE PLANET MARS. So 
 
 added.  Oppositions will occur in April, 1888, and May, 1890. 
 At the times of opposition Mars rises when the sun sets, and 
 may be seen during the entire night. 
 
 Aspect of Mars.—Mars is easily recognized with the naked 
 eye when near its opposition by its fiery-red light. It is much 
 more brilliant at some oppositions than at others, but always 
 exceeds an ordinary star of the first magnitude. The varia- 
 tions of its brilliancy arise from the eccentricity of its orbit, 
 and the consequent variations of its distance from the earth 
 and the sun. The perihelion of Mars is in the same longitude 
 in which the earth is on August 27th; and when an opposition 
 occurs near that date, the planet is only 35 millions of miles 
 from the earth. This is about the closest approach which the 
 two planets can ever make. When an opposition occurs in 
 February or March the planet is near its aphelion—154 mill- 
 ions of miles from the sun and 62 millions from the earth. 
 The result of these variations of distance is that Mars is more 
 than four times brighter when an opposition occurs in August 
 or September than when it occurs in February or March. The 
 opposition of 1877 (September 5th) was quite remarkable in 
 this respect, as it occurred only 9 days after the planet passed 
 its perihelion. The near approach to the earth at this time is 
 rendered memorable by the discovery of two satellites. 
 
 Mars has been an interesting object of telescopic research 
 from the fact that it is the planet which exhibits the greatest 
 analogy with our earth. The equatorial regions, even with a 
 small telescope, can be distinctly seen to be divided into light 
 and dark portions, which some observers suppose to be conti- 
 nents and oceans. Around each pole is a region of brilliant 
 white, which the same class of astronomers suppose to be due 
 to a deposit of snow. The outlines of the dark and light por- 
 tions are sometimes so hard to trace as to give rise to the sus- 
 picion of clouds in a Martial atmosphere. At the same time, 
 a single look at Mars through a large telescope would convince 
 most observers that these resemblances to our earth have a 
 very small foundation in observation, the evidence being neg- 
 ative rather than positive. It must be said in their favor that 
 
328 THE SOLAR SYSTEM. 
 
 if our earth were viewed at the distance at which we view 
 Mars, and with the same optical power, it would present a 
 similar telescopic aspect. But it is also possible that if the 
 
 ‘i < 
 
 optical power of our tele- 
 scopes were so increased 
 that we could see Mars as 
 from a distance of a thou- 
 sand miles, the resemblances 
 would all vanish as com- 
 pletely as they did in the 
 case of the moon. 
 Ha So many drawings of 
 | Mars in various positions 
 li ll have been made by the nu- 
 merous observers who have 
 Fia. 82.—The planet Mars Or ie cee studied te that it has be- 
 hours 45 minutes, as seen by Professor Holden CONC possible to construct 
 with the great Washington telescope. tolerably accurate maps of 
 the surface of the planet. We give a copy of one of these 
 sets of maps by Kaiser, the late Leyden astronomer. Kaiser 
 does not pretend to call the different regions continents and 
 oceans, but merely designates them as light and dark portions. 
 
 then 
 
 as 
 SSS 
 
 40 30 20 $0 O 350 3¢0 330 320 310 300 290 280 270 260 250 240 230 290 210 200 190 180 170 100 150 14.0 730 120 770 700 90 80 70 60 50 LO 30 20 70 0 
 
 Steereees 
 
 os 07 Of 02 OL O Of OF OF OF OF 
 ee RU PT RARE REE 
 50 60 20 20 10 0 10 20 30 40 50 
 
 { 1 
 40 80 20 10 0 950 340 330320 Fi0 300 290 280 270 260 25U 240 230 220 210 200 19U 180 7470 100 750 160 730 120 110 100 90 80 FW 60 5040 20 20 10 O 
 
 Fie. 83.—Map of Mars, after Kaiser, on Mercator’s projection. 
 
 Rotation of Mars.—Mars is the only planet besides the earth 
 of which we can be sure that the time of axial rotation ad- 
 mits of being determined with entire precision. Drawings by 
 Hooke, two centuries ago, exhibit markings which can still be 
 recognized, and from a comparison of them with recent ones 
 Mr. Proctor has found for the period of rotation 24 hours 37 
 
 ne 
 
THE PLANET MARS. 329 
 
 minutes 22.73 seconds, which he considers correct within three 
 or four hundredths of a second. The equator of Mars is in- 
 clined to the plane of its orbit about 27°,so that the vicissitudes 
 of the seasons are greater on Mars than on the earth in the pro- 
 portion of 27° to 285°. Owing to this great obliquity, we can 
 sometimes see one pole of the planet, and sometimes the other, 
 from the earth. When in longitude 350°, that is,in the same 
 
 08 __%0 
 
 Fic. 84.—Northern hemisphere of Mars. Fia. 85.—Southern hemisphere of Mars. 
 
 direction from the sun in which the earth is situated on Sep- 
 tember 10th, the south pole of the planet is inclined towards 
 the sun; and if the planet is then in opposition, it will be in- 
 clined towards the earth also, so that we can see the region of 
 the planet to a distance of 27° beyond the pole. At an op- 
 position in March the north pole of the planet is inclined tow- 
 ards the sun, and towards the earth also. We have just seen 
 that Mars is much farther at the latter oppositions than at the 
 former, so that we can get much better views of the south pole 
 of the planet than of the north pole. | 
 Satellites of Mars.—On the night of August 11th, 1877, 
 Professor Asaph Hall, while scrutinizing the neighborhood of 
 Mars with the great equatorial of the Washington Observato- 
 ry, found a small object about 80 seconds east of the planet. 
 Cloudy weather prevented further observation at that time; 
 but on the night of the 16th it was again found, and two 
 hours’ observation showed that it followed the planet in its 
 
330 THE SOLAR SYSTEM. 
 
 orbital motion. Still, fearing that it might be a small planet 
 which chanced to be in the neighborhood, Professor Hall 
 waited for another observation before announcing his discov- 
 ery. A rough calculation from the observed elongation of the 
 satellite and the known mass of Mars showed that the period 
 of revolution would probably be not far from 29 hours, and 
 that, if the object were a satellite, it would be hidden during 
 most of the following night, but would reappear’ near its orig- 
 inal position towards morning. ‘This prediction was exactly 
 fulfilled, the satellite emerging from the planet about four 
 o'clock on the morning of August 18th. 
 
 But this was not all. The reappearance of the satellite was 
 followed by the appearance of another object, much closer to 
 the planet, which proved to be a second and inner satellite. 
 The reality of both objects was abundantly confirmed by obser- 
 vations on the following nights, not only at Washington, but at 
 the Cambridge Observatory, by Professor Pickering and his as- 
 sistants,and at Cambridgeport, by Messrs. Alvan Clark & Sons. 
 
 The most extraordinary feature of the two satellites is the 
 proximity of the inner one to the planet, and the rapidity of 
 its revolution. The shortest period hitherto known is that of 
 the inner satellite of Saturn—22 hours 87 minutes. But the 
 inner satellite of Mars goes round in 7 hours 38 minutes. Its 
 distance from the centre of the planet is about 6000 miles, 
 and from the surface less than 4000. If there are any as- 
 tronomers on Mars with telescopes and eyes like ours, they 
 can readily find out whether this satellite is inhabited, the dis- 
 tance being less than one-sixtieth that of the moon from us. 
 
 That kind of near approach to simple relationships between 
 the times of revolution is found here which we see in the sat- 
 ellites of Jupiter and Saturn. The inner satellite of Mars re- 
 volves in very nearly one-fourth the period of the outer one, 
 these times being, 
 
 Hrs. Min. 
 CHTLETABALGIICE. oly inne do toe ste vay od Phe eee s Ter fen 5 i tachebans 30 18 
 rie-fourthythis PoriGas 2A teak we fon tetstaceqeadaed den saab 7 3844 
 ECMO LOMINMET BALCLILG .5 5 weve eaeasen can dese Sieeee en dope’ (gees) 
 
 These satellites may also be put down as by far the smallest 
 
THE SMALL PLANETS. 33k 
 
 heavenly bodies yet known. It is hardly possible to make 
 anything like a numerical estimate of their diameters, because 
 they are seen in the telescope only as faint points of light ; 
 and, having no sensible surface, no such thing, as a measure 
 of the diameters is possible. The only datum on which an 
 estimate can be founded is the amount of light which they 
 give. The writer judged the magnitude of the outer one to 
 be between the eleventh and twelfth. According to the esti- 
 mate of Zéllner, Mars itself, at this opposition, is three magni- 
 tudes brighter than a first-magnitude star. The difference of 
 briliancy between Mars and the outer satellite is, therefore, 
 represented by thirteen or fourteen orders of magnitude. 
 From this, it would follow that Mars gives from 200,000 to 
 500,000 times as much light as the satellite; and if both are of 
 the same light-reflecting power, the diameter of the satellite 
 would be from 6 to 10 miles. It may be as small as 5 miles, 
 or as great as 20, but is not likely to le far without these 
 limits. The inner satellite is much brighter than the outer 
 one, and its diameter probably lies between 10 and 40 miles. 
 
 Fig. 85a.—Apparent orbits of the satellites of Mars in 1877, as observed and laid down by 
 Professor Hall. 
 
 § 7. The Small Planets. 
 
 It was impossible to study the solar system, as it was known 
 to modern astronomy before the beginning of the present cen- 
 tury, without being struck by the great gap which existed be- 
 tween Mars and Jupiter. Except this gap, all the planets then 
 known sueceeded each other according to a tolerably regular 
 
332 THE SOLAR SYSTEM. 
 
 law, and by interpolating a single planet at nearly double the 
 distance of Mars the order of distances would be complete. 
 The idea that an unknown planet might really exist in this 
 region was entertained from the time of Kepler. So sure 
 were some astronomers of this that, in 1800, an association of 
 twenty-four observers was formed, having for its object a sys- 
 tematic search for the planet. The zodiac was divided into 
 twenty-four parts, one of which was to be searched through 
 by each observer. But by one of those curious coincidences 
 which have so frequently occurred in the history of science, 
 the planet was accidentally discovered by an outside astrono- 
 mer before the society could get fairly to work. On January 
 Ist, 1801, Piazzi, of Palermo, found a star in the constellation 
 Taurus which did not belong there, and on observing it the 
 night after, he found that it had changed its position among 
 the surrounding stars, and must, therefore, be a planet. He 
 followed it for a period of about six weeks, after which it was 
 lost in the rays of the sun without any one else seeing it. 
 When it was time to emerge again in the following autumn, 
 its rediscovery became a difficult problem. But the skill of the 
 great mathematician Gauss came to the rescue with a method 
 by which the orbit of any planetary body could be complete- 
 ly and easily determined from three or four observations. He 
 was thus able to tell observers where their telescopes must be 
 pointed to rediscover the planet, and it was found without dif- 
 ficulty before the end of the year. Piazzi gave it the name 
 Ceres. The orbit found by Gauss showed it to revolve between 
 Mars and Jupiter at a little less than double the distance of 
 the former, and therefore to be the long-thought-of planet. 
 But the discovery had a sequel which no one anticipated, and 
 of which we have not yet seen the end. In March, 1802, Ol- 
 bers discovered a second planet, which was also found to be 
 revolving between Mars and Jupiter, and to which he gave 
 the name Pallas. The most extraordinary feature of its orbit 
 was its great inclination, which exceeded 34°. Olbers there- 
 upon suggested his celebrated hypothesis that the two bodies 
 might be fragments of a single planet which had been shat: 
 
THE SMALL PLANETS. S30 
 
 tered by some explosion. If such were the case, the orbits of 
 all the fragments would at first intersect each other at the 
 point where the explosion occurred. He therefore thought it 
 likely that other fragments would be found, especially if a 
 search were kept up near the point of intersection of the orbits 
 of Ceres and Pallas. Acting on this idea, Harding, of Lilien- 
 thal, found a third planet in 1804, while Olbers found a 
 fourth one in 1807. These were called Juno and Vesta. The 
 former came quite near to Olbers’s theory that the orbits 
 should all pass near the same point, but the latter did not. 
 Olbers continued a search for additional planets of this group 
 for a number of years, but at length gave it up, and died 
 without the knowledge of any but these four. 
 
 In December, 1845, thirty-eight years after the discovery of 
 Vesta, Hencke, of Driesen, being engaged in the preparation 
 of star-charts, found a fifth planet of the group, and thus re- 
 commenced a series of discoveries which have continued till 
 the present time. No less than three were discovered in 1847, 
 and at least one has been found every year since. To show 
 the rate at which discovery has gone on, we divide the time 
 since 1845 into periods of five years each, and give the num- 
 ber found during each period: 
 
 In 1846-—50......... 8 were discovered. | In 1866-70......... 27 were discovered. 
 
 ELE OOL—OD Acero’ ote Q4.- $6 he Za ey @ Coy (sen eee 45 & es 
 
 *¢ 1856-60... i000 Digs tt es £1876—-80....8600. C2ilaas $5 
 
 Be SO 1—65., ceabe Des MY LL Om hc peace atasage 1 was Mi 
 EPOCH wanrese et ees eo ccks eae Saaeectog sce rhs 220 
 
 It will be seen that the rate of discovery has been pretty 
 steadily increasing during thirty years. This is not because 
 the number of those visible, but not yet found, is so great that 
 it is as easy as ever to find one, but because they are now 
 sought after with more skill and more system than formerly.* 
 
 * In illustration of this the writer has been informed by Professor Peters that 
 in searching for these bodies he falls upon several already known for every new 
 one that he finds. Consequently, were they all lost, he alone could now redis- 
 cover them at a more rapid rate than they actually have been discovered by the 
 efforts of all the observers engaged in the search, 
 
334 THE SOLAR SYSTEM. 
 
 Of those discovered during the last ten years, nearly half 
 have been found by two American observers, Professors Pe- 
 ters and Watson. American discoveries of these bodies were 
 commenced by Mr. James Ferguson, who discovered Euphros- 
 yne at Washington on September 1st, 1854. 
 
 All the planets of this group are remarkable for their mi- 
 nuteness. The disks are all so small as to defy exact meas- 
 urement, presenting the appearance of mere stars. A rough 
 estimate of their diameters can, however, be made from the 
 amount of light which they reflect; and although, in the ab- 
 sence of exact knowledge of their reflecting power, the results 
 of this method are not very certain, they are the best we can 
 obtain. It is thus found that Ceres and Vesta are the largest 
 of the group, their diameters lying somewhere between 200 
 and 400 miles; while, if we omit some very lately discovered, 
 the smallest are Atalanta, Majafand Sappho, of which the di- 
 ameters may be between 20. and 40 miles. We may safely 
 say that it would take several thousand of the largest of these 
 small planets to make one as large as the earth. 
 
 It has sometimes been said that some of these bodies are of 
 irregular shape, and thus favor Olbers’s hypothesis that they 
 are fragments of an exploded planet. But this opinion has 
 no other foundation than a suspected variability of their light, 
 which may be an illusion, and which, if it exists, might result 
 from one side of the planet being darker in color than the 
 other. The latter supposition is not at all improbable, as many 
 of the satellites are known to be variable from this or some 
 analogous cause. As the supposed irregularities of form have 
 never been seen, and are not necessary to account for the va- 
 riations of brilliancy, there is no sufficient reason for believing 
 in their existence. | 
 
 Olbers’s Hypothesis. — The question whether these bodies 
 could ever have formed a single one has now become one of 
 cosmogony rather than of astronomy. If a planet were shat- 
 tered, the orbit of each fragment would, at first, pass through 
 the point at which the explosion occurred, however widely 
 they might be separated through the rest of their course. But 
 
THE SMALL PLANETS. 335 
 
 owing to the secular changes produced by the attractions of 
 the other planets, this coincidence would not continue. The 
 orbits would slowly move away, and after the lapse of a few 
 thousand years no trace of a common intersection would be 
 seen. It is, therefore,curious that Olbers and his contempora- 
 ries should have expected to find such a region of intersection, 
 as it implied that the explosion had occurred within a few 
 thousand years. The fact that the required conditions were 
 not fulfilled was no argument against the hypothesis, because 
 the explosion might have occurred millions of years ago, and 
 in the mean time the perihelion and node of each orbit 
 would have made many entire revolutions ; so that the orbits 
 would have been completely mixed up. 
 
 Desirous of seeing whether the orbits passed nearer a com- 
 mon point of intersection in times past than at present, Encke 
 computed their secular variations. The result seemed to be 
 adverse to Olbers’s hypothesis, as it showed that the orbits 
 were farther from having a common point in ages past than 
 at present. But this result was not conclusive either, because 
 he only determined the rates at which the orbits are now 
 changing, whereas, as previously explained, the orbits of all 
 the planets really go through periodic oscillations ; and it is 
 only by calculating these oscillations that their positions can 
 be determined for very remote epochs. They have since 
 been determined for some of the planets in question, and the 
 result seems to show that the orbits could never have intersect- 
 ed unless some of them have, in the mean time, been altered 
 by the attraction of the small planets on each other. Such an 
 action is not impossible; but it is impossible to determine it, 
 owing to the great number of these bodies, and our ignorance 
 of their masses. We can, however, say that if the explosion 
 ever did occur, an immense interval, probably millions of 
 years, must have elapsed in the mean time. A different ex- 
 planation of the group is given by the nebular hypothesis, of 
 which we shall hereafter speak, so that Olbers’s hypothesis is 
 no longer considered by astronomers. 
 
 The planets in question are distinguished from the others, 
 
336 THE SOLAR SYSTEM. 
 
 not only by their small size, but by the great eccentricities 
 and inclinations of their orbits. If we except Mercury, none 
 of the larger planets has an eccentricity amounting to one- 
 tenth the diameter of its orbit, nor is any orbit inclined more 
 than two or three degrees to the ecliptic. But the inclina- 
 tions of many of the small planets exceed ten degrees, and 
 the eccentricities frequently amount to a fourth of the radii 
 of their orbits. The result is that the same small planet is at 
 very different distances from the sun in various points of its 
 orbit. Add to this the fact that the mean distances of these 
 bodies from the sun have a pretty wide range, and we shall 
 find that they extend through a quite broad zone. The inside 
 edge of this zone seems pretty well marked, its distance being 
 about 180 millions of miles from the sun, or between 30 and 
 40 millions beyond the orbit of Mars. On the outside, it ter- 
 minates more gradually, but nowhere extends within 50 mill- 
 ions of miles of the orbit of Jupiter. If any of the small 
 planets ever ranged outside of certain limits, the attraction of 
 Mars or Jupiter was so great as to completely derange their 
 orbits, so that we have a physical law which sets a limit to the 
 zone; but whether the limit thus set would coincide with the 
 actual limit we cannot at present say. 
 
 There are also within the limits of the group certain posi- 
 tions, in which, if the orbits were placed, they would be greatly 
 changed by the action of Jupiter. These positions are those 
 in which the time of revolution would be some simple exact 
 fraction of that of Jupiter, as 4, 4, 2,3, ete. Professor Daniel 
 Kirkwood has pointed out the curious fact that there are gaps 
 in the series of small planets corresponding to these periodic 
 times. Whether these gaps are really due to the relations of 
 the periodic times, or are simply the result of chance, cannot 
 yet be settled. The fact that quite a number of the small 
 planets have a period very nearly three-eighths that of Jupiter, 
 may lead us to wait for further evidence before concluding 
 that we have to deal witn a real law of nature in the cases 
 pointed out by Professor Kirkwood. 
 
 Number and Total Mass of the Small Planets.—At present it 
 
THE SMALL PLANETS. 337 
 
 is not possible to set any certain limits to the probable number 
 of the small planets. Although a hundred and seventy-two 
 are now known, there is as yet no sensible diminution in the 
 rate at which they are being discovered. The question of 
 their total number depends very largely on whether there is 
 any limit to their minuteness. If there is no such limit, then 
 there may be an indefinite number of them, too small to be 
 found with the telescopes now engaged in searching for them; 
 and the larger the telescopes engaged in the search, the more 
 will be found. On the other hand, if they stop at a certain 
 limit—say twenty miles in diameter—we may say with con- 
 siderable confidence that their total number is also limited, 
 and that by far the largest part of them will be discovered 
 by the present generation of astronomers. 
 
 So far as we can now see, the preponderance of evidence is 
 on the side of the number and magnitude being limited. The 
 indications in this direction are that the newly discovered ones 
 are not generally the smallest objects which could be seen 
 with the telescopes which have made the discovery, and do 
 not seem, on the average, to be materially smaller than those 
 which were discovered ten years ago, It is not likely that the 
 number of this average magnitude which still remain undis- 
 covered can be very great, and new ones will probably be 
 found to grow decidedly rare before another hundred are dis- 
 covered. Then it will be necessary to employ greater optical 
 power in the search. If this results in finding a number of 
 new ones too small to be found with the former telescopes, we 
 shall have to regard the group as unlimited in number. But 
 if no such new ones are thus found, it will show that the end 
 has been nearly reached. 
 
 In gravitational astronomy, the question of the total mass 
 of the small planets is more important than that of their total 
 number, because on this mass depends their effect in altering 
 the motions of the large planets. Any individual small planet 
 is so minute that its attraction on the other planets is entirely 
 insensible. But it is not impossible that the whole group 
 might, by their combined action, produce a secular variation 
 
338 THE SOLAR SYSTEM. 
 
 in the form of the orbits of Mars and Jupiter which, in the 
 course of years, will be clearly shown by the observations. 
 But, although accurate observations of these planets have been 
 made for more than a century, no such effect has yet been no- 
 ticed. The sum total of their masses must, therefore, be much 
 less than that of an average planet, though we cannot say pre- 
 cisely what the limit is. The apparent magnitude of those 
 which have been discovered is entirely accordant with the 
 opinion that the mass of the entire group is so small that it 
 cannot make itself felt by its attraction on the other planets 
 for many years to come. In fact, if their diameters be esti- 
 mated from their brightness, in the manner already indicated, 
 we shall find that if all that are yet known were made into a 
 single planet the diameter would be less than 400 miles; and 
 if a thousand more, of the average size of those discovered 
 since 1850 should exist, their addition to the consolidated 
 planet would not increase its diameter to 500 miles. Such a 
 planet would be only a)'55 of the bulk of the earth, and, un- 
 less we supposed it to possess an extraordinary specific gravity, 
 could not much exceed z,'55 of the mass of the earth, or 35 of 
 the mass of Mercury. We may fairly conclude that unless 
 the group of small planets actually consists of tens of thou- 
 sands of minute bodies, of which only a few of the brightest 
 have yet been discovered, their total volume and mass are far 
 less than those of any one of the major planets. 
 
 The number of these bodies now known is so great that the 
 mere labor of keeping the run of their motions, so that they 
 shall not be lost, is out of proportion to the value of its results. 
 It is mainly through the assiduity of German students that 
 most of them are kept from being lost. Should many more 
 be found, it may be necessary to adopt the suggestion of an 
 eminent German astronomer, and let such of them as seem 
 unimportant go again, and pursue their orbit undisturbed by 
 telescope or computer. 
 
THE PLANET JUPITER. 339 
 
 CHAPTER IV. 
 
 THE OUTER GROUP OF PLANETS. 
 
 § 1. The Planet Jupiter. 
 
 JUPITER is the “giant planet ” of our system, his mass large- 
 ly exceeding that of all the other planets combined. His 
 mean diameter is about 85,000 miles; but owing to his rapid 
 rotation on his axis, his equatorial exceeds his polar diameter 
 
 Fie. 86.—Jupiter as seen with the great Washington telescope, March 21st, 1876, 15 hours 
 
 38 minutes mean time. Drawn by Professor Holden. 
 by 5000 miles. In volume he exceeds our earth about 1300 
 times, while in mass he exceeds it about 2138 times. His spe- 
 citic gravity is, therefore, far less than that of the earth, and 
 even less than that of water. His mean distance from the 
 sun is 480 millions of miles, but, owing to the eccentricity of 
 his orbit, his actual distance ranges between 457 and 508 mill- 
 ions. His time of revolution is fifty days less than twelve 
 years. 
 
340 THE SOLAR SYSTEM. 
 
 Jupiter is easily recognized by his brilliant white light, with 
 which he outshines every other planet except Venus. To fa- 
 cilitate his recognition, we give the dates of opposition during 
 a few years. 
 
 1882... ccecsscessss December 17th. TBSD iatenapastust ee February 20th. 
 LEB sc cntscarasws sags January 19th. ASSG co reesesabaaees March 20th. 
 
 During the four years following 1886 he will be in opposi- 
 tion, on the average about a month, and two or three days 
 later each year, namely, towards the end of April, 1887; 
 about the end of May, 1888, and so on. A month or two 
 before opposition he can be seen rising late in the evening, 
 while during the three months following opposition he will 
 always be seen in the early evening somewhere between south- 
 east and south-west. 
 
 The Surface of Jupiter—Except the sun and moon, there is 
 no object of our system which has during the last few years 
 been the subject of more careful examination than this planet. 
 Unlike Mars, there are no really permanent markings on his 
 surface, and a map of Jupiter is therefore impossible. But 
 this surface always presents a very diversified appearance. 
 The earlier telescopic observers described light and dark belts 
 as extending across it. Until a quite recent period, it has 
 been customary to describe these belts as two in number, one 
 north of the equator, and the other south of it. Commonly, 
 they are seen as dark bands on the bright disk of the planet ; 
 but it is curious that Huyghens represents them as brighter 
 than the rest of the surface. As telescopic power was in- 
 creased, it was.seen that these so-called bands were of a far 
 more complex structure than had been supposed, and consisted 
 of great numbers of stratified, cloud-like appearances of the 
 most variegated forms. ‘These forms change so rapidly that 
 the face of the planet hardly ever presents the same appear- 
 ance on two successive nights. They are most strongly 
 marked at some distance on each side of the Jovian equator, 
 and thus give rise to the appearance of two belts when a very 
 small or imperfect telescope is used. 
 
THE PLANET JUPITER. B4] 
 
 Both the outlines of these belts and the color of some parts 
 of the planet, seem subject to considerable changes. The 
 equatorial regions, and indeed the spaces between the belts 
 generally, are often of a rosy tinge. This coloring is some- 
 times so strongly marked as to be evident to the most super- 
 ficial observer, while at other times hardly a trace of it can be 
 seen. 
 
 Spots which are much more permanent than the ordinary 
 markings on the belt are sometimes visible. By watching 
 these spots from day to day, and measuring their distance 
 from the apparent disk, the time of rotation of Jupiter on his 
 axis has been determined. Commonly the spots are dark; 
 but on some rather rare occasions the planet. is seen with a 
 number of small, round, bright spots like satellites. Of these 
 bright spots no explanation has been given. 
 
 Fie. 87.—View of Jupiter, as seen in Lord Rosse’s great telescope on February 27th, 
 1861, at 12 hours 30 minutes. 
 
 From the changeability of the belts, and indeed of nearly all 
 the visible features on the surface of Jupiter, it is clear that 
 what we see on that planet is not the surface of a solid nu- 
 cleus, but vaporous or cloud-like formations which cover the 
 entire surface and extend to a great depth below. To all ap- 
 pearance, the planet is covered with a deep and dense atmos- 
 
342 THE SOLAR SYSTEM. 
 
 phere, through which light cannot penetrate on account of 
 thick masses of clouds and vapor. In the arrangements of 
 these clouds in streaks parallel to the equator, and in the 
 change of their forms with the latitude, there may be some- 
 thing analogous to the zones of clouds and rain on the earth. 
 But of late years it has been noticed that the physical consti- 
 tution of Jupiter seems to offer more analogies to that of the 
 sun than to that of the earth. Like the sun, he is brighter in 
 the centre than near the edges. This is shown in the most 
 striking manner in the transits of his satellites over his disk. 
 When the satellite first enters on the disk, it commonly seems 
 like a bright spot on a dark background; but as it approaches 
 the centre, it appears like a dark spot on the bright back- 
 ground of the planet. The brightness of the centre is prob- 
 ably two or three times greater than that of the limb. This 
 diminution of light towards the edge may arise, as in the case 
 of the sun, from the light near the edge passing through a 
 greater depth of atmosphere, and thus becoming fainter by 
 absorption. 
 
 A still more remarkable resemblance to the sun has some- 
 times been suspected—nothing less, in fact, than that Jupiter 
 shines partly by his own light. It was at one time supposed 
 that he actually emitted more light than fell upon him from 
 the sun; and if this were proved, it would show conclusive- 
 ly that he was self-luminous. If all the light which the sun 
 shed upon the planet were equally reflected in every direction, 
 we might speak with some certainty on this question; but in 
 the actual state of our knowledge we cannot. Zollner has 
 found that the brightness of Jupiter may be accounted for by 
 supposing him to reflect 62 per cent. of the sunlight which he 
 receives. But if this is his average reflecting power, the re- 
 flecting power of his brighter portions must be much greater; 
 in fact, they are so bright that they must shine partly by their 
 own light, unless they reflect a disproportionate share of the 
 sunlight back in the direction of the earth and sun. Clouds 
 would not be likely to do this. On the other hand, if we as- 
 sume that the planet emits any great amount of light, we are 
 
THE PLANET JUPITER. 343 
 
 met by the fact that, if this were the case, the satellites would 
 shine by this light when they were in the shadow of the 
 planet. As these bodies totally disappear in this position, the 
 quantity of light emitted by Jupiter must be quite small. On 
 the whole, there is a small probability that the brighter spots 
 of this planet are from time to time slightly self-luminous. 
 
 Again, the interior of Jupiter seems to be the seat of an 
 activity so enormous that we can attribute it only to a very 
 high temperature, like that of the sun. This is shown by the 
 rapid movements always going on in his visible surface, which 
 frequently changes its aspect in a few hours. Such a power- 
 ful effect could hardly be produced by the rays of the sun, 
 because, owing to the great distance of the planet, he receives 
 only between one-twenty-fifth and one-thirtieth of the light 
 and heat which we do. It is therefore probable that Jupiter 
 is not yet covered by a solid crust, as our earth is, but that 
 his white-hot interior, whether liquid or gaseous, has nothing 
 to cover it but the dense vapors to which that heat gives rise. 
 In this case the vapors may be self-luminous when they have 
 freshly arisen from the interior, and may rapidly cool off after 
 reaching the upper limit to which they ascend. 
 
 Rotation of Jupiter.—Owing to the physical condition of Ju- 
 piter, no precisely determinate time of rotation can be assign- 
 ed him, as in the case of Mars. Without a solid crust which 
 we can see from time to time, the observed times of rota- 
 tion will be those of liquid or vaporous formations, which may 
 have a proper motion of their own. A spot has, however, on 
 some occasions been observed for several months, and it has 
 thus been pretty certainly determined that the time of rota- 
 tion is about 9 hours 554 minutes. The first observation of a 
 spot of this kind was made by Cassini, who found the time of 
 rotation to be 9 hours 55 minutes 58 seconds. No further 
 exact observations were made until the time of Schroter, who 
 observed a number of transient spots during 1785 and 1786. 
 The times of rotation varied from 9 hours 55 minutes to 9 
 hours 56 minutes, from which he concluded that heavy storms 
 raged on the surface of the planet, and gave the cloudy masses 
 
 QQ 
 
344 THE SOLAR SYSTEM. 
 
 which formed the spots a motion of their own. In Novem- 
 ber, 1834, a remarkable spot was observed by Midler, of Dor- 
 pat, which lasted until the following April, from which the 
 time of rotation came out 9 hours 55 minutes 80 seconds; but 
 the observations showed that the spot did not move uniformly. 
 Professor Airy, who observed the same spot at Cambridge, 
 found the period to be 9 hours 55 minutes 21.3 seconds. 
 
 Jtecent observations and researches indicate that the equa- 
 torial regions of Jupiter rotate in less time,and with more ir- 
 regularity, than the others, thus showing still another analogy © 
 between that planet and the sun. Thus, in 1871, Dr. Lohse, 
 of Bothkamp, observed a spot near Jupiter’s equator, which 
 during several days performed its revolution in a period of 
 9 hours 51 minutes 47 seconds. Other equatorial spots had a 
 very regular motion, but their period was generally less than 
 that found by Midler and Airy. 
 
 § 2. The Satellites of Jupiter. 
 
 One of the earliest telescopic discoveries by Galileo was 
 that Jupiter was accompanied by four satellites, which re- 
 volved round him as a centre, thus forming a miniature copy 
 of the solar system. As in the case of spots on the sun, Gal- 
 ileo’s announcement of this discovery was received with in- 
 credulity by those philosophers of the day who believed that 
 everything in nature was described in the writings of Aris- 
 totle. One eminent astronomer— Clavius—said that to see 
 the satellites one must have a telescope which would produce 
 them; but he changed his mind as soon as he saw them him- 
 self. Another philosopher, more prudent, refused to put his 
 -eye to the telescope lest he should see them and be con- 
 vinced. He died shortly afterwards. “I hope,” said the caus- 
 tic Galileo, “that he saw them while on his way to heaven.” 
 
 A very small telescope, or even a good opera-glass, is suf- 
 ficient to show these bodies. Indeed, very strong evidence is 
 on record that they have been seen with the naked eye. That 
 they could be seen by any good eye, if the planet were out of 
 the way, there is no doubt, the difficulty in seeing them aris- 
 
VHE SATELLITES OF JUPITER. 345 
 
 ing from the glare of the planet on the eye. If the lenses of 
 the eye are so transparent and pure that there is no such 
 glare, it is quite possible that the two outer satellites might 
 be seen, especially if they should happen to be close to 
 pether. , : 
 
 According to the best determinations, which are, however, 
 by no means certain, the diameters of the satellites of Jupiter 
 range between 2200 and 3700 miles, the third from the planet 
 being the largest, and the second the smallest. The volume of 
 the smallest is, therefore, very near that of our moon. 
 
 The light of these satellites varies to an extent which it 
 is difficult to account for, except by supposing very violent 
 changes constantly going on on their surfaces. » It has some- 
 times been supposed that some of them, like our moon, always 
 present the same face to Jupiter, and that the changes in their 
 brillianey are due to differences in the color of the parts of 
 the satellites which are successively turned towards us during 
 one revolution round the planet. But the careful measures 
 of their light made by Auwers, of Berlin, and Engelmann, of 
 Leipsic, show that this hypothesis does not account for the 
 changes of brilliancy, which are sometimes sudden in a sur- 
 prising degree. The satellites are so distant as to elude tele- 
 scopic examination of their surfaces. We cannot, therefore, 
 hope to give any certain explanation of these changes. 
 
 The satellites of Jupiter offer problems of great difficulty 
 to the mathematician who attempts to calculate the effect of 
 their mutual attractions. The secular variations of their or- 
 bits are so rapid that the methods applied in the case of the 
 planets cannot be applied here without material alterations. 
 The most curious and interesting effect of their mutual at- 
 traction is that there is a connection between the motions of 
 the three inner satellites such as exists nowhere else in the 
 solar system. ‘The connection is shown by these two laws: 
 
 1. That the mean motion of the first satellite added to twice the 
 mean motion of the third is exactly equal to three times the mean 
 motion of the second. 
 
 2. That if to the mean longitude of the first satellite we add 
 
346 THE SOLAR SYSTEM. 
 
 twice the mean longitude of the third, and subtract three times the 
 mean longitude of the second, the difference is always 180°. 
 
 The first of these relations is shown in the following table 
 of the mean daily motions of the satellites: 
 
 Satellite I. in‘one day Moves.........:....0sssesceses . 203°.4890 
 . If. “4 SEPMET MT. Sic cvctspceves Mes teseeues 101°.3748 
 
 ‘yo Lil: 4 Re MDtr Lace da. fa. ween bape eae 50°.3177 
 
 See ve ot 4) Ve rT ee es 21°.5711L 
 MOtion OF UOLE OA eee e fas elovnn coe pegs yagha ene aes 203°.4890 
 Twice thatwt Satelite lil. s..... .decephedseneatemnaneny 100°. 6354 
 PT) eee Captains eniss ouich += 540s eqempbeauauerann jeanne 304°.1244 
 
 Three times motion of Satellite [I. .............ccceeeee 804°. 1244 
 
 It was first found from observations that the three satellites 
 moved together so nearly according to this law that no certain 
 deviation could be detected. But it was not known whether 
 this was a mere chance coincidence, or an actual law of nat- 
 ure, till Laplace showed that, if they moved so nearly in this 
 way as observations had shown them to, there would be an ex- 
 tremely minute force arising from their mutual gravitation, 
 sufficient to keep them in this relative position forever. There 
 is, in this case, some analogy to the rotation of the moon, 
 which, being once started presenting the same face to the 
 earth, is always held in that position by a minute residual of 
 the earth’s attraction. 
 
 We have already spoken of the discovery of the progressive 
 motion of light from the eclipses of these satellites, and of 
 the uses of these eclipses for the rough determination of 
 longitudes. Both the eclipses, and the transits of their bodies 
 over the face of Jupiter afford interesting subjects of obser- 
 vation with a telescope of sufficient power, say four inches ap- 
 erture or upwards. ‘To facilitate such observations the times 
 of these phenomena are predicted in both the American and 
 British Nautical Almanacs. 
 
 § 3. Saturn and its System, Physical Aspect, Belts, Rotation. 
 
 Saturn is the sixth of the major planets in the order of dis- 
 tance from the sun, around which it revolves in 294 years at 
 
SATURN AND HIS SYSTEM. 347 
 
 a mean distance of about 880 millions of miles. In mass and 
 size it stands next to Jupiter. To show the disparity in the 
 ‘masses of the planets we may refer to the table already given, 
 showing that although Saturn is not one-third the mass of 
 Jupiter, it has about three times the mass of the six planets, 
 which are smaller than itself put together. Its surroundings 
 are such as to make it the most magnificent object in the solar 
 system. While no other planet is known to have more than 
 
 Fig. S8.—View of Saturn and his rings, 
 
 four satellites, Saturn has no less than eight. It is also sur- 
 rounded by a pair of rings, the interior diameter of which is 
 about 100,000 miles. The aspect of these rings is subject to 
 great variations, for reasons which will soon appear. ‘The 
 great distance of the planet renders the study of its details 
 difficult unless the highest telescopic power is applied. The 
 whole combination of Saturn, his rings, and his satellites is 
 often called the Saturnian System. 
 
 The planet Saturn generally shines with the brilliancy of a 
 
348 THE SOLAR SYSTEM. 
 
 moderate first-magnitude star, and with a dingy, reddish light, 
 as if seen through a smoky atmosphere. Its apparent bright- 
 ness is, however, different at different times: during the years’ 
 1876-1879 it is fainter than the average, owing to its ring be- 
 ing seen nearly edgewise. From 1878 till 1885 it will con- 
 stantly grow brighter, on account both of the opening out of 
 the ring and the approach of the planet to its perihelion. 
 The times of opposition are as follow: 
 
 1879....October 5th. 1881....October 31st. 1883....November 28th. 
 1880....October 18th. | 1882....November 14th. 1884....December 11th. 
 
 In subsequent years opposition will occur about thirteen days 
 later every year, so that by adding this amount to the date for 
 each year the oppositions can be found until-the end of the 
 century without an error of more than a few days. 
 
 The physical constitution of Saturn seems to bear a great 
 resemblance to that of Jupiter; but, being twice as far away, 
 it cannot be so well studied. The farther an object is from 
 the sun, the less brightly it is illuminated; and the farther 
 from the earth, the smaller it looks, so that there is a double 
 difficulty in getting the finest views of the more distant plan- 
 ets. When examined under favorable circumstances, the sur- 
 face of Saturn is seen to be diversified with very faint mark- 
 ings; and if high telescopic powers are used, two or more 
 very faint streaks or belts may be seen parallel to its equator, 
 the strongest ones lying on, or very near, the equator. As in 
 the case of Jupiter, these belts change their aspect from time 
 to time, but they are so faint that the changes cannot be 
 easily followed. It is therefore, in general, difficult to say 
 with certainty whether we do or do not see the same face of 
 Saturn on different nights; and, consequently, it is only on 
 extraordinary occasions that the time of rotation can be de- 
 termined. 
 
 The first occasion on which a well-defined spot was known 
 to remain long enough on Saturn to determine the period of 
 its rotation was in the time of Sir W. Herschel, who, from 
 observations extending over several weeks, found the time of 
 
THE RINGS OF SATURN. 349 
 
 rotation to be 10 hours 16 minutes.* No further opportu- 
 nity for determining this period seems to have offered itself 
 until 1876, when an appearance altogether new suddenly 
 showed eels on the globe of this mlaneh On the evening of 
 December 7th, 1876, eee cor Hall, who had been hater 
 in measures of the coe of Scin with the great Wash- 
 ington telescope, saw a brilliant white spot near the equator 
 of the planet. It seemed as if an immense eruption of white- 
 hot matter had suddenly burst up from the interior. The 
 spot gradually spread itself out in the direction which would 
 be east on the planet, so as to assume the form of a long light 
 streak, of which the brightest point was near the following 
 end. It continued visible until January, when it, became faint 
 and ill-defined, and the planet was lost in the rays of the sun. 
 
 Immediately upon the discovery of this remarkable phenom- 
 enon, messages were sent to other observers in various parts of 
 the country, and on the 10th it was seen by several observers, 
 who noted the time at which it crossed the centre of the disk 
 in consequence of the rotation of the planet. From all the 
 observations of this kind, Professor Hall found the period of 
 Saturn to be 10 hours 14 minutes, taking the brightest part 
 of the streak, which, as we hae said, was near one end. 
 Had the middle of the streak been taken, the time would have 
 been less, because the bright matter seemed to be carried 
 along in the direction of the planet’s rotation. Attributing 
 this to a wind, the velocity of the latter would have been be- 
 tween 50 and 100 miles an hour. 
 
 § 4. The Rings of Saturn. 
 
 The most extraordinary feature of Saturn is the magnificent 
 system of rings by which he is surrounded. To the early 
 telescopists, who could not command sufficient optical power 
 to see exactly what it was, this feature was a source of great 
 
 * It is very curious that nearly all modern writers give about 10 hours 29 min- 
 utes as the time of rotation of Saturn which Herschel finally deduced. I can 
 find no such result in Herschel’s.papers. A suspicious coincidence is that this 
 period agrees with that assigned for the time of rotation of the ring. 
 
350 THE SOLAR SYSTEM. 
 
 perplexity and difference of opinion. To Galileo it made the 
 planet appear triform—a large globe with two small ones af- 
 fixed to it, one on each side. After he had observed it for a 
 year or two, he was greatly perplexed to find that the append- 
 ages had entirely disappeared, leaving Saturn a single round 
 globe, like the other planets. His chagrin was heightened by 
 the fear, not unnatural under the circumstances, that the curi- 
 ous form he had before seen might be due to some optical il- 
 lusion connected with his telescope. It is said (1 do not know 
 on what authority) that his annoyance at the supposed decep- 
 tion into which he had fallen was so great that he never again 
 looked at Saturn. 
 
 A very few years sufticed to show other observers, who had 
 command of more powerful telescopes, that the singularity of 
 form was no illusion, but that it varied from time to time. 
 We give several pictures from Huyghens’s Systema Saturnium, 
 showing how it was represented by various observers during 
 the first forty years of the telescope. If the reader will com- 
 pare these with the picture of Saturn and his rings as they 
 actually are, he will see how near many of the observers came 
 to a representation of the proper apparent form, though none 
 divined to what sort of an appendage the appearance was 
 due. 
 
 The man who at last solved the riddle was Huyghens, of 
 whose long telescopes we have already spoken. Examining 
 Saturn in March and April, 1655, he saw that instead of the 
 appendages presenting the appearance of curved handles, as 
 in previous years, a long narrow arm extended straight out on 
 each side of the planet. The spring following, this arm had 
 disappeared, and the planet appeared perfectly round as Gal- 
 ileo had seen it in 1612. In October, 1655, the handles had 
 reappeared, much as he had seen them a year and a half be- 
 fore. To his remarkably acute mathematical and mechanical 
 mind this mode of disappearance of the handles sufficed to 
 suggest the cause which led to their apparent form. Waiting 
 for entire confirmation by future observations, he communica- 
 ted his theory to his fellow-astronomers in the following com- 
 
THE RINGS OF SATURN. ool 
 
 Fig. 89. Specimens of drawings of Saturn by various observers before the rings were 
 recognized as such: J. Form as given by Galileo in 1610; II. Drawing by Scheiner, in 
 1614, ‘showing ears to Saturn;” III. Drawing by Ricciolus, in 1640 and 1648; IV.,V., 
 VI., and VII. are by Hevelius, and show the changes due to the different angles under 
 which the rings were seen; VIII. and IX. are by Ricciolus, between 1648 and 1650, 
 when the ring was seen at the greatest angle; X. is by a Jesuit who passed under 
 the pseudonym of Eustachius de Divinis; XI. is by Fontana; XII. by Gassendi and 
 Blancanus, and XIII. by Ricciolus. 
 
 bination of letters, printed without explanation at the end of a 
 little pamphlet on his discovery of the satellite of Saturn: 
 
 which, properly arranged, read— 
 
 “ Annulo cingitur, tenui, plano, nusquam coherente, ad eclipticam inclinato ” 
 (It is girdled by a thin plane ring, nowhere touching, inclined to the ecliptic). 
 
 This description is remarkably complete and accurate; and 
 enabled Huyghens to give a satisfactory explanation of the 
 24 
 
352 THE SOLAR SYSTEM. 
 
 various phases which the ring had assumed as seen from the 
 earth. Owing tothe extreme thinness and flatness of the ob- 
 ject, it was completely invisible in the telescopes of that time 
 when its edge was presented towards the observer or towards 
 the sun. This happens twice in each revolution of Saturn, in 
 much the same way that the earth’s equator is twice directed 
 towards the sun in the course of the year. The ring is in- 
 clined to the plane of the planet’s orbit by 27°, corresponding 
 to the angle of 234° between the earth’s equator. and the 
 ecliptic. The general aspect from the earth is very near the 
 same as from the sun. As the planet revolves around the 
 sun, the axis and plane of the ring preserve the same absolute 
 direction in space, just as the axis of the earth and the plane 
 of the equator do. 
 
 When the planet is in one part of its orbit, an observer at 
 the sun or on the earth will see the upper or northern side of 
 the ring at an inclination of 27°. This is the greatest angle. 
 at which the ring can ever be seen, the position occurring 
 when the planet is in 262° of longitude, in the constellation 
 Sagittarius. When the planet has moved through a quarter 
 of a revolution, the edge of the ring is turned towards the sun, 
 aud, owing to its extreme thinness, it is visible only in the 
 most powerful telescopes as an exceedingly fine line of light, 
 stretching out on each side of the planet. In this position the 
 planet is in longitude 352°, in the constellation Pisces. When 
 the planet has moved 90° farther, an observer on the sun or 
 earth again sees the ring at an angle of 27°; but now it is the 
 lower or southern side which is visible. The planet is now in 
 longitude 82°, between the constellations Taurus and Gemini. 
 When it has moved 90° farther, to longitude 172°, in the con- 
 stellation Leo, the edge of the ring is again turned towards 
 the earth and sun. 
 
 Thus there are a pair of opposite points of the orbit of Sat- 
 urn in which the rings are turned edgewise to us, and another 
 pair half-way between the first in which the ring is seen at 
 its maximum inclination of about 27°. Since the planet per- 
 forms a revolution in 294 years, these phases occur at average 
 
THE RINGS OF SATURN. B50 
 
 intervals of about seven years and four months. The follow- 
 ing are some of the times of their occurrence: 
 
 1870. The planet being between Scorpio and Sagittarius, 
 the ring was seen open to its greatest breadth, the north side - 
 being visible. The same phase recurs at the end of 1899. 
 
 1878 (February 7th). The edge of the ring was turned to- 
 wards the sun, so that only a thin line of light was visible. 
 The planet was then between Aquarius and Pisces. 
 
 1885. The planet being in Taurus (the Bull) the south side 
 of the rings will be seen at the greatest elevation. 
 
 1892. The edge of the ring is again turned towards the sun, 
 the planet being in Leo (the Lion). 
 
 Owing to the motion of the earth, the times when the edge 
 of the ring is turned towards it do not accurately correspond 
 to those when it is turned towards the sun, and the points of 
 Saturn’s orbit in which this may occur range over a space of 
 several degrees. The most interesting times for viewing the 
 rings with powerful telescopes are on those rare occasions 
 when the sun shines on one side of the ring, while the dark 
 side is directed towards the earth. On these occasions the 
 plane of the ring, if extended out far enough, would pass be- 
 tween the sun and the earth. This was the case between Feb- 
 ruary 9th and March Ist, 1878; but, unfortunately, at that time 
 the earth and Saturn were on opposite sides of the sun, so that 
 the planet was nearly lost in the sun’s rays, and could be ob- 
 served only low down in the west just after sunset. In 1891 
 the position of Saturn will be almost equally unfavorable for 
 the observation in question, as it can be made only in the early 
 mornings of the latter part of October of that year, just after 
 Saturn has risen. In fact, a good opportunity will not occur 
 till 1907. In northern latitudes the finest telescopic views of 
 Saturn and his ring may be obtained between 1881 and 1889, 
 because during that interval Saturn passes his perihelion, and 
 also the point of greatest northern declination, while the ring 
 is opened out to its widest extent. In fact, these three most 
 favorable conditions all fall nearly together during the years 
 1881-’85. 
 
354 THE SOLAR SYSTEM. 
 
 After Huyghens, the next step forward in discoveries on 
 Saturn’s ring was made by an English observer, named Ball, 
 otherwise unknown in-astronomy, who found that there were 
 really two rings, divided by a narrow dark line. The breadth 
 of the rings is very unequal, the inner ring being several times 
 broader than the outer one. A moderate-sized telescope is 
 sufticient to show this division near the extreme points of the 
 ring if the atmosphere is steady; but it requires both a large 
 telescope and fine seeing to trace it all the way across that 
 part of the ring which is between the observer and the ball of 
 the planet. Other divisions, especially in the outer ring, have 
 at times been suspected by various observers, but if they real- 
 ly existed, they must have been only temporary, forming and 
 closing up again. 
 
 In December, 1850, the astronomical world was surprised 
 by the announcement that Professor Bond, of Cambridge, had 
 discovered a third ring to Saturn. It lay between the rings 
 already known and the planet, being joined to the inner edge 
 of the inner ring. It had the appearance of a ring of crape, 
 being so dark and obscure that it might easily have been | 
 overlooked in smaller telescopes. It was seen in England by 
 Messrs. Lassell and Dawes ‘before it was formally announced 
 by the Bonds. Something of the kind had been seen by Dr. 
 Galle, at Berlin, as far back as 1838; but the paper on the 
 subject by Encke, the director of the observatory, did not de- 
 scribe the appearance very clearly. Indeed, on examining the 
 descriptions of observers in the early part of the eighteenth 
 century, some reason is found for suspecting that they saw 
 this dusky ring; but none of the descriptions are sufficiently 
 definite to establish the fact, though it is strange if an object 
 so plain as this ring now is should have been overlooked by 
 all the older observers. 
 
 The question whether changes of various sorts are going on 
 in the rings of Saturn is one which is still unsettled. There 
 is some reason to believe that the supposed additional divis- 
 ions noticed in the rings from time to time are only errors of 
 vision, due partly to the shading which is known to exist on 
 
THE RINGS OF SATURN. Bdd 
 
 various parts of the ring. By reference to the diagram of 
 Saturn, it will be seen that the outer ring has a shaded line 
 extending around it about two-thirds of the way from its in- 
 ner to its outer edge. This line, however, is not fine and 
 sharp, like the known division, but seems to shade off gradual-° 
 ly towards each edge. As observers who have supposed them- 
 selves to see a division in this ring saw it where this shaded 
 line is, and do not speak of the latter as anything distinct 
 from the former, there is reason to believe that they mistook 
 this permanent shading for a new division. ‘The inner ring is 
 brightest near its outer edge, and shades off gradually towards 
 its inner edge. Here the dusky ring joins itself to it, and ex- 
 tends about half-way in to the planet. 
 
 As seen with the great Washington equatorial in the au- 
 tumn of 1874, there was no great or sudden contrast be- 
 tween the inner or dark edge of the bright ring and the out- 
 er edge of the dusky ring. There was some suspicion that 
 the one shaded into the other by insensible gradations. No 
 one could for a moment suppose, as some observers have, that 
 there was a separation between these two rings. All these 
 considerations give rise to the question whether the dusky 
 ring may not be growing at the expense of the inner bright 
 ring. 
 
 A most startling theory of changes in the rings of Saturn 
 was propounded by Struve, in 1851. This was nothing less 
 than that the inner edge of the ring was gradually approach- 
 ing the planet in consequence of the whole ring spreading in- 
 wards, and the central opening thus becoming smaller. The 
 data on which this theory was founded were the descriptions 
 and drawings of the rings by the astronomers of the seven- 
 teenth century, especially Huyghens, and the measures ex- 
 ecuted by later astronomers up to the time at which Struve 
 wrote. The rate at which the space between the ring and the 
 planet was diminishing seemed to be about 1.3 per century. 
 The following are the numbers used by Struve, which are de- 
 duced from the descriptions by the ancient observers, and the 
 measures by the modern ones: 
 
356 THE SOLAR SYSTEM. 
 | y Distance between Breadth of 
 axe Ring and Planet. Ring. 
 Huyghens. 4.344. s.eacaueeae 1657 6.5 4.6 
 Huyghens and Cassini....... 1695 6.0 5.1 
 Bradley...) ctpioseeees eee A719 5.4 5.7 
 Hersehel. ci ccscssstecateeeeee 1799 5.12 5.98 
 W.. Strive, cencacaee eee gece 1826 4.36 6.74 
 Encke and Galle............... 1838 4,04 7.06 
 Otto Strave.c.ce-ceee eee ee 1851 3.67 7.43 
 
 If these estimates and measures were certainly accurate, 
 they would place the fact of a progressive approach of the 
 rings to the ball beyond doubt, an approach which, if it con- 
 tinted at the same rate, would bring the inner edge of the 
 ring into contact with the planet about the year 2150. But 
 in measuring such an object as the inner edge of the ring of 
 Saturn, which, as we have just said,seems to fade gradually 
 into the obscure ring, different observers will always obtain 
 different results, and the differences among the four observ- 
 ers commencing with W. Struve are no greater than are often 
 seen in measuring an object of such uncertain outline. Hence, 
 considering the great improbability of so stupendous a cosmi- 
 cal change going on with so much rapidity, Struve’s theory has 
 always been viewed with doubt by other astronomers. 
 
 At the same time, it is impossible to reconcile the descrip- 
 tions by the early observers with the obvious aspect of the 
 ring as seen now without supposing some change of the kind. 
 The most casual observer who now looks at Saturn will see 
 that the breadth of the two bright rings together is at least 
 half as great again, if not twice as great, as that of the dark 
 space between the inner edge of the bright ring and the plan- 
 et. But Huyghens describes the dark space as about equal 
 to the breadth of the ring, or a little greater. Supposing the 
 ring the same then, as now, could this error have arisen from 
 the imperfection of his telescope? No; because the effect of 
 the imperfection would have been directly the opposite. The 
 old telescopes all represented planets and other bright objects 
 too large, and therefore would show dark spaces too small, 
 owing to the irradiation produced by their imperfect glasses. 
 A strong confirmation of Struve’s view is found in the old 
 
CONSTITUTION OF THE RING. 357 
 
 pictures given in Ifig. 89 by those observers who could not 
 clearly make out the ring. In nearly all cases the dark spaces 
 were more conspicuous than the edges of the ring. But if 
 we now look at Saturn through a very bad atmosphere, though 
 the elliptical outline of the ring may be clearly made out, 
 the dark space will be almost obliterated by the encroachment 
 of the light of the planet and ring upon it. The question is, 
 therefore, one of those the complete solution of which must 
 be left to future observers. 
 
 § 5. Constitution of the Ring. 
 
 The difficulties which investigators have met with in ac- 
 counting for the rings of Saturn are of the same nature as 
 those we have described as arising from spectroscopic discov- 
 eries respecting the envelopes of the sun. They illustrate the 
 philosophic maxim that surprise—in which term we may in- 
 clude all difficnlty and perplexity which men meet with in 
 seeking to account for the phenomena of nature—is a result 
 of partial knowledge, and cannot exist either with entire ig- 
 norance or complete knowledge. Those who are perfectly 
 ignorant are surprised at nothing, because they expect noth- 
 ing, while perfect knowledge of what is to happen also pre- 
 cludes the same feeling. The astronomers of two centuries 
 ago saw nothing surprising in the fact of a pair of rings sur- 
 rounding a planet, and accompanying it in its orbit, because 
 they were not acquainted with the effects of gravitation on 
 such bodies as the rings seemed to be. But when Laplace in- 
 vestigated the subject, he found that a homogeneous and 
 uniform ring surrounding a planet could not be in a state 
 of stable equilibrium. Let it be balanced ever so nicely, the 
 slightest external force, the attraction of a satellite or of a 
 distant planet, would destroy the equilibrium, and the ring 
 would soon be precipitated upon the planet. He therefore 
 remarked that the rings must have irregularities in their 
 form, such as Herschel supposed he had seen; but he did 
 not investigate the question whether with those irregularities 
 the equilibrium would really be stable. 
 
358 THE SOLAR SYSTEM. 
 
 The question was next taken up in this country by Profess- 
 ors Peirce and Bond. The latter started from the supposed 
 result of observations—that new divisions show themselves 
 from time to time in the ring, and then close up again. He 
 thence inferred that the rings must be fluid, and, to confirm 
 this view, he showed the impossibility of even an irregular 
 solid pair of rings fulfilling all the necessary conditions of 
 stability and freedom of motion. Professor Peirce, taking up 
 the same subject from a mathematical point of view, found 
 that no conceivable form of irregular solid ring would be in a 
 state of stable equilibrium; he therefore adopted Bond’s view 
 that the rings were fluid. Following up the investigation, 
 he found that even a fluid ring would not be entirely stable 
 without some external support, and he attributed that support 
 to the attractions of the satellites. But as Laplace did not 
 demonstrate that irregularities would make the ring stable, so 
 Peirce merely fell back upon the attraction of the satellites as 
 a sort of forlorn hope, but did not demonstrate that the fluid 
 ring would really be stable under the influence of their attrac- 
 tion. Indeed, it now seems very doubtful whether this at- 
 traction would have the effect supposed by Peirce. 
 
 The next, and, we may say, the last, important step was 
 taken by Professor J. Clerk. Maxwell, of England, in the 
 Adams prize essay for 1856. He brought forward objections 
 which seem unanswerable against both the solid and the fluid 
 ring, and revived a theory propounded by Cassini about the 
 beginning of the last century.* This astronomer considered 
 the ring to be formed by a cloud of satellites, too small to 
 be separately seen in the telescope, and too close together to 
 admit of the intervals between them being visible. This is 
 the view of the constitution of the rings of Saturn now most 
 generally adopted. The reason why the ring looks solid and 
 continuous is that the satellites are too small and too numerous 
 to be seen singly. They are like the separate little drops of 
 
 * See Memoirs of the French Academy of Sciences for 1715, p. 47; or Cas- 
 sini’s ‘‘ Elémens d’Astronomie,” p. 338, Paris, 1740. 
 
} 
 THE SATELLITES OF SATURN. 359 
 
 water of which clouds and fog are composed, which, to our 
 eyes, seem like solid masses. In the dusky ring the particles 
 may be so scattered that we can see through the cloud, the 
 reason that it looks dusky being simply the,comparatively 
 small number of the particles, so that to the distant eye they 
 appear like the faint stippling of an engraving. 
 
 The question arises whether the comparative darkness of 
 some portious of the bright ring may not be due to the paucity 
 of the particles, which allows the dark background of the sky 
 to be seen through. This question cannot be positively an- 
 swered until further observations are made; but the prepon- 
 derance of evidence favors the view that the entire bright 
 ring is opaque, and that the dark shading is due entirely to a 
 darker color of that part of the ring. Indeed, for anything 
 we certainly know, the whole ring may be continuous and 
 opaque, the darker shade of some parts arising solely from the 
 particles being there black in color. The only way to settle 
 conclusively the questions whether these parts of the ring look 
 black, owing to the sky beyond showing through openings, as 
 it were, or from a black color of the ring, is to find whether a 
 star or other object can be seen through the dark spaces. But 
 an opportunity for seeing a bright star through the ring has 
 never yet presented itself. The most obvious way of settling 
 the question in respect to the dusky ring is to notice whether 
 the planet itself can be seen through it; but this is much more 
 difficult than might be supposed, owing to the ill-defined as- 
 pect of the ring. The testimony of both Lassell and Trouve- 
 lot is in favor of the view that this ring is partially transpar- 
 ent; but their observations will need to be repeated when the 
 ring is opened out to our sight after 1882. 
 
 $ 6. The Satellites of Saturn. 
 
 When Huyghens commenced his observations of Saturn in 
 1655, he saw a star near the planet which a few days’ observa- 
 tion enabled him to recognize as a satellite revolving round it 
 in about fifteen days. In his “ Systema Saturnium,” he vent- 
 ured to express the opinion that this discovery completed the 
 
360 THE SOLAR SYSTEM. 
 
 solar system, which now comprised six planets (Saturn being 
 then the outermost known planet) and six satellites (one of 
 the earth, four of Jupiter, and this one of Saturn), making 
 the perfect number of twelve. He was, therefore, confident 
 that no more satellites were left to discover, and through fail- 
 ing to search for others, he probably lost the honor of addi- 
 tional discoveries. 
 
 Twelve years after this prediction, Cassini discovered a sec- 
 ond satellite outside that found by Huyghens, and within a 
 few years more he found three others inside of it. The dis- 
 covery of four satellites by one astronomer was so brilliant a 
 result of French science that the Government of France 
 struck a medal in commemoration of it, bearing the inscrip- 
 tion Satwrni Satellites primum cogniti. These five satellites 
 completed the number known for more than a century. In 
 1789 Herschel discovered two new ones still nearer the ring 
 than those found by Cassini. The space between the ring and 
 the inner one is so small that the satellite is generally invisible, 
 even in the most powerful telescopes. Finally, in September, 
 1848, the Messrs. Bond, at the Observatory of Harvard Col- 
 lege, found an eighth satellite, while examining the ring of 
 Saturn. Bya singular coincidence, this satellite was found by 
 Mr. Lassell, of England, only a couple of nights after it was 
 detected by the Bonds. The names which have been given to 
 these bodies are shown in the following list,in which the sat- 
 ellites are arranged in the order of their distance from the 
 planet. The distances are given in semidiameters of Saturn. 
 More exact elements will be found in the Appendix to this 
 volume. 
 
 Distance from 
 
 Plahet: Discoverer. Date. 
 
 Herschel... | 1789, September 17th. 
 Enceladus. : Herschel.. | 1789, August 28th. 
 Tethys..... D. Cassini.... | 1684, March. 
 
 Cassini.... | 1684, March. 
 
 a Cassini.... | 1672, December 23d. 
 
 Titan : Huyghens. | 1655, March 25th. 
 Hyperion. : 1848, September 16th. 
 Japetus.... ; Cassini.... | 1671, October. 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 
URANUS AND ITS SATELLITES. 861 
 
 The brightness, or rather, the visibility, of these satellites 
 follows the same order as their discovery. The smallest tel- 
 escope will show Titan, and one of very moderate size will 
 show Japetus in the western part of its orbit. Four or five 
 inches aperture will show Rhea, and perhaps Tethys and Di- 
 one, while seven or eight inches are required for Enceladus, 
 and even with that aperture it will probably be seen only near 
 its greatest elongation from the planet. Mimas can be seen 
 only near the same position, unless the ring is seen edgewise, 
 and will then require a large telescope, probably twelve inches 
 or upwards. I inally, Hyperion can be recognized only with 
 the most powerful telescopes, not only on account of its faint- 
 ness, but of the difficulty of distinguishing it from minute stars. 
 
 All these satellites, except Japetus, revolve very nearly in 
 the plane of the ring. Consequently, when the edge of the 
 ring is turned towards the earth, the satellites seem to swing 
 from one side of the planet to the other in a straight line, run- 
 ning along the thin edge of the ring, like beads on a string. 
 This phase affords the best opportunity of seeing the inner 
 satellites Mimas and Enceladus, because they are no longer 
 obscured by the brilliancy of the ring. 
 
 Japetus, the outer satellite of all, exhibits this remarkable 
 peculiarity, that while in one part of its orbit it is the bright- 
 est of the satellites, except Titan, in the opposite part it is al- 
 most as faint as Hyperion, and can be seen only in large 
 telescopes. When west of the planet, it is bright; when east 
 of it,faint. This peculiarity has been accounted for only by 
 supposing that the satellite, like our moon, always presents 
 the same face to the planet, and that one side of it is white 
 and the other intensely black. The only difficulty in the way 
 of this explanation is that it is doubtful whether any known 
 substance is so black as one side of the satellite must be to 
 account for such great changes of brillianey. 
 
 § 7. Uranus and its Satellites. 
 
 Uranus, the next planet beyond Saturn, is at a mean dis- 
 tance from the sun of about 1770 millions of miles, and per- 
 
362 THE SOLAR SYSTEM. 
 
 forms a revolution in 84 years. It shines as a star of the sixth 
 magnitude, and can therefore be seen with the naked eye, if 
 one knows exactly where to look for it. It was in opposition 
 February 20th, 1879, and the time of opposition during the 
 remainder of the present century may be found by adding 44 
 days for every year subsequent to 1879. ‘To find it readily, 
 either with a telescope or the naked eye, recourse must be had 
 to the Mautical Almanac, where the position (right ascension 
 and declination) is given for each day in the year. 
 
 Of course the smallest telescopes will show this planet as a 
 star, but to recognize its disk a magnifying power of at least 
 100 should be used, and 200 will be necessary to any one who 
 is not a practised observer. As seen in a large telescope, the 
 planet has a decided sea-green color. No markings have ever 
 been certainly seen on the disk, and therefore no changes 
 which could be due to an axial rotation have ever been estab- 
 lished ; but it may be regarded as certain that it does rotate 
 in the same plane in which the satellites revolve around it. 
 
 Discovery of Uranus.— This planet was discovered by Sir 
 William Herschel, in March, 1781. Perceiving by its disk 
 that it was not a star, and by its motion that it was not a neb- 
 ula, he took it for a comet. The possibility of its being a new 
 planet did not at first occur to him; and he therefore com- 
 municated his discovery to the Royal Society as being one of 
 anew comet. Various computing astronomers thereupon at- 
 tempted to find the orbit of the supposed comet, from the ob- 
 servations of Herschel and others, assuming it to move in a 
 parabola, like other comets. But the actual motion of the 
 body constantly deviated from the orbits thus computed to 
 such an extent that new calculations had to be repeatedly 
 made. After a few weeks it was found that if it moved in a 
 parabola, the nearest distance to the sun must be at least four- 
 teen times that of the earth from the sun, a perihelion distance - 
 many times greater than that of any known comet. This an- 
 nouncement gave the hint that some other hypothesis must be 
 resorted to, and it was then found that all the observations 
 could be well represented by a circular orbit, with a radius 
 
° 
 
 “URANUS AND ITS SATELLITES. 363 
 
 nineteen times that of the earth’s orbit. The object was, there- 
 fore, a planet moving at double the distance of Saturn. 
 
 With a commendable feeling of gratitude towards the royal 
 patron who had afforded him the means of making his dis- 
 coveries, Herschel proposed to call the new planet Georgiwm 
 Sidus (the Star of the Georges). This name, contracted to “the 
 Georgian,’ was employed in England until 1850, but never 
 came into use on the Continent. Lalande thought the most 
 appropriate name of the planet was that of its discoverer, and 
 therefore proposed to call it Herschel. But this name met 
 with no more favor than the other. Several other names were 
 proposed, but that of Uranus at length met with universal 
 adoption. It was proposed by Bode as the most appropriate, 
 on the ground that the most distant body of our system might 
 be properly named after the oldest of the gods. 
 
 After the elliptic orbit of the planet had been accurately 
 computed, and its path mapped out in the heavens, it was 
 found that it had been seen a surprising number of times as a 
 star without the observers having entertained any suspicion of 
 its planetary nature. It had passed through the field of their 
 telescopes, and they had noted the time of its transit, or its 
 declination, or both, but had entered it in their journals simply 
 as an unnamed star of the constellation in which it happened 
 to be at the time. It had been thus seen five times by Flam- 
 steed, the first observation being in 1690, nearly a century be- 
 fore the discovery by Herschel. What is most extraordina- 
 ry, it had been observed eight times in rapid succession by 
 Le Monnier, of Paris, in December, 1768, and January, 1769. 
 Had that astronomer merely taken the trouble to reduce and 
 compare his observations, he would have anticipated Herschel 
 by twelve years. Indeed, considering how easily the planet 
 can be seen with the naked eye, it is illustrative of the small 
 amount of care devoted to cataloguing the stars that it was 
 not discovered without a telescope. 
 
 Satellites of Uranus.—In January and February, 1787, 
 Herschel found that Uranus was accompanied by two satel- 
 lites, of which the inner performed a revolution in a little less 
 
364 THE SOLAR SYSTEM. : 
 
 than’ nine days, and the outer in thirteen days and a half. 
 The existence of these two satellites was well authenticated 
 by his observations, and they have been frequently observed 
 in recent times. They can be seen with a telescope of one- 
 foot aperture or upwards. Afterwards Herschel made a very 
 assiduous search for other satellites. He encountered many 
 difficulties, not only from the extreme faintness of the objects, 
 but from the difficulty of deciding whether any object he 
 might see was a satellite, or a small star which happened to 
 be in the neighborhood. He at length announced the probable 
 existence of four additional satellites, the orbit of one being 
 inside of those of the two certain ones, one between them, and 
 two outside them. ‘This made an entire number of six; and 
 though the evidence adduced by Herschel in favor of the ex- 
 istence of the four additional ones was entirely insufficient, 
 and their existence has been completely disproved, they figure 
 iu some of our books on astronomy to this day. 
 
 For half a century no telescope more powerful than that of 
 Herschel was turned upon Uranus, and no additional light was 
 thrown upon the question of the existence or non-existence of 
 the questionable objects. At length,about 1846, Mr. William 
 Lassell, of England, constructed a reflector of two feet aper- 
 ture, of which we have already spoken, and of very excellent 
 definition, which in optical power exceeded any of the older 
 instruments. With this he succeeded in discovering two new 
 satellites inside the orbits of the two brighter ones,* but found 
 no trace of any of the additional satellites of Herschel. In the 
 climate of England, he could make only very imperfect obser- 
 vations of these bodies; but in 1852 he moved his telescope 
 temporarily to Malta, to take advantage of the purer sky of 
 that latitude, and there he succeeded in determining their or- 
 bits with considerable accuracy. Their times of revolution 
 are about 24 and 4 days respectively. They may fairly be 
 
 * These difficult objects were also sought for by Otto Struve with the fifteen- 
 inch telescope of the Pulkowa Observatory, and occasional glimpses of them were, 
 he believed, attained before they were certainly found by Mr. Lassell, but he wag 
 not able to follow them so continuously as to fix upon their times of revolution. 
 
 — 
 
URANUS AND ITS SATELLITES. 360 
 
 regarded as the most difficult known objects in the planetary 
 system; indeed, it is only with a few of the most powerful 
 telescopes in existence that they have certainly been seen. 
 
 The non-existence of Herschel’s suspected satellites is proved 
 by the fact that they have been sought for in vain, both with 
 Mr. Lassell’s great reflectors and with the Washington twen- 
 ty-six-inch refractor, all of which are optically more powerful 
 than the telescopes of Herschel. There may be additional 
 satellites which have not yet been discovered ; but if so, they 
 must be too fait to have been recognized by Herschel. Pro- 
 fessor Holden, of the Naval Observatory, has sought to show 
 that some of Herschel’s observations of his supposed inner sat- 
 ellites were really glimpses of the objects afterwards discoy- 
 ered by Mr. Lassell. This he has done by calculating the po- 
 sitions of these inner satellites from tables for the date of 
 each of Herschel’s observations, and comparing them with the 
 position of the object noted by Herschel. In four cases, the 
 agreement is sufficiently close to warrant the belief that Her- 
 schel actually saw the real satellites; but Mr. Lassell attributes 
 these coincidences to chance, and contests Professor Holden’s 
 views. 
 
 The most remarkable pecularity of the satellites of Uranus 
 is the great inclination of their orbits to the ecliptic. Instead 
 ef being inclined to it at small angles, like the orbits of all 
 the other planets and satellites, they are nearly perpendicular 
 to it; indeed, in a geometrical sense, they are more than per- 
 pendicular, because the direction of the motion of the satel- 
 lites in their orbits is retrograde. To change the position of 
 the orbit of an ordinary satellite into that. of the orbits of 
 these satellites, it would have to be tipped over 100°; so that, 
 supposing the orbit a horizontal plane, the point correspond- 
 ing to the zenith would be 10° below the horizon, and the up- 
 per surface would be inclined beyond the perpendicular, so as 
 to be the lower of the two surfaces. 
 
 Observations of the satellites afford the only accurate way 
 of determining the mass of Uranus; because, of the adjoining 
 planets, Saturn and Neptune, the observations of the first are 
 
t., 
 
 366 THE SOLAR SYSTEM. 
 
 too’ uncertain and those of the last too recent to give any cer: 
 tain result. Measures made with the great Washington tele- 
 scope show this mass to be gstoy; a result which is probably 
 correct within $5 part of its whole amount.* 
 
 § 8. Neptune and its Satellite. | 
 
 The discovery of this planet is due to one of the boldest and 
 most brilliant conceptions of modern astronomy. The planet 
 was felt, as it were, by its attraction upon Uranus; and its di- 
 rection was thus calculated by the theory of gravitation before 
 it had been recognized by the telescope. An observer was 
 told that if he pointed his telescope towards a certain point in 
 the heavens, he would see a new planet. He looked, and there 
 was the planet, within a degree of the calculated place. It is 
 difficult to imagine a more striking illustration of the certain- 
 ty of that branch of astroromy which treats of the motions of 
 the heavenly bodies and is founded on the theory of gravi- 
 tation. 
 
 To describe the researches which led to this result, we shall 
 have to go back to 1820. In that year, Bouvard, of Paris, 
 prepared improved tables of Jupiter, Saturn, and Uranus, 
 which, although now very imperfect, have formed the basis of 
 most of the calculations smce made on the motions of those 
 bodies. He found that while the motions of Jupiter and Sat- 
 urn were fairly in accord with the theory of gravitation, it 
 was not so with those of Uranus. After allowing for the per- 
 turbations produced by the known planets, it was impossible 
 to find any orbit which would satisfy both the ancient and the 
 recent observations of Uranus. By the ancient observations 
 we mean those accidental ones made by Flamsteed, Le Mon- 
 nier, and others, before the planetary character of the object 
 was suspected ; and by the recent ones, those made after the 
 discovery of the planet by Herschel, in 1781. Bouvard, there- 
 fore, rejected the older observations, founding his tables on the 
 modern ones alone; and leaving to future investigators the 
 
 * Washington Observations for 1873: Appendix, 
 
NEPTUNE AND ITS SATELLITE. 367 
 
 question whether the difficulty of reconciling the two systems 
 arose from the inaccuracy of the ancient observations, or from 
 the action of some extraneous influence upon the planet. 
 
 Only a few years elapsed, when the planet began to deviate 
 from the tables of Bouvard. In 1830 the error amounted to 
 20’; in 1840, to 90’; in 1844, to 2’. From a non-astro- 
 nomical point of view, these deviations were very minute. 
 Had two stars moved in the heavens, the one in the place 
 of the real planet, the other in that of the calculated planet, 
 it would have been an eye of wonderful keenness which 
 could have distinguished the two from a single star, even in 
 1844. But, magnified by the telescope, it is a large and 
 easily measurable quantity, not for a moment to be neglect- 
 ed. The probable cause of the deviation was sometimes’ a 
 subject of discussion among astronomers, but no very definite 
 views respecting it seem to have been entertained, nor did 
 any one express the decided opinion that it was to be attrib- 
 uted to a trans-Uranian planet, natural as it seems to us such 
 an opinion would have been. 
 
 In 1845, Arago advised his then young and unknown friend 
 Leverrier, whom he knew to be an able mathematician and 
 an expert computer, to investigate the subject of the motions 
 of Uranus. Leverrier at once set about the task in the most 
 systematic manner. The first step was to make sure that the 
 deviations did not arise from errors.in Bouvard’s theory and 
 tables; he therefore commenced with a careful recomputation 
 of the perturbations of Uranus produced by Jupiter and Sat- 
 urn, and a critical examination of the tables. The result was 
 the discovery of many small errors in the tables, which, how- 
 ever, were not of a character to give rise to the observed de- 
 viations. 
 
 The next question was whether any orbit could be assigned 
 which, after making allowance for the action of Jupiter and 
 Saturn, would represent the modern observations. The an- 
 swer was in the negative, the best orbit deviating, first on one 
 side and then on the other, by amounts too great to be attrib- 
 
 uted to errors of observation. Supposing the deviations to be 
 R 25 
 
368 THE SOLAR SYSTEM. 
 
 due to the attraction of some unknown planet, Leverrier next: 
 inquired where this planet must be situated. Its orbit conld 
 not lie between those of Saturn and Uranus, because then it 
 would disturb the motions of Saturn as well as those of Uranus. 
 Outside of Uranus, therefore, the planet must be looked for, 
 and probably at not far from double the distance of that 
 body; this being the distance indicated by the law of Titius. 
 Complete elements of the orbit of the unseen planet were 
 finally deduced, making its longitude 325° as seen from the 
 earth at the beginning of 1847. This conclusion was reached 
 in the summer of 1846. 
 
 Leverrier was not alone in reaching this result. In 1848, 
 Mr. John C. Adams, then a student at Cambridge University, 
 England, having learned of the discordances in the theory of 
 Uranus from a report of Professor Airy, attacked the same 
 problem which Leverrier took hold of two years later. In 
 October, 1845, he communicated to Professor Airy elements 
 of the planet so near the truth that, if a search had been made 
 with a large telescope in the direction indicated, the planet 
 could hardly have failed to be found. The Astronomer Royal 
 was, however, somewhat incredulous, and deferred his search 
 for further explanations from Mr. Adams, which, from some 
 unexplained cause, he did not receive. Meanwhile the planet, 
 which had been in opposition about the middle of August, 
 was lost in the rays of the sun, and could not be seen before 
 the following summer. A most extraordinary circumstance 
 was that nothing was immediately published on the subject of 
 Mr. Adams’s labors, and no effort made to secure his right to 
 priority, although in reality his researches preceded those of 
 Leverrier by nearly a year. 
 
 In the summer of 1846, M. Leverrier’s elements appeared, 
 and the coincidence of his results with those of Mr. Adams 
 was so striking, that Professor Challis, of the Cambridge Ob- 
 servatory, commenced a vigorous search for the planet. Un- 
 fortunately, he adopted a mode of search which, although it 
 made the discovery of the planet certain, was extremely la- 
 borious. Instead of endeavoring to recognize it by its disk, 
 
NEPTUNE AND ITS SATELLITE. 369 
 
 he sought to detect it by its motion among the stars—a 
 course which required all the stars in the neighborhood to 
 have their positions repeatedly determined, so as to find 
 which of them had changed its position. Observations of 
 the planet as a star were actually made on August 4th, 1846, 
 and again on August 12th; but these observations, owing to 
 Mr. Challis’s other engagements, were not reduced, and so the 
 fact that the planet was observed did not appear. His mode 
 of proceeding was much like that of a man who, knowing that 
 a diamond had dropped near a certain spot on the sea-beach, 
 should remove all the sand in the neighborhood to a conven- 
 ient place for the purpose of sifting it at his leisure, and 
 should thus have the diamond actually in his possession with- 
 out being able to recognize it. : 
 Early in September, 1846, while Professor Challis was still 
 working away at his observations, entirely unconscious that 
 the great object of search was securely imprisoned in the pen- 
 cilled figures of his note-book, Leverrier wrote to Dr. Galle, at 
 Berlin, suggesting that he should try to find the planet. It 
 happened that a map of the stars in the region occupied by 
 the planet was just completed, and on pointing the telescope 
 of the Berlin Observatory, Galle soon found an object which 
 had a planetary disk, and was not on the star map. Its posi- 
 tion was carefully determined, and on the night following it 
 was re-examined, and found to have changed its place among 
 the stars. No further doubt could exist that the long-songht- 
 for planet was found. The date of the optical discovery was 
 September 23d, 1846. The news reached Professor Challis 
 October Ist, and, looking into his note-book, he found his own 
 observations of the planet, made nearly two months before. 
 As between Leverrier and Adams, the technical right of 
 priority in this wonderful investigation Jay with Leverrier, al- 
 though Adams had preceded him by nearly a year, for the 
 double reason that the latter did not publish his results before 
 the discovery of the planet, and that it was by the directions 
 of Leverrier to Dr. Galle that the actual discovery was made. 
 But this does not diminish the credit due to Mr. Adams for 
 
370 THE SOLAR SYSTEM. 
 
 his boldness in attacking, and his skill in successfully solving, 
 so noble a problem. The spirit of true science is advancing 
 to a stage in which contests about priority are looked upon as 
 below its dignity. Discoveries are made for the benefit of 
 mankind; and if made independently by several persons, it is 
 fitting that each should receive all the credit due to success in 
 making it. We should consider Mr. Adams as entitled to the 
 same unqualified admiration which is due to a sole discoverer ; 
 and whatever claims to priority he may have lost by the more 
 fortunate Leverrier will be compensated by the sympathy 
 which must ever be felt towards the talented young student 
 in his failure to secure for his work that immediate publicity 
 which was due to its interest and importance. 
 
 The discovery of Neptune gave rise to a series of research- 
 es, in which American astronomers took a distinguished part. 
 One of the first questions to be considered was whether the 
 planet had, like Uranus, been observed as a star by some pre- 
 vious astronomer. This question was taken up by Mr. Sears C. 
 Walker, of the Naval Observatory. A few months’ observa- 
 tion sufficed to show that the distance of the planet from the 
 sun was not far from 30 (the distance of the earth being, as 
 usual, unity), and, assuming a circular orbit, he computed the 
 approximate place of the planet in past years. He traced its 
 course back from year to year in order to find whether at any 
 time it passed through a region which was at the same time 
 being swept by the telescopes of observers engaged in prepar- 
 ing catalogues of stars. He was not successful till he reached 
 the year 1795. On the 8th and 10th of May of that year, 
 Lalande, of Paris, had swept over the place of the planet. It 
 must now be decided whether any of the stars observed on 
 those nights could have been Neptune. Although the exact 
 place of the planet could not yet be fixed for an epoch so 
 remote, it was easy to mark ont the apparent position of its 
 orbit as a line among the stars, and it must then have been 
 somewhere on that line. After taking out the stars which 
 were too far from the line, and those which had been seen by 
 subsequent observers, there remained one, observed on May 
 
NEPTUNE AND ITS SATELLITE. swee 
 
 10th, which was very near the computed orbit. Walker at 
 once ventured on the bold prediction that if this region of 
 the heavens were examined with a telescope, that star would 
 be found missing. He communicated this opinion officially 
 to Lieutenant Maury and other scientific men in Washington, 
 and asked that the search might be made. On the first clear 
 evening the examination was made by Professor Hubbard, 
 and, surely enough, the star was not there. 
 
 There was, however, one weak point in the conclusion that 
 this was really the planet Neptune. Lalande had marked his 
 observation of the missing star with a colon, to indicate that 
 there was a doubt of its accuracy: therefore it was possible 
 that the record of the supposed star might have been the sim- 
 ple result of some error of observation. Happily, the origirfal 
 manuscripts of Lalande were carefully preserved at the Paris 
 Observatory; and as soon as the news of Walker’s researches 
 reached that city an examination of the observations of May 
 8th and 10th, 1795, was entered upon. The extraordinary dis- 
 covery was made that there was no mark of uncertainty in the 
 original record, but that Lalande had observed the planet both 
 on the 8thand 10th of May. The object having moved slight- 
 ly during the two days’ interval, the observations did not 
 agree ; and. Lalande supposed that one of them must be wrong, 
 entirely unconscious that in that little discrepancy lay a dis- 
 covery which would have made his name immortal. Without 
 further examination, he had rejected the first observation, and 
 copied the second as doubtful on account of the discrepancy, 
 and thus the pearl of great price was dropped, not to be 
 found again till a half-century had elapsed. 
 
 For several years the investigation. of the motion of the new 
 planet was left in the hands of Mr. Walker and Professor 
 Peirce. The latter was the first one to compute the perturba- 
 tions of Neptune produced by the action of the other planets. 
 The results of these computations, together with Mr. Walk- 
 er’s elements, are given in the Proceedings of the American 
 Academy of Arts and Sciences. | 
 
 Physical Aspect of Neptune-—On the physical appearance of 
 
312 THE SOLAR SYSTEM. 
 
 ‘this planet very little can be said. In the largest telescopes 
 and through the finest atmosphere, it presents the appearance 
 of a perfectly round disk about 3’’ in diameter, of a pale-blue 
 color. No markings have been seen upon it. When first 
 seen by Mr. Lassell, he suspected a ring, or some such append- 
 age; but future observations under more favorable circum- 
 stances showed this suspicion to be without foundation. To 
 recognize the disk of Neptune with ease,a magnifying power 
 of 800 or upwards must be employed. 
 
 Satellite of Neptune-—Soon after the discovery of Neptune, 
 Mr. Lassell, scrutinizing it with his two-foot. reflector, saw on 
 various occasions a point of light in the neighborhood. Dur- 
 ing the following year it proved to be a satellite, having a pe- 
 riod of revolution of about 5 days 21 hours. During 1847 
 and 1848 the satellite was observed, both at Cambridge by the 
 Messrs. Bond, and at Pulkowa by Struve. These observations 
 showed that its orbit was inclined about 30° to the ecliptic, 
 but it was impossible to decide in which direction it was mov- 
 ing, since there were two positions of the orbit, and two di- 
 rections of motion, in which the apparent motion, as seen from 
 the earth, would be the same. After a few years the change 
 in the direction of the planet enabled this question to be de- 
 cided, and showed that the motion was retrograde. The case 
 was more extraordinary than that of the satellites of Uranus, 
 since, to represent both the position of the orbit and the di- 
 rection of motion in the usual way, the orbit would have to be 
 tipped over 150°; it is, in fact, nearly upside down. The de- 
 terminations of the elements of the satellite have been ex- 
 tremely discordant, a circumstance which we must attribute 
 to its extreme faintness. It is a minute object, even in the 
 most powerful telescopes. 
 
 Measures of the distance of the satellite from the planet, 
 made with the great Washington telescope, show the mass of 
 Neptune tobe y5}z5- The mass deduced from the perturba- 
 tions of Uranus is +5455, an agreement as good as could be 
 expected in a quantity so difficult to determine. 
 
ASPECTS AND FORMS OF COMETS. 373 
 
 CHAPTER V. 
 
 COMETS AND METEORS. 
 
 § 1. Aspects and Forms of Comets. 
 
 Tuer celestial motions which we have hitherto described 
 take place with a majestic uniformity which has always im- 
 pressed the minds of men with a sense of the: unchangeable- 
 ness of the heavens. But this uniformity is on some occasions 
 broken by the apparition of objects of an extraordinary as- 
 pect, which hover in the heavens for a few days or weeks, like 
 some supernatural visitor, and then disappear. We refer to 
 comets, bodies which have been known from the earliest times, 
 but of which the nature is not yet deprived of mystery. 
 
 Comets bright enough to be noticed with the naked eye 
 consist of three parts, which, however, are not completely dis- 
 tinct, but run into each other by insensible degrees. These 
 are the nucleus, the coma, and the tavl. 
 
 The nucleus is the bright centre which to the eye presents 
 the appearance of an ordinary star or planet. It would hard- 
 ly excite remark but for the coma and tail by which it is ac- 
 companied. 
 
 The coma (which is Latin for hac) is a mass of cloudy or 
 vaporous appearance, which surrounds the nucleus on all sides. 
 Next to the nucleus, it is so bright as to be hardly distinguish- 
 able from it, but it gradually shades off in every direction. 
 Nucleus and coma combined present the appearance of a star, 
 more or less bright, shining through a small patch of fog, and 
 are together called the head of the comet. 
 
 The tail is a continuation of the coma, and consists of a 
 stream of milky light, growing wider and fainter as it recedes 
 from the comet, until the eye can no longer trace it. A curi- 
 
374 THE SOLAR SYSTEM. 
 
 ous feature, noticed from the earliest times, is that the tail is 
 always turned from the sun. The extent of the tail is very 
 different in different comets, that appendage being brighter 
 and longer the more brilliant the comet. Sometimes it might 
 almost escape notice, while in many great comets recorded in 
 history it has extended half-way across the heavens. The 
 actual length, when one is seen at all, is nearly always many 
 millions of miles. Sometimes, though rarely, the tail of the 
 comet is split up into several branches, extending out in 
 slightly different directions. 
 
 Such is the general appearance of a comet visible to the 
 naked eye. When the heavens were carefully swept with tel- 
 escopes, it was found that comets thus visible formed but a 
 smali fraction of the whole number. If a diligent search is 
 kept up, as many comets are sometimes found with the tele- 
 scope in a single year as would be seen in a lifetime with the 
 unaided eye. These “telescopic comets” do not always pre- 
 sent the same aspect as those seen with the naked eye. The 
 coma, or foggy light, generally seems to be developed at the 
 expense of the nucleus and the tail. Sometimes either no 
 nucleus at all can be seen with the telescope, or it is so faint 
 and ill-defined as to be hardly distinguishable. In the cases 
 of such comets, it is generally impossible to distinguish the 
 coma from the tail, the latter being either entirely invisible, 
 or only an elongation of the coma... Many well-known comets 
 consist of hardly anything but a patch of foggy light of more 
 or less irregular form. 
 
 Notwithstanding these great apparent differences between 
 the large comets and the telescopic ones, yet, when we close- 
 ly watch their respective modes of development, we find them 
 all to belong to one class. The differences are like those be- 
 tween some animals, which, to the ordinary looker-on, have 
 nothing in common, but in which the zoologist sees that every 
 part of the one has its counterpart in the other—indeed, the 
 analogy between what the astronomer sees in the growth of 
 comets and the zoologist in the growth of animals is quite 
 worthy of remark. As a general rule, all comets look nearly 
 
ASPECTS AND FORMS OF COMETS. 375 
 
 November, 3. November,71. 
 
 December i 
 
 Fig. 90.—Views of Encke’s comet in 1871, by Dr. Vogel. 
 
 alike when they first come within reach of the telescope, the 
 subsequent diversities arising from the different developments 
 of corresponding parts. The first appearance is that of a lit- 
 tle foggy patch without any tail, and very often without any 
 visible nucleus. Thus, in the case of Donati’s comet of 1858, 
 one of the most splendid on record, it was more than two 
 months after the first discovery before there was any appear- 
 
376 THE SOLAR SYSTEM. 
 
 ance of a tail. To enable the reader to see the relation of 
 this to a very diffused telescopic comet, we present a telescopic 
 view of the head of this great comet when near its brightest, 
 and three drawings of Encke’s comet, made by Dr. Vogel, in 
 November and December, 1871. 
 
 When the nucleus of a telescopic comet begins to show it- 
 self, it is commonly on the side farthest from the sun. Sev- 
 eral little branches will then be seen stretched out in the di- 
 rection of the sun, so that it will appear as if the comet had 
 a small fan-shaped tail directed towards the sun, instead of 
 from it, as is usual. Thus, in the pictures of Encke’s comet 
 in Figs. 1 and 2, the sun is towards the left, and we see what 
 
 Fig. 91.—Head of Donati’s great comet of 1858, after Bond. 
 
 looks like three little tails, the middle one pointed towards the 
 sun. But if we look at the view of Donati’s comet, Fig. 91, 
 we see several little lines branching upwards from the centre 
 of the head, and it is to these, and not to the tail, that the lit- 
 tle tails in the figures of Encke’s comet correspond. In fact, 
 the general rule is that the heads of comets have a fan-shaped 
 structure, the handle of the fan: being in the nucleus, and the 
 middle arm pointing towards the sun; and it is this append- 
 age which first shows itself. 
 
 In the larger comets, this fan is surrounded by one or more 
 
MOTIONS, ORIGIN, AND NUMBER OF COMETS. 38177 
 
 semicircular arches, or envelopes, the inner one forming its 
 curved border; but this arch does not show itself in very faint 
 comets. The true tail of the comet, when it appears, is always 
 directed from the sun, and therefore away from the fan. In 
 Fig. 90, No. 8, a very faint true tail will be seen extending 
 out towards the lower right-hand corner of the picture, which 
 was opposite to the direction of the sun. On the other hand, 
 though the branches turned towards the sun have disappeared, 
 the fan-like form can still be traced in the head. In Fig. 91, 
 the true tail is turned downwards: owing to the large scale of 
 the picture, only the commencement of it can be seen. The 
 central line of the tail, it will be remarked, is comparatively 
 dark. This is very generally the case with bright comets. i 
 
 § 2. Motions, Origin, and Number of Comets. 
 
 When it was found by Kepler that all the planets moved 
 around the sun in coni¢ sections, and when Newton showed 
 that this motion was the necessary result of the gravitation of 
 the planets towards the sun, the question naturally arose wheth- 
 er comets moved according to the same law. It was found by 
 Newton that the comet of 1680 actually did move in such an 
 orbit, but instead of being, like the. planetary orbits, nearly 
 circular, it was very eccentric, being to all appearance a pa- 
 rabola. 
 
 A parabola being one of the orbits which gravitation would 
 cause to be described, it was thus made certain that comets 
 gravitated towards the sun, like planets. It was, however, im- 
 possible to say whether the orbit was really a parabola or a 
 very elongated ellipse. The reason of this difficulty is that 
 comets are visible in only a very small portion of their orbits, 
 quite close to the sun, and in this portion the forms of a pa- 
 rabola and of a very eccentric ellipse are so nearly the same, 
 that they cannot always be distinguished. 
 
 There is this very important difference between an elliptical 
 and a parabolic orbit—that the former is closed up, and a 
 comet moving in it must come back some time, whereas the 
 two branches of the latter extend out into infinite space with- 
 
318 THE SOLAR SYSTEM. 
 
 out .ever meeting. A comet moving in a parabolic orbit will, 
 therefore, never return, but, after once sweeping past the sun, 
 will continue to recede into infinite space forever. The same 
 thing will happen if the comet moves in an hyperbola, which is 
 
 _- 
 - 
 wma. 
 
 ~ 
 ~~. 
 ~~. 
 ~ 
 - 
 - 
 Seeee, 
 
 = 
 
 ~~. 
 
 = 
 - 
 = 
 —_ 
 -— 
 
 Seen cesar sence 
 
 Parabolic orbit. 
 
 Fia. 92.—Parabolic and elliptic orbit of a comet. The comet is invisible in the dotted part 
 of the orbits, and the forms of the visible parts, a, b, cannot be distinguished in the 
 two orbits. But the ellipse forms a closed curve, while the two branches of the pa- 
 
 rabola continue forever witLout meeting. 
 the third class of orbit that may be described under the influ- 
 ence of gravitaticn. In a parabola, the slightest retardation 
 of a comet would change the orbit into an ellipse, the velocity 
 being barely sufficient to carry the comet off forever, whereas 
 
 in an hyperbola there is more or less velocity to spare. Thus 
 
 the parabola is a sort of dividing curve between the hyperbola 
 and the ellipse. 
 
 The astronomer, knowing the position of an orbit, can tell 
 exactly what velocity is necessary at any point of it in order 
 that a body moving in it may go off, never to return. A body 
 thrown from the earth’s surface with a velocity of seven miles 
 
MOTIONS, ORIGIN, AND NUMBER OF COMETS. 379 
 
 a second, and not retarded by the atmosphere, would never 
 return to the earth, but would describe some sort of an orbit 
 round the sun. It would, in fact, be a little planet. If the 
 earth were out of the way, a body moving past the earth’s 
 orbit at the rate of twenty-six miles a second would have just 
 the velocity necessary to describe a parabola. If the velocity 
 of a comet exceeds this limit at that point of its orbit which 
 is 924 millions of miles from the sun, then the comet must 
 go off into infinite space, never to return to our system. But 
 with a less velocity the comet must be brought back by the 
 sun’s attraction at some future time, the time being longer the 
 more nearly the velocity reaches twenty-six miles per second. 
 It is by the velocity that the astronomer must, in general, de- 
 - termine the form of the orbit. If it corresponds exactly to 
 the calculated limit, the orbit is a parabola; if it exceeds this 
 limit, it is an hyperbola; if it falls short of it, it is an ellipse. 
 
 Now, in the large majority of comets the velocity is so near 
 the parabolic limit that it is not possible to decide, from ob- 
 servations, whether it falls short of it or exceeds it. In the 
 case of a few comets the observations indicate an excess of 
 velocity, but the excess is so minute that its reality cannot be 
 confidently asserted. It cannot, therefore, be said with cer- 
 tainty that any known comet revolves in a hyperbolic orbit, 
 and thus it is possible that all comets belong to our system, 
 and will ultimately return to it. It is, however, certain that 
 in the majority of cases the return will be delayed many cen- 
 turies, nay, perhaps many thousand years. There are quite a 
 number of comets which are known to be periodic, returning 
 to the sun at regular intervals in elliptic orbits. Some of 
 these have been observed at several returns, so that their exact 
 period has been determined with great certainty: in the case 
 of others, the periodicity has been inferred only from the fact 
 that the velocity fell so far short of the parabolic limit that 
 there could be no doubt of the fact that the comet moved in 
 an cllipse. 
 
 In this question of cometary orbits is involved the very in- 
 teresting one, whether comets should be considered as belong: 
 
380 THE SOLAR SYSTEM. 
 
 ing to our system, or as mere visitors from the stellar spaces. 
 We may conceive of them as stray fragments of original neb- 
 ulous matter scattered through the great wilderness of space 
 around us, drawn towards our sun one by one as the long ages 
 elapse. If no planets surrounded the sun, or if, surrounding 
 it, they were immovable, a comet thus drawn in would whirl 
 around the sun in a parabolic orbit, and leave it again, not to 
 return until millions of years had elapsed, because the veloci- 
 ty it would acquire by falling towards the sun would be just 
 sufficient to carry it back into the infinite void from which it 
 came. But owing to the motions of the several planets in 
 their orbits, the comet would have its velocity changed in 
 passing each of them, the change being an acceleration or a 
 retardation, according to the way in which it passed. If the 
 total accelerations produced by all the planets exceeded the 
 retardations, the comet would leave our system with more 
 than the parabolic velocity, and would certainly never return. 
 If the retarding forces chanced to be in excess, the orbit 
 would be changed into an ellipse more or less elongated, ac- 
 cording to the amount of this excess. In the large majority 
 of cases, the retardation would be so slight that the most del- 
 icate observations could not show it, and it could be known 
 only by calculation, or by the return of the comet after tens 
 or hundreds of thousands of years, But should the comet 
 chance to pass very near a planet, especially a large planet 
 like Jupiter, the retardation might be so great as to make the 
 comet revolve in an orbit of quite short period, and thus be- 
 come a seemingly permanent member of our system. So near 
 an approach of a comet to a planet would not be likely to oc- 
 cur more than once in a number of centuries, but every time 
 it did occur there would be an even chance for an additional 
 comet of short period, the orbit of which would, at first, al- 
 most intersect that of the planet which had deranged it. It 
 might not, however, be a known comet, because the orbit 
 might be wholly beyond the reach of our vision. 
 
 All the facts connected with periodic comets tend to 
 strengthen the view that they become members of our system 
 
 ee = 
 
 a i 
 
MOTIONS, ORIGIN, AND NUMBER OF COMETS. 381 
 
 in this way. The majority of those of short period have been 
 entrapped by Jupiter. Those orbits which do not pass near 
 Jupiter generally pass near to some other planet, to whose 
 action the introduction of the comet is probably due. The 
 gradual fading away of most of the comets of short period, 
 which we shall describe more fully hereafter, gives additional 
 color to this view. 
 
 Number of Comets.—It was the opinion of Kepler that the 
 celestial spaces were as full of comets as the sea of fish, only 
 a small proportion of them coming within the range of our 
 telescopes. That only an insignificant fraction of all existing 
 comets have ever been observed, we may regard as certain. 
 Owing to their extremely elongated orbits, they, can be seen 
 only when near their perihelion, and as it is probable that the 
 period of revolution of the large majority of those which have 
 been observed is counted by thousands of years—if, indeed, 
 they ever return at all—our observations must be continued 
 for many thousand years before we have seen all which come 
 within range of our telescopes. It is also probable that all 
 which can ever be seen will be but a small fraction of the 
 number which exist, because a comet can seldom be seen un- 
 less its perihelion is either inside the orbit of the earth, or but 
 little outside of it. There are a few exceptions to the rule 
 that only such comets are seen, the most notable one being 
 that of the comet of 1729, which, at perihelion, was more than 
 four times the earth’s distance from the sun. This comet must 
 have been one of extraordinary magnitude, as almost every 
 other known comet would have disappeared entirely from the 
 most powerful telescopes of that time, if placed at the dis- 
 tance at which it was observed. 
 
 The actual number of comets recorded as visible to the 
 naked eye since the Christian era is given in the table on the 
 following page.* 
 
 — 
 
 * This table is taken at second-hand, principally from Arago (‘‘ Astronomie 
 Populaire,” livre xvii., chap. xv.). Arago mentions but edght as visible during 
 the eighteenth century. I have considered the number thirty-six, given by Klein, 
 as more probable. 
 
382 THE SOLAR SYSTEM. 
 
 Years of our Era. Paes Years of our Era. Pepe dc 
 
 From. Ost0esl 00. sc aes 22 rom O01 3to LOR aes 36 
 les Lt) BOAT PS aba 23 a) S101" S200 eee 26 
 S20) FAS VOU eS 44 15 111201 S30 Gee. ae 26 
 ol) boc tO) oe eee 27 oe) 1301) © 2400S eee 29 
 SSE EA} sao U0 care taesnees 16 “ee 1401 -* Ta00 ss. 27 
 CONDO Mt aeGO0 eee ee 25 & T5014 41600 Aoeeeeceae 3L 
 ChAT GO) ees OO eae nee Die © 160LS L700 ne eee 12 
 oe TOL “P -C00. eee 16 ee OTTO 1800s tee eceee 36 
 66) S01. 1 9900 nce 42 66 66 180 LOSS yas, ee ce eee 16 
 fe” O01, *S 10002. anaes 26 
 
 In round numbers, about five hundred comets visible to the 
 naked eye have been recorded since our era, making a general 
 average of one every four years. Besides these, nearly two 
 hundred telescopic comets have been observed since the in- 
 vention of the telescope; so that the total number of these 
 bodies observed during the period in question does not fall 
 far short of seven hundred. Several new telescopic comets 
 are now discovered nearly every year, the number sometimes 
 ranging up to six or eight. It is probable that the annual 
 number of this class discovered depends very largely on the 
 skill, assiduity, and good -fortune of the astronomers who 
 chance to be engaged in searching for them. 
 
 § 3. Remarkable Comets. 
 
 In unenlightened ages comets were looked on with terror, 
 as portending pestilence, war, the death of kings, or other 
 calamitous or remarkable events. Hence it happens that in 
 the earlier descriptions of these bodies, they are generally 
 associated with some contemporaneous event. The descrip- 
 tions of the comets themselves are, however, so vague and 
 indefinite as to be entirely devoid of either instruction or in- 
 terest, as it often happens that not even their course in the 
 heavens is stated. 
 
 The great comet of 1680 is, as already said, remarkable for 
 being not only a brilliant comet, but the one by which New- 
 ton proved that comets move under the influence of the gravi- 
 tation of the sun. It first appeared in the autumn of 1680, 
 and continued visible most of the time till the following spring. 
 
 —— 
 
REMARKABLE COMETS. 383 
 
 It fell down almost in a direct line to the sun, passing nearer 
 to that luminary than any comet before known. It passed its 
 perihelion on December 18th, and, sweeping round a large 
 arc, went back in a direction not very different from that from 
 which it came. The observations have been calculated and 
 the orbit investigated by many astronomers, beginning with 
 Newton; but the results show no certain deviation from a 
 parabolic orbit. Hence, if the comet ever returns, it is only 
 at very long intervals. Halley, however, suspected, with some 
 plausibility, that the period might be 575 years, from the fact 
 that great comets had been recorded as appearing at that in- 
 terval. The first of these appearances was in the month of 
 September, after Julius Ceesar was killed; the second, in the 
 year 531; the third, in February, 1106; while that of 1680 
 made the fourth. If, as seems not impossible, these were four 
 returns of one and the same comet, a fifth return will be seen 
 by our posterity about the year 2255. Until that time the 
 exact period must remain doubtful, because observations made 
 two centuries ago do not possess the exactitude which will 
 decide so delicate a point. 
 
 Halley's Comet.—Two years after the comet last described, 
 one appeared which has since become the most celebrated of 
 modern times. It was first seen on August 19th, 1682, and 
 observed about a month, when it disappeared. Halley com- 
 puted the position of the orbit, and, comparing it with previ- 
 ous orbits, found that it coincided so exactly with that of a 
 comet observed by Kepler in 1607, that there could be no 
 doubt of the identity of the two orbits. So close were they 
 together that, if drawn on the heavens, the naked eye would 
 almost see them joined into a single line. The chances against 
 two separate comets moving in the same orbit were so great 
 that Halley could not doubt that the comet of 1682 was the 
 same that had appeared in 1607, and that it therefore revolved 
 in a very elliptic orbit, returning about every seventy-five years. 
 His conclusion was confirmed by the fact that a comet was 
 observed in 1531, which moved in apparently the same orbit. 
 Again subtracting the period of seventy-five years, it was 
 
384 THE SOLAR SYSTEM. 
 
 found that the comet had appeared in 1456, when it spread 
 such terror throughout Christendom that Pope Calixtus or- 
 dered prayers to be offered for protection against the Turks 
 and the comet. This is supposed to be the circumstance which 
 gave rise to the popular myth of the Pope’s Bull against the 
 Comet. . 
 
 This is the earliest occasion on which observations of the 
 course of the comet were made with such accuracy that its 
 orbit could be determined. If we keep subtracting 754 years, 
 we shall find that we sometimes fall on dates when the appa- 
 rition of a comet was recorded; but without any knowledge 
 of the orbits of these bodies, it cannot be said with certainty 
 that they are identical. However, in the returns of 1456, 
 1531, 1607, and 1682, at nearly equal intervals, Halley had 
 good reason for predicting that the comet would return again 
 about 1758. This gave the mathematicians time to investi- 
 gate its motions; and the establishment, in the mean time, of 
 the theory of gravitation showed them how to set about the 
 work. It was necessary to calculate the effect of the attrac- 
 tion of the planets on the motion of the comet during the en- 
 tire seventy-six years. ‘This immense labor was performed by 
 Clairaut, who found that, in consequence of the attractions of 
 Jupiter and Saturn, the return of the comet would be delayed 
 618 days, so that it would not reach its perihelion until the 
 middle of April, 1759. Not having time to finish his calcula- 
 tions in the best way, he considered that this result was uncer- 
 tain by one month. The comet actually did pass its perihelion 
 at midnight on March 12th, 1759. 
 
 Seventy-six years more were to elapse, and the comet would 
 again appear about 1835. Meanwhile, great improvements 
 were made in the methods of computing the effects of planet- 
 ary attraction on the motions of a comet, so that mathemati- 
 cians, without expending more labor than Clairaut did, were 
 enabled to obtain much more accurate results. The French 
 were still the leading nation of the world in this sort of inves- 
 tigation, and the computation of the return of the comet was 
 undertaken independently by two of their leading astronomers, 
 
REMARKABLE COMETS. 385 
 
 De Damoiseau and De Pontécoulant. Of these, the first an- 
 nounced that it would reach its perihelion on November 4th, 
 1835; while De Pontécoulant, after revising his computations 
 with more exact determinations of the masses of the planets, 
 assigned November 138th, at 2 a.m.,as the date. The expected 
 comet ,was, of course, looked for with the greatest assiduity, 
 aud was first seen on August 5th. Approaching the sun, it 
 passed its perihelion on November 16th, at eleven o’clock in 
 the morning, only three days after the time predicted by De 
 Pontecoulant. 
 
 This was the last return of the celebrated comet of Halley. 
 It was followed until May 17th, 1836, when it disappeared 
 from the sight of the most powerful telescopes’ of the time, 
 and has not been seen since. But the astronomer can follow 
 it with the eye of science with almost as much certainty as if 
 he had it in the field of view of his telescope. We cannot yet 
 fix the time of its return with certainty; but we know that it 
 reached the farthest limit 
 of its course, whieh ex- 
 tends some distance be- | 
 yond the orbit of Nep- 
 tune, about 1873, and 
 that it is now on its re- 
 turn journey. We pre- 
 sent a diagram of its or- 
 bit, showing its position 
 in 1874. Its velocity 
 will constantly increase 
 from year to year, and 
 we may expect it to 
 reach perihelion about the year 1911. The exact date cannot 
 be fixed until the effect of the action of all the planets is com- 
 puted, and this will be a greater labor than before, not only 
 because greater accuracy will be aimed at, but because the 
 action of more planets must be taken into account. When 
 Clairaut computed the return of 1759, Saturn was the outer- 
 most known planet. When the return of 1835 was computed, 
 
 Fie. 93.—Orbit of Halley’s comet. 
 
386 THE SOLAR SYSTEM. 
 
 Uranus had been added to the list, and its action had to be 
 taken into account. Since that time Neptune has been dis- 
 covered; and the astronomer who computes the return of 1911 
 must add its action to that of the other planets. By doing so, 
 we may hope that the time of reaching perihelion will be pre- 
 dicted within one or two days. . 
 
 The Lost Biela’s Comet.—Nothing could more strikingly il- 
 lustrate the difference between comets and other heavenly 
 bodies than the fact of the total dissolution of one of the for- 
 mer. In 1826, a comet was discovered by an Austrian named 
 Biela, which was found to be periodic, and to have been ob- 
 served in 1772, and again in 1805. The time of revolution 
 was found to be six years and eight months. In the next two 
 returns, the earth was not in the right part of its orbit to ad- 
 mit of observing the comet; the latter was therefore not seen 
 again till 1845. In November and December of that year 
 it was observed as usual, without anything remarkable being 
 noticed. But in January following, the astronomers of the 
 Naval Observatory found it to have suffered an accident ney- 
 er before known to happen to a heavenly body, and of which 
 no explanation has ever been given. The comet had sepa- 
 rated into two distinct parts, of quite unequal brightness, so 
 that there were two apparently complete comets, instead of 
 one. During the month following, the lesser of the two con- 
 tinually increased, until it became equal to its companion. 
 Then it grew smaller, and in March vanished entirely, though 
 its companion was still plainly seen for a month longer. The 
 distance apart of the two portions, according to the’ computa- 
 tions of Professor Hubbard, was abont 200,000 miles. 
 
 The next return of the comet took place in 1852, and was, 
 of course, looked for with great interest. It was found still 
 divided, and the two parts were far more widely separated 
 than in 1846, their distance having increased to about a mill- 
 ion and a half of miles. Sometimes one part was the bright- 
 er, and sometimes the other, so that it was impossible to de- 
 cide which ought to be regarded as representing the principal 
 comet. The pair passed out of view about the end of Sep- 
 
REMARKABLE COMETS. 387 
 
 tember, 1852, and have not been seen since. They would, 
 since then, have made three complete revolutions, returning in 
 1859, 1865, and 1872. At the first of these returns, the rela- 
 tive positions of the comet and the earth were so unfavorable 
 that there was no hope of:seeing the former. In 1865, it 
 could not be found; but it was thought that this might be due 
 to the great distance of the comet from us. In 1872, the rela- 
 tive positions were extremely favorable, yet not a trace of the 
 object conld be seen.* It had seemingly vanished, not into 
 thin air, but into something of a tenuity compared with which 
 the thinnest air was as a solid millstone. Some invisible frag- 
 ments were, however, passing along the comet’s orbit, and pro- 
 duced a small meteoric shower, as will be explained in a later 
 section. 
 
 The Great Comet of 1843.—This remarkable comet burst 
 suddenly into view in the neighborhood of the sun about the 
 end of February, 1848. It was visible in full daylight, so that 
 some observers actually measured the angular distance be- 
 tween the comet and the sun. It was followed until the mid- 
 dle of April. The most remarkable feature of the orbit of 
 this comet has been already mentioned: it passed nearer the 
 sun than any other known body —so near it, in fact, that, 
 with a very slight change in the direction of its original mo- 
 tion, it would actually have strnek it. Its orbit did not cer- 
 - tainly deviate from a parabola. The most careful investigation 
 of it—that of Professor Hubbard, of Washington—indicated 
 a period of 530 years; but the velocity which would produce 
 this period is so near the parabolic limit that the difference 
 does not exceed the uncertainty of the observations. 
 
 Donati’s Comet of 1858.—This great comet, one of the most 
 magnificent of modern times, which hung in the western sky 
 during the autumn of 1858, will be well remembered by all 
 who were then old enough to notice it. It was first seen at 
 
 * Just after the meteoric shower, Mr. Pogson, of Madras, obtained observa- 
 tions of an object which, it was supposed, might have been a fragment of this 
 comet. But the object was some two months behind the computed position of 
 the comet, so that the identity of the two has never been accepted by astronomers. 
 
388 THE SOLAR SYSTEM. 
 
 Florence, on June 2d, 1858, by Donati, who described it as a 
 very faint nebulosity, about 3’ in diameter. About the end 
 of the month it was discovered independently by three Amer- 
 ican observers: H: P. Tuttle, at Cambridge; H. M. Parkhurst, 
 at Perth Amboy, New Jersey; and Miss Maria Mitchel, at 
 Nantucket. During the first three months of its visibility it 
 gave no indications of its future grandeur. No tail was no- 
 ticed until the middle of August, and at the end of that 
 month it was only half a degree in length, while the comet 
 itself was barely visible to the naked eye. It continued to 
 approach the sun till the end of September, and during this 
 
 Fig. 94.—Great comet of 1858, 
 
 month developed with great rapidity, attaining its greatest 
 brilliancy about the first half of October. Its tail was then 
 40° in length, and 10° in breadth at its outer end, and of a 
 curious feather-like form. About October 20th it passed so 
 far south as to be no longer visible in northern latitudes ; but 
 it was followed in the southern hemisphere until March fol- 
 lowing. 
 
 Observations of the position of this comet soon showed its 
 orbit to be decidedly elliptic, with a period of about 2000 
 years or less. A careful investigation of all the observations 
 was made by Mr. G. W. Hill, who found a period of 1950 
 
THE GREAT SOUTHERN COMET OF 1880. 3889 
 
 years. If this period is correct, the comet must have appeared 
 about ninety-two years before our era, and must appear again 
 about the year 8808; but the uncertainty arising from the im- 
 perfections of the observations may amount to fifty years. 
 
 The Great Southern Comet of 1880.—On the evening of 
 February 2d, 1880, astronomers in South America, the Cape 
 of Good Hope, and Australia were surprised to see what was 
 evidently the tail of a huge comet rising above the horizon 
 in the south-west. Its length was 40°. Detailed observations 
 were made by Dr. Gould, who observed it at Cordoba, in the 
 Argentine Republic. It was not until two days afterwards, 
 February 4th, that he finally saw the head of the comet through 
 the large telescope. It was then moving in a northerly direc- 
 tion, and,.it was supposed, would soon pass the sun and be visi- 
 ble in the northern hemisphere. But, instead of continuing its 
 northern course, it moved rapidly around the sun, and bent its 
 course once more towards the south. In consequence, it did 
 not become visible in the northern hemisphere at all. 
 
 This rapid motion around the sun showed that the comet 
 must have passed very near that object, thus reminding astron- 
 omers of the great comet of 1843. When the elements of the 
 orbit were computed it was found that the two bodies moved 
 in almost the same orbit, so that it seemed scarcely possible 
 to avoid the conclusion that this comet was a return of the 
 former one. Notwithstanding the seeming evidence in favor 
 of this view, there are several difficulties in the way of its un- 
 reserved acceptance. In the first place, the most careful com- 
 putations on the comet of 1843 showed no deviation from a 
 parabolic orbit. In the next place, if this was a return of the 
 former comet, it should have appeared at regular intervals 
 of thirty-six years and eleven months in former times. Now, 
 there is no record of such a comet having been seen at the 
 times when its return to perihelion should have occurred. It 
 is true, as Dr. Gould showed, that, by supposing a continuous 
 change in the period, certain comets which were in perihelion 
 in 1688 and 1702 might have been identical with the two in 
 question. This would have required the period to change 
 
390 THE SOLAR SYSTEM. 
 
 from thirty-four years between the first two returns to thirty- 
 six years and eleven months between the last two. Such a 
 change js so improbable that we can hardly regard the dif- 
 it appearances as belonging to absolutely Arey same bodies. 
 The most probable explanation seems to be that they were 
 originally two nebulous masses far out in the stellar spaces, 
 and that the nearer one was drawn into the sun thirty-seven 
 years in advance of the more distant one. 
 
 Great Comet of 1881.—This comet is so recent that most 
 readers will remember it. It was first heard of in our hemi- 
 sphere through a telegram from Dr. Gould, stating that the 
 comet of 1807 was in five hours of right ascension, and thirty 
 degrees south declination. Curiosity respecting the object was 
 not, however, gratified until the morning of June 23d, when 
 it was seen by observers in almost every part of the northern 
 hemisphere about the beginning of the morning twilight. Con- 
 tinuing its northern course, it reached the circle of perpetual 
 apparition early in July, and during the remainder of the 
 period of its visibility neither rose nor set. Passing near the 
 north pole of the heavens, it was visible all night for several 
 weeks. The length of the tail was variously estimated, as the 
 distance to which it could be traced depended largely on the 
 acuteness of the observer’s vision. ‘To most observers it pre- 
 sented a length of ten or fifteen degrees, though some traced 
 it much farther. | 
 
 There are two very remarkable features connected with the 
 motion of this comet. One is, that during almost its entire 
 period of visibility to the naked eye it moved on the same 
 meridian as the sun, and, indeed, while passing from the south- 
 ern to the northern. hemisphere, it may have passed over the 
 sun’s disk. The other feature is the remarkable resemblance 
 between its orbit and that of the comet of 1807. It was this 
 resemblance which led Dr. Gould to telegraph it as a return 
 of this comet. The most careful determination of the ele- 
 ments show, however, that the two bodies could not possibly 
 be identical, as both were moving in orbits differing so little 
 from a parabola that many centuries at least must elapse be- 
 
 * 
 
e 
 
 ENCKE’S COMET, AND THE RESISTING MEDIUM. 391 
 
 fore the return of either. We have, therefore, another case 
 similar to that of the great comets of 1843 and 1880—name- 
 ly, two different bodies following each other in nearly the 
 same orbit. : 
 
 § 4. Hncke's Comet, and the Resisting Medium. 
 
 -. The comet which in recent times has most excited the atten- 
 tion of astronomers is that known as Encke’s, from the astron- 
 omer who first carefully investigated its motion. It was first 
 seen in January, 1786, but the observations only continued 
 through two days, and were insufficient to determine the orbit. 
 In 1795, a comet was found by Miss Caroline Herschel, on 
 which observations were continued about three weeks; but no 
 very accurate orbit was derived from these observations. In 
 1805, the same comet returned again to perihelion, but its iden- 
 tity again failed to be recognized. As in the previous returns, 
 the observations continued through less than a month. It was 
 found, for the fourth time, by Pons, of Marseilles, in 1818. 
 When its orbit was calculated, it was seen to coincide so 
 closely with that of the comet of 1805 as to leave no doubt 
 that the two were really the same body. But the first astron- 
 omers who noticed this were unable to decide whether this 
 was its first return since 1805, or whether it had in the mean 
 time made several revolutions. 
 
 The motions of the comet were now taken up by Encke, of 
 Berlin, and investigated with a thoroughness before unknown. 
 He found the period to be about 1200 days, four complete 
 revolutions having been made between 1805 and 1818. Know- 
 ing this, there was no longer any difficulty in identifying the 
 comet of 1795 as also being the same, three complete revolu- 
 tions having been made between that date and 1805. In the 
 intermediate returns to perihelion, its position had been so 
 unfavorable that it had not been observed at all. This result 
 was received by astronomers with the greatest interest, because 
 it was the first known case of a comet of short period. Its re- 
 turn in 1822 was duly predicted, but it was found that when 
 near its greatest brilliancy it would be visible only in the 
 
4% 
 392 THE SOLAR SYSTEM. 
 
 southern hemisphere. Happily, Sir Thomas Brisbane had an 
 observatory at Paramatta, New South Wales, and his assistant, 
 Rtumker, was so fortunate as to find the comet. It was so 
 near the position predicted by Encke that, by constantly point- 
 ing the telescope in the direction predicted by that astronomer, 
 the comet was in the field of view during its whole course. 
 Encke continued to investigate the course of the comet dur- 
 ing each revolution up to the time of his death, in 1865. At 
 some returns it could not be seen, owing to its distance from 
 the earth, or the otherwise unfavorable position of our planet ; 
 but generally very accurate observations of its course were 
 made. By a comparison of its motions with those which 
 would result from the gravitation of the sun and planets, he 
 found that the periodic time was constantly diminishing, and 
 was thus led to adopt the famous hypothesis of Olbers, that 
 the comet met with a resisting medium in space. The dimi- 
 nution of the period was about two hours and a half in each 
 revolution. The conclusion of Encke and Olbers was that the 
 planetary spaces are filled with a very rare medium—so rare 
 that it does not produce the slightest effect on the motion of 
 such massive bodies as the planets. The comet being a body 
 of extreme tenuity, probably far lighter than air, it might be 
 affected by such a medium. The existence of this medium 
 cannot, however, be considered as established by Encke’s re- 
 searches. In the first place, if we grant the fact that the 
 time of revolution is continually diminishing, as maintained 
 by the great German astronomer, it does not follow that a re- 
 sisting medium is the only cause to which we can attribute it. 
 But the main point is, that the computations on which Encke 
 founded his hypothesis are of such intricacy as to be always 
 liable to small errors, and their results cannot be received 
 with entire confidence until some one else has examined the 
 subject by new and improved methods. ; 
 Such an examination is now being made by Dr. Von Asten, 
 of Pulkowa; and, although it is still unfinished, it seems like- 
 ly, in the end, to confirm Encke’s results, at least in part. Dr. 
 Von Asten commenced by calenlating the motion of the comet 
 
 ——s oo 8 ee ted D6 ee ei we ot 
 
ENCKE’S COMET, AND THE RESISTING MEDIUM. 398 
 
 from the theory of gravitation during the period from 1865 
 to 1871, within which the comet made two entire revolutions, 
 and was surprised to find that during this time there was no 
 deviation from the computed positions which could be attrib- 
 uted to the action of a resisting medium. But on carrying 
 the calculation back to 1861, he found that between that epoch 
 and 1865 there must have been a retarding action like that 
 supposed by Encke. Carrying his work forward to 1875, he 
 found that between 1871 and 1875 there was once more evi- 
 dence of a retardation about two-thirds as great as that found 
 by Encke. The absence of such an action between 1865 and 
 1871, therefore, seems quite exceptional, and difficult of ex- 
 planation. 
 
 To judge whether the deviations in the motion of Encke’s 
 comet are really due to a resisting medium, we should know 
 whether the motions of other comets exhibit similar anom- 
 alies. So far as is yet known, no other one does. There is 
 at least one which has returned a sufficient number of times, 
 and of which the motions have been computed with sufficient 
 care, to lead to an entirely definite conclusion on this point, 
 namely, the periodic comet of Faye, which has been investi- 
 gated by Moller.* This comet was discovered in 18438 by the 
 astronomer whose name it bears, and was soon found to move 
 in an elliptic orbit, with a period of a little more than seven 
 years. As it has been observed at several returns since, Moller 
 investigated its motions with a view of finding whether its 
 period was affected by any resisting medium. At first he 
 thought there was such an effect, his general result being of 
 the same nature with that reached by Encke. But on repeat- 
 ing his calculations with the improved data afforded by a first 
 calculation, he found that the result arose from the imperfec- 
 tion of the latter, and that the comet really showed no sign of 
 a change in its mean motion. It therefore seems certain that, 
 if there is a resisting medium, it does not extend out far 
 enough from the sun to meet the orbit of Faye’s comet. 
 
 * Professor Axel Moller, director of the observatory at Lund, Sweden. 
 
 S) 
 
394 THE SOLAR SYSTEM. 
 
 § 5. Other Periodic Comets. 
 
 We give, in No. IV. of the Appendix, a table of eleven 
 periodic comets which have been seen at more than one re- 
 turn to the sun. Of these, Biela’s may be regarded as totally 
 lost. All the others have, however, been seen at their several 
 returns, when their position with respect to the earth asd sun 
 admitted of it. Besides this, there are quite a number of com- 
 ets which observation showed were not moving in parabolic 
 orbits, and which, therefore, from this fact alone, we conclude 
 must return. A remarkable case of this kind is afforded by a 
 comet discovered in June, 1770, which was bright enough to 
 be seen by the naked eye. The astronomers of the time were 
 greatly surprised to find it moving in an ellipse, with a period 
 of less than six years. Therefore, not only should it have been 
 seen at previous returns, but at some twenty returns since. 
 But not only was it never seen before, but it has never been 
 seen since. Doth its appearance and disappearance are now 
 known to be due to the attraction of Jupiter. On returning 
 to its aphelion, about the beginning of 1779, it encountered 
 this planet, the attraction of which was so powerful as to 
 throw it into some entirely new orbit. 
 
 Of periodic comets seen at only one return many have pe- 
 riods so long that no especial interest attaches to the ellipticity 
 of the orbits at the present time. In other cases the observa- 
 tions are so uncertain that great doubt attaches to the reality 
 of the period. The following are all the cases in which the 
 period is reasonably probable: 
 
 A comet which passed its perihelion on November 19th, 
 1788, was found by Dr. C. Tl. F. Peters to have a period of 
 less than six years. But it was never seen before or since. 
 Its orbit was probably deranged by that of Jupiter, near 
 which it approaches. 
 
 The comet of 1812 was found by Encke to have a period 
 of seventy-one years, with an uncertainty of three years. It 
 may, therefore, be expected that this comet will reappear be- 
 fore the close of 1886. 
 
METEORS AND SHOOTING-STARS. 395 
 
 The comet of 1815 was found by Bessel to have a period 
 of seventy-four years. Its return may, therefore, be expected 
 within a few years of 1889. 
 
 The third comet of 1819 was found by Encke to have a 
 period of five years and seven months, but nothing more was 
 ever heard of it. 
 
 The fourth comet of the same year was found by the same 
 computer to have a period of less than five years, but it has 
 not been seen again. 
 
 The fourth comet of 1819 has a period of less than one 
 hundred years, but it is quite uncertain. 
 
 The same year Dr. C. H. F. Peters, at Naples, discovered, a 
 comet of quite short period, which should have returned sev- 
 eral times before now; but it has not again been seen. 
 
 The same statement applies to De Vico’s comet of 1844. 
 Therefore, besides the eleven comets which have actually been 
 observed at two returns, there are but three whose periods are 
 certain. 
 
 The next subject to which we would ask the attention of 
 the reader is that of the physical constitution of comets. But 
 this subject can be discussed only in connection with another, 
 to which, at first sight, it seems to have no relation, though 
 so curious a relatidn has really been discovered as greatly to 
 modify our views of what a comet probably is. We refer to 
 the phenomena of meteors, meteoric showers, and shooting- 
 stars, which next claim our attention. 
 
 § 6. Meteors and Shooting-stars. 
 
 If we carefully watch the heavens on a cloudless night, we 
 shall frequently see an appearance as of a star eens shoot- 
 ing through a short space in the sky, and then suddenly dis- 
 appearing. Three or four such shooting-stars may generally 
 be seen in the course of an hour. Generally they are visible 
 only for a second or two, but sometimes move slowly, and are 
 seen much longer. Occasionally they are so brilliant as to 
 illuminate the whole heavens, and they are then known as 
 meteors—a term which is equally applicable to the ordinary 
 
396 THE SOLAR SYSTEM. 
 
 shooting-stars. In general, they are seen only one at a time, 
 and are so minute as hardly to attract attention. But they 
 have on some occasions shown themselves in such numbers as 
 to fill the beholders with terror, lest the end of the world had 
 come. The Chinese, Arabian, and other historians have hand- 
 ed down to us many accounts of such showers of meteors, 
 which have been brought to light by the researches of Edward 
 Biot, Quetelet, Professor H. A. Newton, and others. As an ex- 
 ample of these accounts, we give one from an Arabian writer: 
 
 “Jn the year 599, on the last day of Moharrem, stars shot 
 hither and thither, and flew against each other like a swarm 
 of locusts; this phenomenon lasted until daybreak; people 
 were thrown into consternation, and made supplication to the 
 Most High: there was never the like seen except on the com- 
 ing of the messenger of God, on whom be benediction and 
 peace.” 
 
 In 1799, on the night of November 12th, a remarkable 
 shower was seen by Humboldt and Bonpland, who were then 
 on the Andes. Humboldt described the shower as commen- 
 cing a little before two o’clock, and the meteors as rising above 
 the horizon between east and north-east, and moving over tow- 
 ards the south. From not continuing his observations long 
 enough, or from some other cause, he failed to notice that the 
 lines in which the meteors moved all seemed to converge tow- 
 ards the same point of the heavens, and thus missed the dis- 
 covery of the real cause of the phenomenon. 
 
 The next great shower was seen in this country in 1833. 
 All through the Southern States, the negroes, like the Arabs of 
 a previous century, thought the end of the world had come at 
 last. The phenomenon was observed very carefully at New 
 Haven by Professor Olmsted, who worked out a theory of its 
 cause. Although his ideas are in many respects erroneous, 
 they were the means of suggesting the true theory to others. 
 The recurrence of the shower at this time suggested to the 
 astronomer Olbers the idea of a thirty-four-year period, and 
 led him to predict a return of the shower in 1867. <A few 
 years before the expected time, the subject was taken up by 
 
METEORS AND SHOOTING-STARS. 397 
 
 Professor Newton, of Yale College, to whose researches our 
 knowledge of the true cause of the phenomenon is very large- 
 ly due. 
 
 The phenomena of shooting-stars branch out in yet another 
 direction. As we have described them, they are seen only in 
 the higher and rarer regions of the atmosphere, far above the 
 clouds: no sound is heard from them, nor does anything reach 
 the surface of the earth from which the nature of the object 
 can be inferred. But on rare occasions meteors of extreme 
 brillianey are followed by a loud sound, like the discharge of 
 heavy artillery ; while on yet rarer occasions large masses of 
 metallic.or stony substances fall to the earth. These aérolites 
 were the puzzle of philosophers. Sometimes there was much 
 scepticism as to the reality of the phenomenon itself, it ap- 
 pearing to the doubters more likely that those who described 
 such things were mistaken than that heavy metallic masses 
 should fall from the air. When their reality was placed be- 
 yond doubt, many theories were propounded to account for 
 them, the most noteworthy of which was that they were 
 thrown from volcanoes in the moon. The problem of the 
 motion of a body projected from the moon was investigated 
 by several great mathematicians, the result being that such a 
 body could not reach the earth unless projected with a veloci- 
 ty far exceeding anything seen on our planet. 
 
 When aérolites were examined by chemists and mineralo- 
 gists, it was found that although they contained no new chem- 
 ical elements, yet the combinations of these elements were 
 quite unlike any found on the earth, so that they must have 
 originated outside the earth. Moreover, these combinations 
 exhibited certain characteristics peculiar to aérolites, so that 
 the mineralogist, from a simple examination and analysis of 
 a substance, could detect it as part of such a body, though 
 it had not been seen to fall. Great masses of matter thus 
 known to be of meteoric origin have been found in various 
 parts of the earth, especially in Northern Mexico, where, at 
 some unknown period, an immense shower of these bodies 
 seems to have fallen. 
 
(898 THE SOLAR SYSTEM. 
 
 Cuuse of Shooting-stars.—It is now universally conceded that 
 the celestial spaces are crowded with innumerable minute 
 bodies moving around the sun in every possible kind of orbit. 
 When we say crowded, we use the word in a relative sense ; 
 they may not average more than one in a million of cubic 
 miles, and yet their total number exceeds all calculation. Of 
 the nature of the minuter bodies of this class nothing is cer- 
 tainly known. But whatever they may be, the earth is con- 
 stantly encountering them in its motion around the sun. They 
 are burned by passing through the upper regions of our at- 
 mosphere, and the shooting-star is simply the light of that 
 burning. We shall follow Professor Newton in calling these 
 invisible bodies meteorords. 
 
 The question which may be asked at this stage is, Why are 
 these bodies burned? Especially, how can they burn so sud- 
 denly, and with so intense a light, as to be visible hundreds 
 of miles away? These questions were the stumbling-block of 
 investigators until they were answered, clearly and conclusive- 
 ly, by the discovery of the mechanical theory of heat. It is 
 now established that heat is only a certain form of motion ; 
 that hot air differs from cold air only in a more rapid vibra- 
 tion of its molecules, and that it communicates its heat to 
 other bodies simply by striking them with its molecules, and 
 thus setting their molecules in vibration. Consequently, if a 
 body moves rapidly through the air, the impact of the air 
 upon it ought to heat it just as warm air would, even though 
 the air itself were cold. This result of theory has been ex- 
 perimentally proved by Sir William Thomson, who found that 
 a thermometer placed in front of a rapidly moving body rose 
 one degree when the body moved through the air at the rate 
 of 125 feet per second. With higher velocities, the increase 
 of temperature was proportional to the square of the velocity, 
 being 4 degrees with a velocity of 250 feet, 16 degrees with 
 one of 500 feet per second, and so on. This resuit is in exact 
 accordance with the mechanical theory of heat. To find the 
 effective temperature to which a meteoroid is exposed in mov- 
 ing throngh our atmosphere, we divide its velocity in feet per 
 
METEORS AND SHOOTING-STARS. 399 
 
 second by 125; the square of the quotient will give the tem- 
 perature in degrees. 
 
 Let us apply this principle to the case of the meteoroids. 
 The earth moves in its orbit at the rate of 98,000 feet per 
 second; and if it met a meteoroid at rest, our atmosphere 
 would strike it with this velocity. By the rule we have given 
 for the rise of temperature (98,000 ~ 125)* = 784’ = 600,000 
 degrees, nearly. This is many times any temperature ever 
 produced by artificial means.’ If, as will commonly be the 
 case, the meteoroid is moving to meet the earth, the velocity, 
 and therefore the potential temperature, will be higher. We 
 know that the meteoroids which produce the November show- 
 ers already described move in a direction nearly opposite that 
 of the earth with a velocity of 26 miles per second, so that the 
 relative velocity with which the meteoroids meet our atmos- 
 phere is 44 miles per second. By the rule we have given, 
 this velocity corresponds to a temperature of between three 
 and four million degrees. We do not mean that the meteor- 
 oids are actually heated up to this temperature, but that the 
 air acts upon them as if it were heated up to the point men- 
 tioned; that is, it burns or volatilizes them in less than a sec- 
 ond with an enormous evolution of light and heat, just as a 
 furnace would if heated to a temperature of three million de- 
 grees. It is not at all necessary that the body should be com- 
 bustible; the light and heat of ordinary burning are nothing 
 at all compared with the deflagration which such a tempera- 
 ture would cause by acting on the hardest known body. A 
 few grains of platinum or iron striking the atmosphere with 
 the velocity of the celestial motions might evolve as much light 
 and heat as are emitted by the burning of a pint of coal-oil or 
 several pounds of gunpowder; and as the whole operation is 
 over in a second, we may imagine how intense the light must be. 
 
 The varied phenomena of aérolites, meteors, shooting-stars, 
 and meteoric showers depend solely on the number and nat- 
 ure of the meteoroids which give rise to them. If one of 
 these bodies is so large and firm as to pass through the atmos- 
 
 phere and reach the earth without being destroyed by the po: 
 27 
 
400 THE SOLAR SYSTEM. 
 
 tential heat, we have an aérolite. As this passage only occu- 
 pies a few seconds, the heat has not time to penetrate far into 
 the interior of the body, but expends itself in melting and vol- 
 atilizing the outer portions. When the body first strikes the 
 denser portion of the atmosphere, the resistance becomes so 
 enormous that the aérolite is frequently broken to pieces with 
 such violence that it seems to explode. J urther color is given 
 to the idea of an explosion by the loud detonation which fol- 
 lows, so that the explosion is frequently spoken of as a fact, 
 and as the cause of the detonation. Jeally, there is good rea- 
 son to. believe that both of these phenomena are due to the 
 body striking the air with a velocity of ten, twenty, or thirty 
 miles a second. 
 
 If, on the other hand, the meteoroid is so small or so fusible 
 as to be dissipated in the upper regions of the atmosphere, we 
 have a common shooting-star, or a meteor of greater or less 
 brilliancy. Very careful observations have been made from 
 time to time, with a view of finding the height of these bodies 
 above the earth at their appearance and disappearance. An 
 attempt of this kind was made by the Naval Observatory on 
 the occasion of the meteoric shower of November 138th, 1867, 
 when Professor Harkness was sent to Richmond to map the 
 paths of the brighter meteors as seen from that point. By 
 comparing these paths with those mapped at Washington, the 
 parallaxes, and thence the altitudes, of these bodies were de- 
 termined. The lightning-like rapidity with which the mete- 
 ors darted through their course rendered it impossible to ob- 
 serve them with astronomical precision; but the general re- 
 sult was that they were first seen at an average height of 75 
 miles, and disappeared at a height of 55 miles. There was 
 no positive evidence that any meteor commenced at a height 
 much greater than 100 miles. It is remarkable that this cor- 
 responds very nearly to the greatest height at which the most 
 brilliant meteors are ever certainly seen. These phenomena 
 seem to indicate that our atmosphere, instead of terminating 
 at a height of 45 miles, as was formerly supposed, really ex- 
 tends to a height of between 100 and 110 miles. 
 
METEORS AND SHOOTING-STARS. 401 
 
 The ordinary meteors, which we may see on every clear 
 evening, move in every direction, thus showing that their or- 
 bits lie in all possible positions, and are seemingly scattered 
 entirely at random. But the case is quite different with those 
 meteoroids which give rise to meteoric showers. Here we 
 have a swarm of these bodies, all moving in the same direc- 
 tion in parallel lines. If we mark, en a celestial globe, the 
 
 320 
 
 GYGNUS 
 
 LACERTA 
 . 
 
 PEGASUS 
 
 VEVET IC! 
 
 784) 
 
 Pisces 
 
 psai- 2 
 BD 
 
 P TER\UN 
 
 Fluvin’s 
 
 ERIDANUS 
 
 Fie. 95.—Meteor paths, illustrating the radiant point. 
 
 apparent paths of the meteors which fall during a shower, o7 
 if we suppose them marked on the celestial sphere, and then 
 continue them backwards, we shall find them all to meet in 
 the same point of the heavens. This is called the radiant 
 point. It always appears in the same position, wherever the 
 observer is situated, and does not partake of the diurnal mo- 
 
402 THE SOLAR SYSTEM. 
 
 ~ tion of the earth; that is, as the stars seem to move towards 
 the west in their diurnal course, the radiant point moves with 
 them. The point in question is purely an effect of perspec- 
 tive, being the “vanishing point” of the parallel lines in 
 which the meteors really move. These lines do not appear 
 in their real direction in space, but are seen as projected on 
 the celestial sphere. A good visible illustration of the effect 
 in question may be afforded by looking upwards and watch- 
 ing falling snow during a calm. The flakes which are fall- 
 ing directly towards the observer do not seem to move at all, 
 while the surrounding flakes seem to separate from them on 
 all sides. So with the meteoric showers. A meteor coming 
 directly towards the observer does not seem to move at all, 
 and marks the radiant point from which all the others seem 
 to diverge. The great importance of the determination of 
 the radiant point arises from the fact that it marks the direc- 
 tion in which the meteors are moving relatively to the earth, 
 aud thus affords some data for determining their orbits. 
 
 § 7. Relations of Comets and Meteoroids, 
 
 We have now to mention a series of investigations which 
 led to the discovery of a curious connection between meteor- 
 oids and comets. ‘These investigations were commenced by 
 Professor Newton on the November meteoric showers. Tra- 
 cing back the historical accounts of these showers to which 
 we have already alluded, he found that the thirty-three-year 
 period, which had been suspected by Olbers, was confirmed by 
 records reaching back a thousand years. Moreover, the show- 
 ers in question occurred only at a certain time of the year: in 
 1799 and 1838, it was on November 12th or November 138th. 
 In other words, the shower occurred only as the earth passed 
 a certain point of its orbit. But this point was found not to 
 be always the same, the showers being found to occur about 
 a couple of days earlier every century as they were traced 
 back. The principal conclusions to which these facts led 
 were as follows: 
 
 1. That the swarm of meteoroids which cause the Novem- 
 
 OT ———— 
 
RELATIONS OF COMETS AND METEOROIDS. 408 
 
 ber showers revolve around the sun in a definite orbit, which 
 intersects the orbit of the earth at the point which the latter 
 now passes on November 13th. 
 
 2. The point of intersection of the two orbits moves for- 
 wards about 52” per annum, or nearly a degree and a half a 
 century, owing to a change in the position of the meteoric 
 orbit. 
 
 3. The swarm of meteoroids is not equally scattered all 
 around their orbit, but the thickest portion extends along 
 about one-fifteenth of the orbit. 
 
 4. The earth meets this swarm, on the average, once in 
 33.25 years. At other times the swarm has not arrived at 
 the point of crossing, or has already passed it, and a meteoric 
 shower cannot occur unless the earth and the swarm cross at 
 the same time. 
 
 Professor Newton did not definitely determine the time of 
 revolution of the meteors in their orbit, but showed that it 
 must have one of five values. The greatest of these values, 
 and the one which it seems most natural to select, is that of 
 the mean interval between the showers, or 384 years. Adopt- 
 ing this period, it would follow that between 1799, when 
 Humboldt saw the meteoric shower, and 1833, when it was 
 seen throughout the United States, the swarm of meteoroids 
 had been flying out as far as the planet Uranus in a very el- 
 liptical orbit, and returning again. But the periodic time 
 might also be one year and about eleven days. Then the 
 group which Humboldt saw on November 12th, 1799, wonld 
 not reach the same point of its orbit until November 23d, 
 1800, when the earth would have passed by. Passing 11 days 
 later every year, it would make about 33 revolutions in 34 
 years, and thus would pass about the middle of November 
 once more, and another shower would occur. In a word, giv- 
 ing exact numbers, we might suppose that in the period of 
 334 years the meteoroids made one revolution, or 324, 344, 
 653, or 673 revolutions, and the conditions of the problem 
 would be equally satisfied. 
 
 At the same time, Professor Newton gave a test by which 
 
404 THE SOLAR SYSTEM. 
 
 the frne time could be determined. As we have said, he 
 showed that the node of the orbit changed its position 52” a 
 century, and there could be no doubt that this change was 
 due to the attraction of the planets. If, then, the effect of 
 this attraction was calculated for each of the five orbits, it 
 would be seen which of them would give the required change. 
 This was done by Professor Adams, of England, and the result 
 was that the thirty-three-year period, and that alone, was ad- 
 missible. 
 
 These researches of Professor Newton were published in 
 1864, and ended with a prediction of the return of the shower 
 on November 15th of one or more of the three following 
 years—probably 1866. This prediction was verified by a re- 
 markable meteoric shower seen in Europe on that very day, 
 which, however, was nearly over before it could become visi- 
 ble in this country. On the same date. of the year following, 
 a shower was visible in this country, and excited great public 
 interest. J*rom the data derived from the first of these show- 
 ers, Schiaparelli, an Italian astronomer, was led to the discovery 
 of a remarkable relation between meteoric and cometary orbits. 
 Assuming the period of the November meteoroids to be 334 
 years, he computed the elements of their orbit from the ob- 
 served position of the radiant point. A similar computation 
 was made by Leverrier, and the results were presented to the 
 French Academy of Sciences on January 21st, 1867. 
 
 The exact orbit which these bodies followed throngh space, 
 crossing the earth’s orbit at one point, and extending out 
 beyond the planet Uranus at another, was thus ascertained. 
 But, as these bodies were absolutely invisible, no great inter- 
 est seemed to attach to their orbit until it was found that a 
 comet was moving in that very orbit. This was a faint tele- 
 scopic comet discovered by Tempel, at Marseilles, in Decem- 
 ber, 1865. It was afterwards independently discovered by 
 Mr. H. P. Tuttle, at the Naval Observatory, Washington. It 
 passed its perihelion in January, and, receding from the sun, 
 vanished from sight in March. It was soon fonnd to move 
 in an elliptic orbit, but, owing to the uncertainty of observa- 
 
 elena at 
 
RELATIONS OF COMETS AND METEOROIDS. 405 
 
 tions on such a body, 
 there was at first some 
 disagreement as to the 
 exact periodic — time. 
 The subject was taken 
 up by Dr. Oppolzer, of 
 Vienna, who, in Janu- 
 ary, 1867, was able to 
 present a definitive or- 
 bit of the comet, which 
 was published in the As- 
 tronomische Nachrichten 
 on the 28th of that 
 month. We now pre- 
 sent the orbit of the 
 comet, as found by Op- 
 polzer, and that of the 
 x meteors, as found by 
 
 Leverrier, premising 
 that these orbits were 
 computed and publish- 
 ed within a few days 
 
 OF VV 
 pee eb, 
 
 R 
 Be 
 
 Fie. 96.—Orbit of November meteors and the comet of each other, without 
 
 Of are any knowledge on the 
 part of either astronomer of the results obtained by the other : 
 The Comet. Meteoroids. _ 
 | Period of revolution....22.......<06.. 33.18 yrs. 33.25 yrs. 
 WCCODUIGIEVenvecneas ct ccapoc dys -asees 0.9054 0.9044 
 Perihelion distance..........<..00+0 0.9765 0.9890 
 UnGlifiation of orbit. 2..........0.0006 162° 42’ T6a19' 
 Longitude of the node............++. 51° 26 51° 18’ 
 Longitude of perihelion............. 42° 24! Near node. 
 
 The similarity of these orbits is too striking to be the result 
 of chance. The only element of which the values differ ma- 
 terially is the inclination, and this difference proceeds from 
 Leverrier not having used a very exact position of the radiant 
 point in making his computations. Professor Adams found 
 by a similar calculation that the inclination of the orbit of the 
 
406 THE SOLAR SYSTEM. 
 
 meteoroids was 163° 14’, only half a degree different from that 
 of the orbit of Tempel’s comet. The result of these investiga- 
 tions was as follows: | 
 
 The November meteoric showers arise from the earth encountering 
 a swarm. of particles following 
 Tempel’s comet in its orbit. 
 
 When this fact came out, 
 Schiaparelli had been working 
 on the same subject, and had 
 come to a similar conclusion 
 with regard to another group 
 of meteors. It had long been 
 known that about August 9th 
 of every year an unusual num- 
 ber of meteors shoot forth from 
 the constellation Perseus. At 
 times these showers have been 
 inferior only to those of No- 
 vember. Thus, on August 9th, 
 1798, they succeeded each oth- 
 er so rapidly as to keep the 
 eye of the observer almost con- 9| 0a8!7 OF URANus 
 stantly engaged, and several 
 hundred may nearly always be 
 counted on the nights of the 
 9th, 10th, and 11th. These 
 August meteors are remarka- ets 
 ble in that they leave trails of iceman Ld 
 luminous vapor which often 
 last several seconds. Assum- 
 ing the orbit of this group to 
 be a parabola, it was calculated 
 by Schiaparelli, and is substan- 
 tially the same with that of a 
 comet observed in 1862. The 
 following are the elements of 
 the orbits of the two bodies: Fig. 97.—Orbit of the second comet of 1862, 
 
 oRBIT_OF NEPTUNE 
 
 ——— a 
 
RELATIONS OF COMETS AND METEOLOIDS. 407 
 
 Comet II., August 
 1862, Meteoroids. 
 
 eenmneinony distaneersmeccasccn cies: <c 0.9626 0.96438 
 iuchioation ofsorbresee. ae... 113° 35' 11557" 
 
 Longitude of the node............... een ere “188° 16’ 
 Longitude of the‘perihelion........} 344° 41’ 343° 28’ 
 
 ; 
 
 It appears that the August meteors are caused by a long 
 stream of bodies following the second comet of 1862 in its 
 orbit, or, rather, moving in the same orbit with it. The orbit 
 of this comet is decidedly elliptic; the difference from the 
 parabola is, however, too small to be determined with great 
 precision. According to Oppolzer, the period derived from 
 the observations would be 124 years, which, however, may be 
 ten years or more in error. 
 
 A third striking case of the connection between comets and 
 meteors which we are showing is afforded by the actual pre- 
 diction of a meteoric shower on the night of November 27th, 
 1872. I have already described Biela’s comet as first break- 
 ing into two pieces and then entirely disappearing, as though 
 its parts had become completely scattered. This is one of 
 the few comets which may come very near the earth, the lat- 
 ter passing the orbit of the comet on November 27th of each 
 year. By calculation, the comet should have passed the point 
 of crossing early in September, 1872, while the earth reached 
 the same point between two and three months later. Judg- 
 ing from analogy, there was every reason to believe that the 
 earth would encounter a stream of meteoroids consisting of the 
 remains of the lost comet, and that a small meteoric shower 
 would be the result. Moreover, it was shown that the mete- 
 ors would all diverge from a certain point in the constellation 
 Andromeda, as the radiant point, because that would be the di- 
 rection from which a body moving in the orbit of the comet 
 would seem to come. The prediction was fully verified in 
 every respect. The meteors did not compare, either in num- 
 bers or brilliancy, with the great displays of November ; but, 
 though faint, they succeeded each other so rapidly that the 
 most casual observer could not fail to notice them, and they 
 all moved in the predicted direction. 
 
408 THE SOLAR SYSTEM. 
 
 That the meteoroids in these cases originally belonged to 
 the comet, few will dispute. Accepting this, the phenomena of 
 the November showers lead to the conclusion that the comet 
 of 1866, with which they are associated, was not an original 
 member of our system, but has been added to it within a 
 time which, astronomically speaking, is still recent. The sep- 
 arate meteoroids which form the stream will necessarily have 
 slightly different periodic times. Such being the case, they 
 will, in the course of many revolutions, gradually scatter them- 
 selves around their entire orbit; and then we shall have an 
 equal meteoric shower on every 18th of November. This 
 complete scattering seems to have actually taken place in the 
 case of the August meteoroids, since we have nearly the same 
 sort of shower on every 9th or 10th of August. But in the 
 case of the November meteors, the stream is not yet scattered 
 over one-tenth of the orbit. If we suppose that the motions 
 of the slowest and the swiftest bodies of the stream only dif- 
 fer by a thousandth part of their whole amonunt—which is not 
 an unreasonable supposition—it would follow that the stream 
 had only made about 100 revolutions around the sun, and had 
 therefore been revolving only about 3800 years. Though this 
 number is purely hypothetical, we may say with confidence 
 that the stream has not been in existence many thousand 
 years. | 
 This opinion is strongly supported by the fact that the orbit 
 of this meteoric comet passes very near that of Uranus as well 
 as that of the earth, so that there is reason to believe that. it 
 was introduced into onr system by the attraction of one of 
 these planets, probably of Uranus. If the comet is seen on its 
 next return, in 1899, we may hope that its periodic time will 
 be determined with sufficient accuracy to enable us to fix with 
 some probability the exact date at which Uranus brought it 
 into our system. Indeed, Leverrier has attempted to do this 
 already, having fixed upon the year 126 of our era as the 
 probable date of this event; but, unfortunately, neither the 
 position of the orbit nor the time of revolution is yet known 
 with such accuracy as to inspire confidence in this result. 
 
THE PHYSICAL CONSTITUTION OF COMETS. 409 
 
 The idea that this November group is something compara- 
 tively new is strengthened by a comparison with that which 
 produces the August meteors, where we find a decided mark 
 of antiquity. Here the swiftest of the group has, in the course 
 of numerous revolutions, overtaken the slowest, so that the 
 group is now spread almost equally around the entire orbit. 
 The time of revolution being, in this case, more than a cen- 
 tury, this equal distribution would take a much longer time 
 than in the other case, where the period is only thirty-three 
 years ; so that we can say, with considerable probability, that 
 the Angust group has been in our system at least twenty 
 times as long as the November group. 
 
 § 8. The Physical Constitution of Comets. 
 
 A theory of the physical constitution of comets, to be both 
 complete and satisfactory, must be founded on the properties 
 of matter as made known to us here at the surface of the 
 earth. That is, we must show what forms and what combina- 
 tions of known substances would, if projected into the celes- 
 tial spaces, present the appearance of a comet. Now, this has 
 never yet been completely done. Theories without number 
 have been propounded, but they fail to explain some of the 
 phenomena, or explain them in a manner not consistent with 
 the known laws of matter or force. We cannot stop even to 
 mention most of these theories, and shall therefore confine our 
 attention to those propositions which are to some extent sus- 
 tained by facts, and which, on the whole, seem to have most 
 probability in their favor. 
 
 The simplest form of these bodies is seen in the telescopic 
 comets, which consist of minute particles of a cloudy or vapor- 
 ous appearance. Now, we know that masses which present 
 this appearance at the surface of the earth, where we can ex- 
 amine them, are composed of detached particles of solid or 
 liquid rnatter. Clouds and vapor, for instance, are composed 
 of minute drops of water, and smoke of very minute particles 
 of carbon. Analogy would lead us to suppose that the tele- 
 scopic comets are of the same constitution. They are gener- 
 
410 THE SOLAR SYSTEM. 
 
 ally tens of thousands of miles in diameter, and yet of such 
 tenuity that the smallest stars are seen through them. ‘The 
 strongest evidence of this constitution is, however, afforded by 
 the phenomena of meteoric showers described in the last sec- 
 tion. We have seen that these are caused by our atmosphere 
 encountering the débris of comets, and this débris presents it- 
 self in the form of detached meteoroids, of very small magni- 
 tude, but hundreds of miles apart. 
 
 The only alternative to this theory is that the comet is a 
 mass of true gas, continuous throughout its whole extent. 
 This gaseous theory derives its main support from the spec- 
 troscope, which shows the spectrum of the telescopic comets 
 to consist of bright bands, the mark of an incandescent gas. 
 Moreover, the resemblance of these bands to those produced 
 by the vapor of carbon is so striking that it is quite common 
 among spectroscopists to speak of a comet as consisting of 
 the gas of some of the compounds of carbon. But there are 
 several difficulties which look insuperable in the way of the 
 theory that a comet is nothing but a mass of gas. In the 
 first place, the elastic force of such a mass would cause it 
 to expand beyond all limits when placed in a position where 
 there is absolutely no pressure to confine it, as in the celestial 
 spaces. Again, a gas cannot, so far as experiment has ever 
 gone, shine by its own light until it is heated to a high tem- 
 perature, far above any that can possibly exist at distances 
 from the sun so great as those at which comets have been 
 situated when ‘under examination with the spectroscope. '1- 
 nally, in the event of a purely gaseous comet being broken 
 up and dissipated, as in the case of Biela’s comet, it is hardly 
 possible to suppose that it would separate into innumerable 
 widely detached pieces, as this comet did. The gaseous the- 
 ory can, therefore, not be regarded as satisfactory. It may be 
 that comets will hereafter be found to consist of some combi- 
 nation of solid and gaseous matter, the exact nature of which 
 is not yet determined; or it may be that this matter is of a 
 nature or in a form wholly unlike anything that we are ac- 
 quainted with or can produce here on the earth. As the case 
 
THE PHYSICAL CONSTITUTION OF COMETS. 411 
 
 now stands, we must regard the spectrum of a ‘comet as some- 
 thing not yet satisfactorily accounted for. 
 
 When we turn from telescopic comets to those brilliant 
 ones which exhibit a nucleus and a tail, we can trace certain 
 operations which are not seen in the case of the others. ‘What 
 the nucleus is—whether it is a solid body several hundred miles 
 in diameter, or a dense mass of the same materials which com- 
 pose a telescopic comet—we are quite unable to say. But 
 there can hardly be any reasonable doubt that it is composed 
 of some substance which is vaporized by the heat of the solar 
 rays. The head of such a comet, when carefully examined 
 with the telescope, is found to be composed of successive en- 
 velopes or layers of vapor; and when these’ envelopes are 
 watched from night to night, they are found to be gradually 
 rising upwards, growing fainter and more indistinct in ont- 
 line as they attain a greater elevation, until they are lost in 
 the outlying parts of the coma. These rising masses form the 
 fan-shaped appendage described in a preceding section. 
 
 The strongest proof that some evaporating process is going 
 on from the nucleus of the comet is afforded by the move- 
 ments of the tail. It has long been evident that the tail could 
 not be an appendage which the comet carried along with it, 
 and this for two reasons: first, it is impossible that there could 
 be any cohesion in a mass of matter of such tenuity that the 
 smallest stars could be seen through a million of miles of it, 
 and which, besides, constantly changes its form; secondly, as 
 a comet flies around the sun in its immediate neighborhood, 
 the tail appears to move from one side of the sun to another 
 with a rapidity which would tear it to pieces, and send the 
 separate parts flying off in hyperbolic orbits, if the movement 
 were real. The inevitable conclusion is that the tail is not a 
 fixed appendage of the comet, which the latter carries with it, 
 but a stream of vapor rising from it, like smoke from a chim- 
 -ney. As the line of smoke which we now see coming from 
 the chimney is not the same which we saw a minute ago, be- 
 cause the latter has been blown away and dissipated, so we do 
 not see the same tail of a comet all the time, because the mat- 
 
412 THE SOLAR SYSTEM. 
 
 ter which makes up the tail is constantly streaming outwards, 
 and constantly being replaced by new vapor rising from the 
 nucleus. The evaporation is, no doubt, due to the heat of the 
 sun, for there can be no evaporation without heat, and the 
 tails of comets increase enormously as they approach the sun. 
 Altogether, a good idea of the operations going on in a comet 
 will be obtained if we conceive the nucleus to be composed of 
 water or other volatile fluid which is boiling away under the 
 heat of the sun, while the tail is a column of steam rising 
 from it. 
 
 We now meet a question to which science has not yet been 
 able to return a conclusive answer. Why does this mass of 
 vapor always fly away from the sun? That the matter of the 
 comet should be vaporized by the sun’s rays, and that the nu- 
 cleus should thus be enveloped in a cloud of vapor, is perfect- 
 ly natural, and entirely in accord with the properties of mat- 
 ter which we observe around us. But, according to all known 
 laws of matter, this vapor should remain around the head, ex- 
 cept that the outer portions would be gradually detached and 
 thrown off into separate orbits. There is no known tendency 
 of vapor, as seen on the earth, to recede from the sun, and no 
 known reason why it should so recede in the celestial spaces. 
 Various theories have been propounded to account for it; but 
 as they do not rest on causes which we have verified in other 
 cases, they must be regarded as purely hypothetical. 
 
 The first of these explanations, in the order of time, is due 
 to Kepler, who conceived the matter of the tail to be driven 
 off by the impulsion of the solar rays, which thus bleached 
 the comet as they bleach cloths here. If light were an emis- 
 sion of material particles, as Newton supposed it to be, this 
 view would have some plausibility. But light is now con- 
 ceived to consist of vibrations in an ethereal medium; and 
 there is no known way in which they could exert any propel- 
 ling force on matter. Two or three years ago, it was for 
 a while supposed that the “radiometer” of Mr. Crookes might 
 really indicate such an action of the solar rays upon matter 
 in a vacuum, but it is now found that the action exhibited is 
 
THE PHYSICAL CONSTITUTION OF COMETS. 413 
 
 really due to a minute quantity of air left in the instrument. 
 Had Mr. Crookes shown that the motion of his radiometer 
 was really due to the impulsion of the solar rays, we might 
 be led to the remarkable conclusion that Kepler’s theory, 
 though rejected for more than two centuries, was, after all, . 
 quite near the truth. 
 
 Sir Isaac Newton, being the author of the emission theory 
 of light, could not dispute the possibility of Kepler’s views 
 being correct, but nevertheless gave the preference to anoth- 
 er hypothesis. He conceived the celestial spaces to be filled 
 with a very rare medium, through which the sun’s rays passed 
 without heating it, as they pass through cold air. But the 
 comet being warmed up by the rays, the medium surrounding 
 it is warmed up by contact, and thus a warm current. is sent 
 out from the comet, just as a current of warm air rises from 
 a heated body on the surface of the earth. This current car- 
 ries the vapor of the comet with it, and thus gives rise to the 
 tail in the same way that the current of warm air rising from 
 a chimney carries up a column of smoke. It has long been 
 established that there is no medium in the planetary spaces 
 in which such an effect as this is possible: Newton’s theory 
 is, therefore, no longer considered. — 
 
 In recent times, Zdllner has endeavored to account for the 
 tail of the comet by an electrical action between the sun and 
 the vapor rising from the nucleus of the comet: The various 
 papers in which he has elaborated his views of the constitu- 
 tion of comets are marked by profound research; and we 
 must regard his theories as those which, on the whole, most 
 completely explain all the phenomena. But they still lack 
 the one thing needful to secure their reception: there is no 
 evidence that the sun acts as an electrified body; and until 
 such evidence is adduced by experiment, or by observation on 
 other bodies than comets, the electric theory of the comet’s 
 tail can only be regarded as a more or less probable hypothe- 
 sis. Indeed, some physicists claim that any such electric ac- 
 tion in the planetary spaces is impossible. Before any theory 
 can be definitely settled upon, accurate observations must be 
 
414 THE SOLAR SYSTEM. 
 
 made upon the tails of comets with a view of learning the 
 law according to which the vapor is repelled from the sun. 
 Such observations were made by Bessel on Halley’s comet in 
 1835, and by various observers on the great comet of 1858. 
 The former were investigated by Bessel himself, and the lat- 
 ter by several mathematicians, among them Professor Peirce, 
 whose results are found in a paper communicated to the 
 American Academy in 1859. He found the repulsive force 
 of the sun upon the particles which form the front edge of 
 the tail to be 14 times its attractive force upon ordinary 
 bodies at the same distance. It seemed constantly to diminish 
 as the back edge of the tail was approached; but, owing to 
 the poor definition of this edge, and the uncertainty whether it 
 was composed of a continuous stream of particles, the amount 
 of the diminution could not be accurately fixed. The suc- 
 cessive envelopes were found to ascend uniformly towards 
 the sun at the rate of about thirty-five miles an hour. Bond, 
 from a careful examination of all the observations, was led to 
 the result that the rate of ascent diminished as the height 
 became greater. 
 
 An apparently necessary conclusion from this constant evap- 
 oration and expulsion of vapor from comets with tails is, that 
 such bodies are constantly wasting away when in the neigh- 
 borhood of the sun. This conclusion is strengthened by the 
 fact that not a single comet of very short period has a consid- 
 erable tail, the probability being that all the volatile matter 
 which once went to form the tail has been evaporated. In- 
 deed, from the descriptions of the old chroniclers, it has been 
 supposed that Halley’s comet had a much more conspicuous 
 tail at the time of its earliest recorded apparitions than it has 
 exhibited at its last few returns. There is, however, no neces- 
 sity for supposing the diminution so rapid as this, for the 
 amount of matter really necessary to make the most splendid 
 tail is so extremely small that a comet might lose it a hundred 
 times over without becoming perceptibly smaller. This con- 
 stant loss of matter through the tail affords an additional 
 ground for the view that comets in general are visitors intro- 
 
we 
 
 THE PHYSICAL CONSTITUTION OF COMETS. A415 
 
 duced into our system by the action of the planets. If, for 
 instance, such a comet as Halley’s had been a member of our 
 system for millions of years, and had returned to perihelion a 
 hundred thousand times, all its volatile matter must lone ago 
 have evaporated. 
 
 The question of the mass and density of comets is also one 
 of those on which it is difficult to reach satisfactory conclu- 
 sions. We cannot certainly decide from mere telescopic ob- 
 servation whether the nucleus is a single large body, like a 
 planet or satellite, or whether it is merely the densest part of 
 an immense cloud of meteoroids. The mass of nebulous mat- 
 ter which surrounds the nucleus increases so gradually as we 
 approach the central parts, that it is hardly possible to decide 
 where the nucleus begins: the more powerful the telescope, 
 the smaller the nucleus generally appears. Moreover, in the 
 same comet, the apparent magnitude of the nucleus is subject 
 to immense variations, thus showing that it cannot be a solid 
 body out to its apparent limits. If we considered only this 
 circumstance, and the general analogy with telescopic comets, 
 we should say that even the densest part of the comet was 
 nothing but a cloud of solid or liquid particles so thick that it 
 looked solid, as a cloud does in our sky. But if this was the 
 case, as Professor Peirce showed in his investigations of the 
 comet of 1858, the comets of 1680 and of 1843 must have 
 been completely pulled apart by the enormons tidal forces 
 generated by their near approach to the sun. In the opinion 
 of this investigator, the fact that they went through such an 
 ordeal shows them to be of metallic density. 
 
 The question is frequently asked, What would be the effect 
 if a comet should strike the earth? This would depend upon 
 what sort of a comet it was, and what part of the comet came 
 in contact with our planet. The latter might pass through 
 the tail of the largest comet without the slightest effect being 
 produced, the tail being so thin and airy that a million miles 
 thickness of it looks only like gauze in the sunlight. It is 
 not at all unlikely that such a thing may have happened with- 
 
 out ever being noticed. A passage through a telescopic comet 
 
416 THE SOLAR SYSTEM. 
 
 would be accompanied by a brilliant meteoric shower, prob- 
 ably a far more brilliant one than has ever been recorded. 
 No more serious danger would be encountered than that aris- 
 ing from a possible fall of meteorites. But a collision between 
 the nucleus of a large comet and the earth might be a serious 
 matter. If,as Professor Peirce supposes, the nucleus is a solid 
 body of metallic density, many miles in diameter, the effect 
 where the comet struck would be terrific beyond conception. 
 At the first contact in the upper regions of the atmosphere, 
 the whole heavens would be illuminated with a resplendence 
 beyond that of a thousand suns, the sky radiating a light which 
 would blind every eye that beheld it, and a heat which would 
 melt the hardest rocks. A few seconds of this, while the huge 
 body was passing through the atmosphere, and the collision at 
 the earth’s surface would in an instant reduce everything there 
 existing to fiery vapor, and bury it miles deep in the solid 
 earth. Happily, the chances of such a calamity are so minute 
 that they need not cause the slightest uneasiness. There is 
 hardly a possible form of death which is not a thousand times 
 more probable than this. So small is the earth in comparison 
 with the celestial spaces, that if one should shut his eyes and 
 fire a gun at random in the air, the chance of bringing down 
 a bird would be better than that of a comet of any kind strik- 
 ing the earth. 
 
 § 9. The Zodiacal Light. 
 
 This object consists of a very soft, faint column of light, 
 which may be seen rising from the western horizon after twi- 
 light on any clear winter or spring evening: it may also be 
 seen rising from the eastern horizon just before daybreak in 
 the summer or autumn. It really extends ont on each side 
 of the sun, and lies nearly in the plane of the ecliptic. The 
 reason it cannot be well seen in the summer and autumn 
 evenings is, that in our latitudes the course of the ecliptie in 
 the south-west is, during those seasons, so near the horizon that 
 the light in question is extinguished by the great thickness of 
 atinosphere through which it has to pass. Near the equator, 
 
 , 
 Oe ee — 
 
THE ZODIACAL LIGHT. ALT 
 
 where the ecliptic always rises high above the horizon, the 
 light can be seen about equally well all the year round. It 
 grows fainter the farther it is from the sun, and can gener- 
 ally be traced to about 90° from that luminary, when it grad- 
 ually fades away. But in a very clear atmosphere, between 
 the tropics, it has been traced all the way across the heavens, 
 from east to west, thus forming a complete ring. 
 
 Such is the zodiacal light as it appears to the eye. Put- 
 ting its appearances all together, we may see that it is due to 
 a lens-shaped appendage of some sort surrounding the sun, 
 and extending out a little beyond the earth’s orbit. It lies 
 very nearly in the plane of the ecliptic, but its exact position 
 is difficult to determine, not only owing to its indistinct out- 
 line, but because in northern latitudes the southern edge will 
 be dimmed by the greater thickness of atmosphere through 
 which it is seen, and thus the light will look farther north 
 than it really is. The nature of the substance from which 
 this light emanates is entirely unknown. Its spectrum has 
 been examined by several observers, some of whom have re- 
 ported it as consisting of a single yellow line, and therefore 
 arising from an incandescent gas. This would indicate a len- 
 ticular-shaped atmosphere of inconceivable rarity surrounding 
 the sun, and extending out near the plane of the ecliptic be- 
 yond the orbit of the earth. But Professor Wright, of Yale 
 College, who has made the most careful observations of this 
 spectrum, finds it to be continuous. For several reasons, too 
 minute to enter into now, this observation seems to the writer 
 more likely to be correct. Accepting it, we should be led to 
 the conclusion that the phenomenon in question is due to re- 
 flected sunlight, probably from an immense cloud of meteor- 
 oids filling up the space between the earth and sun. But fur- 
 ther researches must be made betore ¢ a conclusive result can 
 be reached. 
 
 One important question respecting the zodiacal light is sug- 
 gested by the motion of the perihelion of Mercury arose 
 decocihed! This motion seems to prove one of two things: 
 either that the sun’s gravitation does not strictly follow the 
 
418 THE SOLAR SYSTEM. 
 
 law -of the inverse square of the distance, or that there is a 
 mass of matter of some kind between the earth and the sun. 
 Can this matter be that from which the “zodiacal light” is 
 reflected? It is impossible to make a positive auswer to this 
 question. 
 
 Another mysterious: phenomenon associated with the zodi- 
 acal light is known by its German appellation, the Gegen- 
 schein. It is said that in that point of the heavens directly 
 opposite the sun there is an elliptical patch of light, a few de- 
 grees in extent, of such extreme faintness that it can be seen 
 only by the most sensitive eyes, under the best conditions, and 
 through the clearest atmosphere. This phenomenon seems so 
 difficult to account for that its existence is sometimes doubted; 
 yet the testimony in its favor is difficult to set aside.* 
 
 * The latest observations upon this phenomenon have been made near Phila- 
 delphia by Mr. Lewis, and are found in the American Journal of Science and 
 Arts for 1879. 
 
ee a 
 
 PART IV—THE STELLAR UNIVERSE. 
 
 INTRODUCTORY REMARKS. 
 
 Hirnerto our attention has been principally occupied with 
 the bodies which surround our sun and make up the solar sys- 
 tem. Notwithstanding the immense distances at which these 
 bodies are found, we may regard them, in comparison with the 
 fixed stars, as an isolated family immediately surrounding us, 
 since a sphere as large as the whole solar system would only 
 appear as a point to the vision if viewed from the nearest 
 star. The space which separates the orbit of Neptune from 
 the fixed stars and the fixed stars from each other is, so far as 
 we can learn, entirely void of all visible matter, except occa- 
 sional waste nebulous fragments of a meteoric or cometary 
 nature which are now and then drawn in by the attraction of 
 our sun. 
 
 The widest question which the study of the stars presents 
 to us may be approached in this way: We have seen, in our 
 system of sun, planets, and satellites, a very orderly and 
 beautiful structure, every body being kept in its own orbit 
 through endless revolutions by a constant balancing of gravi- 
 tating and centrifugal forces. Do the millions of suns and 
 clusters scattered through space, and brought into view by the 
 telescope, constitute a greater system of equally orderly struct- 
 ure? and, if so, what is that structure? If we measure the 
 importance of a question, not by its relations to our interests 
 and our welfare, but by the intrinsic greatness of the subject 
 to which it relates, then we must regard this question as one 
 of the noblest with which the human mind has ever been 
 
42.0 THE STELLAR UNIVERSE. 
 
 occupied. In piercing the mystery of the solar system, and 
 showing that the earth on which we dwell was only one of 
 the smaller of eight planets which move around the sun, we 
 made a great step in the way of enlarging our ideas of the 
 immensity of creation and of the comparative insignificance 
 of our sublunary interests. But when, on extending our view, 
 we find our sun to be but one out of unnumbered millions, we 
 see that our whole system is but an insignificant part of crea- 
 tion, and that we have an immensely greater fabric to study. 
 When we have bound all the stars, nebulee, and clusters which 
 our telescopes reveal into a single system, and shown in what 
 manner each stands related to all the others, we shall have 
 solved the problem of the material universe, coneeenegy not | in 
 its details, but in its widest scope. 
 
 From fe time that Copernicus showed the stars to be self- 
 luminous bodies, situated far outside of our solar system, the 
 question thus presented has occupied the attention of the phil- 
 osophical class of astronomers. The original view, which has 
 been the starting-point of all speculation on the subject, we 
 have described in the Introduction as that of a spherical uni- 
 verse. The apparent sphericity of the vault of heaven, the 
 uniformity of the diurnal revolution, and the invariability of 
 the relative positions of the stars, all combined to strengthen 
 the idea that the latter were set on the interior surface of a 
 hollow sphere, having the earth or the sun in its centre. This 
 sphere constituted the firmament of the ancients, outside of 
 which was situated the empyrean, or kingdom of fire. Coper- 
 nicus made no advance whatever on this idea. Galileo and 
 Kepler seem to have made the first real advance—the former 
 by resolving the Milky Way into stars with his telescope, the 
 latter by suggesting that our sun might be simply one of nu- 
 merous stars scattered through space, looking so bright only 
 on account of our proximity to it. In the problem of the 
 stellar system this conception held the same important place 
 which that of the earth as a planet did in the problem of the 
 solar system. But Kepler was less fortunate than Copernicus 
 in that he failed to commend his idea, even to his own judg- 
 
INTRODUCTORY REMARKS. 421 
 
 ment. It was by affording a starting-point for the researches 
 of Kant and Herschel that Kepler’s suggestion really bore 
 fruit. 
 
 Notwithstanding the amount of careful research which 
 Herschel and his successors have devoted to it, we are still 
 very far from having reached even an approximate solution 
 of the problem of which we speak. In whatever direction we 
 pursue it, we soon find ourselves brought face to face with the 
 infinite in space and time. Especially is this the case when 
 we seek to know, not simply what the universe is to-day, but 
 what causes are modifying it from age to age. All the knowl- 
 edge that man has yet gathered is then found to amount to 
 nothing but some faint glimmers of light shining here and 
 there through the seemingly boundless darkness. The glim- 
 mer is a little brighter for each successive generation, but 
 many centuries must elapse before we can do much more 
 than tell how the nearer stars are situated in space. Indeed, 
 we see as yet but little hope that an inhabitant of this planet 
 will ever, from his own observations and those of his prede- 
 cessors, be able to completely penetrate the mystery in which 
 the structure and destiny of the cosmos are now enshrouded. 
 However this may be in the future, all we can do at present 
 is to form more or less probable conjectures, founded on all 
 we know of the general character of natural law. In a strictly 
 scientific treatise, such conjectures would find no place; and 
 if we had to grope in absolute darkness, they would be en- 
 tirely inappropriate in any but a poetical or religious produc- 
 tion. But the subject is too fascinating to permit us to neg- 
 lect the faintest light by the aid of which we may penetrate 
 the mystery; we shall therefore briefly set forth both what 
 men of the past have thought on the subject, what the science 
 of to day enables us to assert with some degree of probability, 
 and what knowledge it wholly denies us. To proceed in sci- 
 entific order, we must commence by laying a wide foundation 
 of facts. Our first step will therefore be to describe the heav- 
 ens as they appear to the naked eye, and as they are seen in 
 the telescope. 
 
4292, THE STELLAR UNIVERSE. 
 
 GH ag tn 1, 
 THE STARS AS THEY ARE SEEN. 
 
 $1. Number and Orders of Stars and Nebule. 
 
 Tur total number of stars in the celestial sphere visible 
 with the average naked eye may be estimated, in round num- 
 bers, as 5000. The number varies so much with the perfec- 
 tion and training of the eye, and with the atmospheric condi- 
 tions, that it cannot be stated very definitely. When the tele- 
 scope is pointed at the heavens, it is found that for every star 
 visible to the naked eye there are hundreds, or even thousands, 
 too minute to be seen without artificial aid. From the counts 
 of stars made by Herschel, Struve has estimated that the total 
 number of stars visible with Herschel’s twenty-foot telescope 
 was about 20,000,000. The great telescopes of modern times 
 would, no doubt, show a yet larger number; but a reliable 
 estimate has not been made. The number is probably some- 
 where between 30,000,000 and 50,000,000. 
 
 At a very early age, the stars were classified according to 
 their apparent brightness or magnitude. The fifteen brightest 
 ones were said to be of the first magnitude; the fifty next in 
 order were termed of the second magnitude, and so on to the 
 sixth, which comprised the faintest stars visible to the naked 
 eye. The number of stars of each order of magnitude be- 
 tween the north pole and the circle 35° south of the equator 
 is about as follows: 
 
 Of magnitude 1 there are about...........cccccecceeees 14 stars, 
 We 2 AE 1G Pe aaeentteene eee se 48-05 ° § 
 We 3 Phe dtr txt aa MCEe Riess 5.69 0,6 152.55 
 Be d wie gl MAUR ac eae tet sais bess) B13 aes" 
 43 5 So MUNN ET OER ARER cs iets vay ses 854 
 he 6 eet  DMAAAVecedde te, boesccues 2010 ‘* 
 
NUMBER AND ORDERS OF STARS AND NEBULZ. 423 
 
 This limit includes all the stars which, in the Middle States, 
 culminate at a greater altitude than 15°. The number of the 
 sixth magnitude which can be seen depends very much upon 
 the eye of the observer and the state of the sky. The forego- 
 ing list includes all that can be seen by an ordinary good eye 
 in a clear sky when there is no moonlight; but the German 
 astronomer Heis, from whom these numbers are taken, gives a 
 list of 1964 more which he believes he can see without a glass. 
 
 The system of expressing the brightness of the stars by a 
 series of numbers is continued to the telescopic stars. The 
 smallest star visible with a six-inch telescope under ordinary 
 circumstances is commonly rated as of the thirteenth magni- 
 tude. On the same scale, the smallest stars visible with the 
 largest telescopes of the world would be of about the six- 
 teenth magnitude, but no exact scale for these very faint stars 
 has been arranged. 
 
 Measures of the relative brilliancy of the stars indicate 
 that, as we descend in the scale of magnitude, the quantity 
 of light emitted diminishes in a geometrical ratio, the stars 
 of each order being, in general, between two-fifths and one- 
 third as bright as those of the order next above them. This 
 order of diminution is not, however, exact, because the arrange- 
 ment of magnitudes has been made by mere estimation of in- 
 dividual observers who may have hit on different and varying 
 ratios; but it is a sufficient approach to the truth for common 
 purposes. From the second to the fifth magnitude the dimi- 
 nution-is probably one-third in each magnitude, after that 
 about two-fifths. Supposing the ratio two-fifths to be exact, 
 we find that it would take about 
 
 23 stars of the second magnitude to make one of the first. 
 
 6 oe third 66 (a4 66 
 
 16 cf fourth gs oh $6 
 
 40 (74 fifth 66 66 (74 
 
 TOO Mites ye sixth es es i 
 10,000 ake eleventh Ue ie ar 
 1,000,000 by sixteenth he oe Me 
 
 The number of stars of the several scales of magnitude 
 vary in a ratio not far different from the inverse of that of 
 
A924 THE STELLAR UNIVERSE. 
 
 their ‘brightness, the ratio being a little greater in the case of 
 the hibnes magnitudes, and piababls a little less in the case 
 of the albwer ones. Thus, we see that there are about three 
 times as many stars of ne second magnitude as of the first, 
 three times as many of the third as of the second, and after 
 that something less than three times as many of each magni- 
 tude as of the magnitude next above. Comparing this with 
 the table of relative brightness just given, we may conclude 
 that if all the stars of each magnitude were condensed into a 
 single one, the brightness of the combined stars thus formed 
 would not vary cna from one to another until we 
 had passed beyond the ninth or tenth magnitude. But it is 
 certain that the brightness would Hiner diminish, because 
 otherwise there would be no limit to the total amount of hght 
 given by the stars, and the whole heavens would shine like 
 the sun. 
 
 The reader will, of course, understand that this arrange- 
 ment by magnitude is purely artificial. Really the stars are 
 of every order of brightness, varying by gradations which are 
 entirely insensible, so that it is impossible to distinguish be- 
 tween the brightest star of one magnitude and the faintest of 
 the magnitude next above it. Hence, those astronomers who 
 wish to express magnitudes with the greatest exactness, divide 
 them into thirds or even tenths; so that, for instance, stars be- 
 tween the sixth and seventh magnitudes are called 6.1, 6.2, 
 6.3, and so on to 6.9, according to their brilliancy. Various 
 attempts have been made to place the problem of the relative 
 amounts of light emitted by the stars upon a more exact basis 
 than this old one of magnitudes, but this is a very difficult 
 thing to do, because there is no way of measuring light except 
 by estimation with the eye. In order to measure the relative 
 intensity of two lights, it is necessary to have some instrument 
 by which the intensity of one or both the lights may be varied 
 until the two appear to be equal. Instruments for this pur- 
 pose are known as photometers, and are of various construc- 
 tions. For comparing the light of different stars, the photom- 
 eter most used at the present time is that of Zollner. By 
 
NUMBER AND ORDERS OF STARS AND NEBULZ. 425 
 
 this instrument the light of the stars, as seen through a small 
 telescope, is compared both in color and intensity with that of 
 an artificial star, the ight of which can be varied at pleasure. 
 A. complete set of measures with this instrument, including 
 most of the brighter stars, is one of the wants of astronomy 
 which we may soon hope to see supphed. The most extended 
 recent series of photometric estimates with which the writer 
 is acquainted is that of Professor Seidel, of Munich, which in- 
 cludes 209 stars, the smallest of which are of the fifth magni- 
 tude. An interesting result of these estimates is that Sirius 
 gives us four times as much light as any other star visible in 
 our latitude. 
 
 Catalogues of Stars—In nearly every age in which astron- 
 omy has flourished catalogues of stars have been made, giving 
 their positions in the heavens, and the magnitude of each. 
 The earliest catalogue which has come to us is found in the 
 “Almagest” of Ptolemy, and is supposed to be that of Hippar- 
 chus, who flourished 150 years before the Christian era. It 
 is said, but not on the best authority, that he constructed it in 
 order that future generations might find whether any change 
 had in the mean time taken place in the starry heavens. An 
 examination of the catalogue shows that the constellations pre- 
 sented much the same aspect two thousand years ago that they 
 do now. There are two or three stars of his catalogue which 
 cannot now be certainly identified ; but it is probable that the 
 difficulty arises from the imperfection of the catalogue, and 
 from the errors which may have crept into the numerous 
 transcriptions of it during the sixteen centuries which elapsed 
 before the art of printing was discovered. The catalogue of 
 Hipparchus contains only about 1080 stars, so that he could 
 not have given all that he was able to see. He probably omit- 
 ted many stars of the smaller magnitudes. The actual num- 
 ber given in the “ Almagest” is still less, being only 1030. 
 
 The next catalogue in the order of time is that of Ulugh 
 Beigh, a son of the Tartar monarch Tamerlane, which dates 
 from the fifteenth century. For the most part, the stars are 
 the same as in the catalogue of Ptolemy, only the places were 
 
426 THE STELLAR UNIVERSE. 
 
 redetermined from the observations at Samarcand. It con- 
 tains 1019 stars, eleven less than Ptolemy gives. Tycho Brahe, 
 having made so great an improvement in the art of observa- 
 tion, very naturally recatalogued the stars, determining their 
 positions with yet greater accuracy than his predecessors. His 
 catalogue is the third and last important one formed before 
 the invention of the telescope. It contains 1005 stars. 
 
 Our modern catalogues may be divided into two classes: 
 those in which the position of each star in the celestial sphere 
 (right ascension and declination) is given with all attainable 
 precision, and those in which it is only given approximately, 
 so as to identify the star, or distinguish it from others in its 
 neighborhood. The catalogues of the former class are very 
 numerous, but the more accurate ones are necessarily incom- 
 plete, owing to the great labor of making the most exact de- 
 termination of the position of a star. There are, perhaps, 
 between ten or twenty thousand stars the positions of which 
 are catalogued with astronomical precision, and a hundred 
 thousand more in which, though entire precision is aimed at, 
 it is not attained. Of the merely approximate catalogues, the 
 greatest one is the “Sternverzeichniss” of Argelander, which 
 enumerates all the stars down to the ninth magnitude between 
 the pole and two degrees south of the equator. The work 
 fills three thin quarto volumes, and the entire number of stars 
 catalogued in it exceeds three hundred thousand. ‘This “star 
 census” is being continued to the south pole at the observa- 
 tory of Cordoba, South America, by Dr. Gould. Of the mill- 
 ions of stars of the tenth magnitude and upwards, hardly one 
 in a thousand is, or can be, individually known or catalogued. 
 Except as one or another may exhibit some remarkable pecu- 
 liarity, they must pass unnoticed in the crowd. 
 
 Division into Constellations.—A. single glance at the heavens 
 shows that the stars are not equally scattered over the sky, but 
 that great numbers of them, especially of the brighter ones, 
 are collected into extremely irregular groups, known as con- 
 stellations. At a very early age the heavens were represented 
 as painted over with figures of men and animals, so arranged 
 
NUMBER AND ORDERS OF STARS AND NEBULAE. 4297 
 
 as to include the principal stars of each constellation. There 
 is no historic record of the time when this was done, nor of the 
 principles by which those who did it carried out their work; 
 but many of the names indicate that it was during the heroic 
 age. Some have sought to connect it with the Argonautic ex- 
 pedition, from the fact that several heroes of that expedition 
 were among those thus translated to the heavens; but this is 
 little more than conjecture. So little pains was taken to fit 
 the figures to the constellations that we can hardly suppose 
 them to have all been executed at one time, or on any well- 
 defined plan. Quite likely, in the case of names of heroes, 
 the original object was rather to do honor to the man than to 
 serve any useful purpose in astronomy. Whatever their ori- 
 gin, these names have been retained to the present day, al- 
 though the figures which they originally represented no longer 
 serve any astronomical purpose. The constellation Hercules, 
 for instance, still exists; but it no longer represents the figure 
 of a man among the stars, but a somewhat irregular portion 
 of the heavens, including the space in which the ancients 
 placed that figure. In star-maps, designed for school instruc- 
 tion and for common use, it is still customary to give these 
 figures, but they are not generally found on maps designed 
 for the use of astronomers. 
 
 Naming the Stars.—The question how to name the individ- 
 ual stars in each constellation, so as to readily distinguish 
 them, has always involved some difficulty. In the ancient 
 catalogues they were distinguished by the part of the figure 
 representing the constellation in which they were found; as, 
 the eye of the Bull, the tail of the Great Bear, the right shoul- 
 der of Orion, and so on. The Arabs adopted the plan of giv- 
 ing special names to each of the brighter stars, or adopting 
 such names from the Greeks. Thus, we have the well-known 
 stars Sirius, Arcturus, Procyon, Aldebaran, and so on. Most 
 of these names have dropped entirely out of astronomical use, 
 though still found on some school maps of the stars. The 
 system now most in use for the brighter stars was designed by 
 Bayer, of Augsburg, Germany, about 1610. He published a 
 
498 THE STELLAR UNIVERSE. 
 
 set of star-maps, in which the individual stars of each constel- 
 lation were designated by the letters of the Greek alphabet— 
 a, (3, y, etc. The first letters were given to the brightest stars, 
 the next ones to the next brightest, and so on. After the 
 Greek letter is given the Latin name of the constellation in 
 the genitive case. Thus, Alpha (a) Scorpii, or Alpha of the 
 Scorpion, is the name of Antares, the brightest star in Scor- 
 pius; a Lyre, of the brightest star in the Lyre; and so on. 
 We have here a resemblance to our system of naming men, 
 the Greek letter corresponding to the Christian name, and the 
 constellation to the surname. When the Greek alphabet was 
 exhausted, without including all the conspicuous stars, the 
 Latin alphabet was drawn upon. 
 
 The Bayer system is still applied to all the stars named by 
 him. Most of the other stars down to the fifth magnitude are 
 designated by a system of numbers assigned by Flamsteed in 
 his catalogue. Yet other stars are distinguished by their num- 
 bers in some well-known catalogue. When this method fails, 
 owing to the star not being catalogued, the position in the 
 heavens must be given. 
 
 The Milky Way, or Galaxy.—To the naked eye so much of 
 the Galaxy as can be seen at one time presents the appearance 
 of a white, cloud-like arch, resting on two opposite points of 
 the horizon, and rising to a greater or less altitude, according 
 to the position of the celestial sphere relative to the observer. 
 Only half of the entire arch can be seen above the horizon at 
 once, the other half being below it, and directly opposite the 
 visible half. Indeed, there is a portion of it which can never 
 be seen in our latitude, being so near the south pole that it 
 is always below our horizon. If the earth were removed, or 
 made transparent, so that we could see the whole celestial 
 sphere at once, the Galaxy would appear as a complete belt 
 extending around it. The telescope shows that the Galaxy 
 arises from the light of countless stars, too minute to be sep- 
 arately visible with the naked eye. We find, then, that the 
 telescopic stars, instead of being divided up into a limited 
 number of constellations, are mostly condensed in the region 
 
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 429 
 
 of the Galaxy. They are least numerous in the regions most 
 distant from the galactic belt, and grow thicker as we ap- 
 proach it. ‘The more powerful the telescope, the more marked 
 the condensation is. With the naked eye, thé condensation is 
 hardly noticeable, unless by actual count: a very small tele- 
 scope will show a decided thickening of the stars in and near 
 the Galaxy; while,if we employ the most powerful telescopes, — 
 a large majority of the stars they show are found to lie act-, 
 ually in the Galaxy. In other words, if we should blot out 
 all the stars visible with a twelve-inch telescope, we should 
 find that the greater part of the remaining stars were in the 
 Galaxy. The structure of the universe which this fact seems 
 to indicate will be explained in a subsequent section. 
 
 Clusters. — Besides this gradual and regular condensation 
 towards the galactic belt, occasional condensations of stars 
 into clusters may be seen. Indeed, some of these clusters are 
 visible to the naked eye, sometimes as separate stars, like the 
 Pleiades, but more commonly as milky patches of light, be- 
 cause the stars are too small to be seen separately. The num- 
 ber visible in powerful telescopes is, however, much greater. 
 Sometimes there are hundreds, or even thousands, of stars visi- 
 ble in the field of the telescope at once; and sometimes the 
 number is so great, and the individual stars so small, that they 
 cannot be counted even in the most powerful telescopes ever 
 made. 
 
 Nebule.—Another class of objects which are found in the 
 celestial spaces are irregular masses of soft, cloudy light, 
 which are hence termed nebule. Many objects which look 
 like nebulze in small telescopes are found by more powerful 
 ones to be really star clusters. But, as we shall hereafter 
 show, many of these objects are not composed of stars at all, 
 but of immense masses of gaseous matter. 
 
 § 2. Description of the Principal Constellations. 
 
 For the benefit of the reader who wishes to make himself 
 acquainted with the constellations in detail, or to identify any 
 bright star or constellation which he may see, we present a 
 
430 THE STELLAR UNIVERSE. 
 
 brief description of the principal objects which may be seen 
 in the heavens at different seasons, illustrated by five maps, 
 showing the stars to the fifth magnitude inclusive. The 
 reader who does not wish to enter into these details can pass 
 to the next section without any break of the continuity of 
 thought. 
 
 For the purpose of learning the constellations, the star- 
 maps will be a valuable auxiliary. It will be better to begin 
 with the northern, or circumpolar, constellations, because these 
 are nearly always visible in our latitude. The first one to be 
 looked for is Ursa Major (the Great Bear, or the Dipper), from 
 which the pole star can always be found by means of the 
 pointers, as shown in Fig. 2, page 10. Supposing the observer 
 to look for it at nine o’clock in the evening, he will see it in 
 various positions, depending on the time of year, namely, in 
 
 A pPtil Gna 7. 52. esses sesces -north of the zenith. 
 
 Julysand August. cicecowespenven to the west of north, the pointers lowest. 
 October and Novembet.......... close to the north horizon. 
 
 January and February........... to the east of north, the pointers highest. 
 
 These successive positions are in the same order with those 
 which the constellation occupies in consequence of its diurnal 
 motion around the pole. The pointers are in the body of the 
 bear, while the row of stars on the other end of the constella- 
 tion forms his tail. 
 
 Ursa Minor, or the Little Dipper, is the constellation to 
 which the pole star belongs. It includes, besides the pole 
 star, another star of the second magnitude, which lies nearly 
 in the direction of the tail of Ursa Major. 
 
 Cassiopeia, or the Lady in the Chair, is on the opposite side 
 of the pole from Ursa Major, at nearly the same distance. 
 The constellation can be readily recognized from its three or 
 four bright stars, disposed in a line broken into pieces at right 
 angles to each other. In the ancient mythology, Cassiopeia is 
 the queen of Cepheus; and in the constellation she is repre- 
 sented as seated in a large chair or throne, from which she is 
 issuing her edicts. 
 
 Perseus is quite a brilliant constellation, situated in the 
 
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 431 
 
 Milky Way, east* of Cassiopeia, and a little farther from the 
 pole. It may be recognized by a row of conspicuous stars 
 extending along the Milky Way, which passes directly through 
 this Pe eictiations 
 
 Other circumpolar constellations are Cepheus, the Camelo- 
 pard, the Lynx, the Dragon (Draco), and the Lizard; but they 
 do not contain any stars so bright as to attract especial atten- 
 tion. The reader who wishes to learn them can easily find 
 them by comparing the star-maps with the heavens. 
 
 Owing to the annual motion of the sun among the stars, the 
 constellations which are more distant from the pole cannot be 
 seen at all times, but must be looked for at certain seasons, 
 unless inconvenient hours of the night be chosen. We shall 
 describe the more remarkable constellations as they are seen 
 by an observer in middle north latitudes in four different 
 positions of the starry sphere. The sphere takes all four of 
 these positions every day, by its diurnal motion; but some of 
 these positions will occur in the daytime, and tigi late at 
 night or early in the morning. 
 
 First Position, Orion on the Meridian.—The constellations 
 south of the zenith are those shown on Maps II. and IIL, the 
 former being west of the meridian, the latter east. This posi- 
 tion occurs on 
 
 Wecemuear. ESE. sce se iseaauech taser ricecastanrcetore cs at midnight. 
 SPANIAL Vie LEGA alan eve sasegs dnneame ties re Ree A at 10 o'clock P.M. 
 CIT Mai Me LOCH A! coeur se dueaterestinetacaddatnstpauassaevats at 8 o'clock P.M. 
 PE AEC ee i Bic oe panaies wae ees coke ett eacrdck a aaaeehs talk come .at 6 o’clock P.M. 
 
 And so on through the year. In this position, Cassiopeia and 
 Ursa Major are near the same altitude, the former high up in 
 
 * In the celestial sphere the points of the compass have, of necessity, a mean- 
 ing which may seem different from that which we attribute to them on the earth. 
 North always means towards the north pole; sowth, from it; west, in the direc- 
 tion of the diurnal motion ; east, in the opposite direction. In Fig. 2, the arrows 
 all point west, and by examining the figure it will be seen that below the pole 
 north is upwards, and east is towards the west horizon. Really, these definitions 
 hold equally true for the earth, the same differences being found between the 
 points of the compass at different places on the earth—here and in China, for in- 
 stance—that we see on the celestial sphere. 
 
 29 
 
432 THE STELLAR UNIVERSE. 
 
 the north-west, the latter in the north-east. The Milky Way 
 spans the heavens like an arch, resting on the horizon in the 
 north-north-west and south-south-east. We shall first describe 
 the constellations in its course. 
 
 Cygnus, the Swan, is sinking below the horizon, where the 
 Milky Way rests upon it in the north-north-west, and only a 
 few stars of it are visible. It will be better seen at another 
 season. 
 
 Next in order come Cepheus, Cassiopeia, and Perseus, which 
 we have already described as circumpolar constellations. 
 
 Above Perseus les Auriga, the Charioteer, which may be 
 readily recognized by a bright star of the first magnitude, 
 called Capella, the Goat, now a few degrees north-west of the 
 zenith. Auriga is represented as holding a goat in his arm, 
 in the body of which this star is situated. About ten degrees 
 east of Capella is the star (3 Aurigze of the second magnitude ; 
 while still farther to the east is a group of small stars which 
 also belongs to the same constellation. The latter extends 
 some distance south of the zenith. 
 
 The Milky Way next passes between Taurus and Gemini, 
 which we will describe presently, and then crosses the equator 
 east of Orion, the most brilliant constellation in the heavens, 
 having two stars of the first magnitude and four of the second. 
 The former are Betelguese, or a Orionis, which is highest up, 
 and may be recognized by its reddish color, and Rigel, or (3 
 Orionis, a sparkling white star, lower down, and a little to the 
 west. The former is in the shoulder of the figure, the latter 
 in the foot. Between the two, three stars of the second mag- 
 nitude, in a row, form the belt of the warrior. 
 
 Cams Minor, the Little Dog, lies just across the Milky Way 
 from Orion, and may be recognized by the bright star Pro- 
 eyon, of the first magnitude, due east from Betelguese. 
 
 Canis Major, the Great Dog, lies south-east of Orion, and is’ 
 easily recognized by Sirius, the brightest fixed star in the heay- 
 ens. A number of bright stars south and south-east of Sirius 
 belong to this constellation, making it one of great brilliancy.. 
 
 As the Milky Way approaches the south horizon, it passes 
 
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 483 
 
 through Argo Navis, the Ship Argo, which is partly below the 
 horizon. It contains Canopus, the next brightest star to Siri- 
 us; but this object is below the horizon, unless the observer is 
 as far south as 35° of north latitude. 
 
 We can next trace such of the zodiacal constellations as are 
 high enough above the horizon. In the west, one-third of the 
 way from the horizon to the zenith, will be seen Aries, the 
 Ram, which may be recognized by three stars of the second, 
 third, and fourth magnitudes, respectively, forming an obtuse- 
 angled triangle, the brightest star being the highest. The 
 arrangement of these stars, and of some others of the fifth 
 magnitude, may be seen by Map IL. 
 
 Taurus, the Bull, is next above Aries, and may be recog- 
 nized by the Pleiades, or “seven stars,” as the group is com- 
 monly called. . Really there are only six stars in the group 
 clearly visible to ordinary eyes, and an eye which is good 
 enough to see seven will be likely to see four others, or eleven 
 in all. A telescopic view of this group will be given in con- 
 nection with the subject of clusters of stars. Another group 
 in this constellation is the Hyades, the principal stars of which 
 are arranged in the form of the letter V, one extremity of the 
 V being formed by Aldebaran, a red star ranked as of the 
 first magnitude, but not so bright as a Orionis. 
 
 Geman, the ‘Twins, lies east ae the Milky Way, and may be 
 found on the left nde of Map II. and the right of Map IIL 
 The brightest stars of this constellation are Castor and Pollux, 
 or a and (3, which lie twenty or thirty degrees south-east or 
 east of the. zenith, about one-fourth or one-third of the way 
 to the horizon. They are almost due north from Procyon; 
 that is, a line drawn from Procyon to the pole star passes be- 
 tween them. The constellation extends from Castor and Pol- 
 lux some distance south and west to the borders of Orion. 
 
 Cancer, the Crab, lies east of Gemini, but contains no bright 
 star. The most noteworthy object within its borders is Pre- 
 sepe, a group of stars too small to be seen singly, which ap- 
 pears as a spot of milky light. To see it, well, the night must 
 be perfectly clear, and the moon not in the neighborhood. 
 
434 THE STELLAR UNIVERSE. 
 
 Lo, the Lion, contains the bright star Regulus, about two 
 hours above the eastern horizon. ‘This star, with five or six 
 smaller ones, forms a sickle, Regulus being the handle. The 
 sickle is represented as in the breast, neck, and head of the 
 lion, his tail extending nearly to the horizon, where it ends at 
 the star Denebola, now just risen. 
 
 Such are the principal constellations visible in the supposed 
 position of the celestial sphere. If the hour of observation is 
 different from that supposed, the positions of the constellations 
 will be different by the amount of diurnal rotation during the 
 interval. For instance, if, in the middle of March, we study 
 the heavens at eight o’clock instead of six, the western stars 
 will be nearer the horizon, the southern ones farther west, and 
 the eastern ones higher up than we have described them. 
 
 Second Position of the Celestial Sphere. —The meridian in 
 twelve hours of right ascension, near the left-hand edge of 
 Map IIL.,and the right-hand edge of Map IV. The stars on 
 Map III. are west of the meridian, those of Map IV. east of it. 
 This position occurs on 
 
 Mate 23st tii ist desea strtaskcccerecteoece sever son aan ete at midnight. 
 April 20th noid. iasvegec beara tetat esas ee aeerceep ee tetera eee at 10 o'clock. 
 May 21 6b; cieios 4. ctocesnastarabvowsarsassucn esata tars cuseseaeaak at 8 o'clock. 
 
 In this position Ursa Major is near the zenith, and Cassiopeia: 
 in the north horizon. The Milky Way is too near the horizon 
 to be visible; Orion has set in the west; and there are no very 
 conspicuous constellations in the south. Castor and Pollux are 
 visible in the north-west, at a considerable altitude, and Pro- 
 eyon in the west, about an hour and a half above the horizon. 
 Leo is west of the meridian, extending nearly to it, while three 
 new zodiacal constellations have come into sight in the east. 
 
 Virgo, the Virgin, has a single bright star—Spica—about 
 the brilliancy of Regulus, now about one hour east of the me- 
 ridian, and a little more than half-way from the zenith to the 
 horizon. 
 
 Inbra, the Balance, has no stars which will attract attention. 
 The constellation may be recognized by its position between 
 Virgo and Scorpius. 
 
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 435 
 
 Scorpius, the Scorpion, is just rising in the south-east, and is 
 not yet high enough to be well seen. 
 
 Among the constellations north of the zodiac we have: 
 
 Coma Berenices, the Hair of Berenice, now exactly on the 
 meridian, and about ten degrees south of the zenith. It is a 
 close, irregular group of very small stars, quite different from 
 anything else in the heavens. In the ancient mythology, Ber- 
 enice had vowed her hair to the goddess Venus; but Jupiter 
 carried it away from the temple in which it was deposited, 
 and made it into a constellation. 
 
 Bootes, the Bear-keeper, is a large constellation east of Coma. 
 It is marked by Arcturus, a very bright but somewhat red 
 star, an hour and a half east of Coma Berenices. 
 
 Canes Venatici, the Hunting Dogs, are north of Coma. They 
 are held in a leash by Bodtes, and are chasing Ursa Major 
 round the pole. 
 
 Corona Borealis, the Northern Crown, lies next east of Bootes 
 in the north-east. It is principally composed of a pretty semi- 
 circle of stars, supposed to form a chaplet, or crown. 
 
 Third Position of the Sphere.-—The southern constellations 
 are those shown on Maps IV. and V., those of Map IV. being 
 west of the meridian, and those of Map V. east of it. This 
 position occurs on 
 
 SUNG DUShct geek cos cecee ean eerste tease bass nes coabdeneees at midnight. 
 
 MULY 2 LSC Macca t et scnceetertenareramenenee iL iverscscacedsetenssens at 10 o'clock, 
 
 PSTUIQTISG PO LSE. . Jue Ses seen oe Need enh eeica sade 6 seize sinos oon acoder at 8 o’clock. 
 OPUS et cas ore Veh Meee eens av) w cas nanos lot caneeenen etc. 
 
 In this position the Milky Way is once more in sight, and 
 seems to span the heavens, but we do not see the same part 
 ef it which was visible in the first position. Cassiopeia is 
 now in the north-east, and Ursa Major has passed over to the 
 north-west. Arcturus is two or three hours high in the west, 
 and Corona is above it, two or three hours west of the zenith. 
 Commencing, as in the first position, with the constellations 
 which lie along the Milky Way, we start upwards from Cas- 
 siopeia, pass Cepheus and Lacerta, neither of which contains 
 any striking stars, and then reach 
 
436 THE STELLAR UNIVERSE. 
 
 Cygnus, the Swan, now north-east from the zenith, which 
 may be recognized by four or five stars forming a cross, di- 
 rectly in the Milky Way. The brightest of these stars some- 
 what exceeds the brightest ones of Cassiopeia. 
 
 Lyra; the Harp, is west and south-west of Cygnus, and near 
 the zenith. It contains the bright star Vega, or a Lyre, of 
 the first magnitude, of a brilliant white color with a tinge of 
 blue. ; 
 
 Passing south, over Vulpecula, the Little Fox, and Sagitia, 
 the Arrow, the next striking constellation we reach is 
 
 Aquila, the Eagle, now midway between the zenith and the 
 horizon, and two hours east of the meridian. It contains a 
 bright star— Altair, or a Aquils—situated between two 
 smaller ones, the row of three stars running nearly north and 
 south. 
 
 We next pass west of the Milky Way, and direct our atten- 
 tion to a point two hours west of the meridian, and some dis- 
 tance towards the south horizon. Here we find 
 
 Scorpius, the Scorpion, a zodiacal constellation and a quite 
 brilliant one, containing Antares, or a Scorpii, a reddish star 
 of nearly the first magnitude, with a smaller star on each side 
 of it, and a long curved row of stars to the west. 
 
 Sagittarius, the Archer, comprises a large collection of sec- 
 ond-magnitude stars east of Scorpius, and in and east of the 
 Milky Way, and now extending from the meridian to a point 
 two hours east of it. 
 
 Capricornus, the Goat, another zodiacal constellation, is now 
 in the south-east, but contains no striking stars. The same 
 remark applies to Aquarius, the Water-bearer, which has just 
 risen, and Pisces, the Fishes, partly below the eastern horizon. 
 
 Leaving the zodiac again, we find, north of Scorpius and 
 west of the Milky Way, a very large pair of constellations, 
 called Ophiuchus, the Serpent-bearer, and Serpens, the Serpent. 
 Ophiuchus stands with one foot on Scorpius, while his head is 
 marked by a star of the second magnitude twelve degrees 
 north of the equator, and now on the meridian. It is, there- 
 fore, one-third or one-fourth of the way from the zenith to the 
 
DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 437 
 
 horizon. The Serpent, which he holds in his hands, lies with 
 its tail in an opening of the Milky Way, south-west of Aquila, 
 while its neck and head are formed by a collection of stars of 
 the second, third, and fourth magnitudes some distance north 
 of Scorpius, and extending up to the borders of Bootes. 
 
 Hercules is a very large constellation, bounded by Corona 
 on the west, Lyra on the east, Ophiuchus on the south, and 
 Draco on the north. It is now in the zenith, but contains no 
 striking stars. 
 
 Draco, the Dragon, lies with his head just north of Hercules, 
 while his body is marked by a long curved row of stars ex- 
 tending round the-pole between the Great and the Little Bear. 
 His head is readily recognized by a collection of stars of the 
 second and third magnitudes which might well suggest such 
 an object. 
 
 Fourth Position of the Sphere-—The southern constellations 
 are now found on Maps V. and II.—those of Map V. west of 
 the meridian, those of Map II. east of it. The times are: 
 
 eptember, 2lstermeccvs teas arcetws seis crieesckes es id's vce dss .at midnight. 
 October 21st nepeen tant wate eee ainieeeeccaes at 10 o’clock. 
 November QUth oes ee coe cock ada ah eee tases cours ob pace at 8 o'clock. 
 Wecember 2st. epearan eck east sae vae stats ween enw hccs .at 6 o'clock. 
 
 In this position Cassiopeia is just north of the zenith, while 
 Ursa Major is glimmering in the north horizon. Following 
 the Milky Way from Cassiopeia towards the west, we shall 
 cross Cepheus, Cygnus, Lyra, and Aquila, while towards the 
 east we pass Perseus and Auriga, all of which have been de- 
 scribed. 
 
 In the south, the principal constellation is Pegasus, the Fly- 
 ing Horse, distinguished by four stars of the second magni- 
 tude, which form a large square, each side of which is about 
 fourteen degrees. : 
 
 Andromeda, her hands in chains, is readily found by a row 
 of three bright stars extending north-east from the north-east 
 corner of Pegasus in the direction of Perseus. 
 
 Cetus, the Whale, is a large constellation in the south, ex- 
 tending from the meridian to a point three hours east of it. 
 
438 THE STELLAR UNIVERSE. 
 
 Its brightest stars are [3 Ceti, now near the meridian, at an al- 
 titude of 20°, which stands by itself, and a Ceti, about 20° be- 
 low Aries, which is now about 30° south-east from the zenith. 
 The reader who wishes to consult the constellations in 
 greater detail can readily do so by means of the star-maps. 
 
 § 3. New and Variable Stars. 
 
 The large majority of stars always appear to be of the same 
 brightness, though it is quite possible that, if the quantity of 
 light emitted by a star could be measured with entire preci- 
 sion, it would be found in all cases to vary slightly, from time 
 to time. There are, however, quite a number of stars in which 
 the variation is so decided that it has been detected by com- 
 paring their apparent brightness with that of other stars at dif- 
 ferent times. More than a hundred such stars are now known; 
 but in a large majority of cases the variation is so slight that 
 only careful observation with a practised eye can perceive it. 
 There are, however, two stars in which it is so decided that 
 the most casual observer has only to look at the proper times, 
 in order to see it. These are (3 Persei and o Ceti, or Algol 
 aud Mira, to which we might add n Argus, a star of the south- 
 ern hemisphere, which exhibits variations of a very striking 
 character. 
 
 Variations of Algol.—This star, marked 3 in the constel- 
 lation Perseus, may be readily found on Maps I. and IL, in 
 right ascension 3 hours and declination 40° 23’. When once 
 found, it is readily recognized by its position nearly in a line 
 between two smaller stars. The most favorable seasons for 
 seeing it in the early evening are the autumn, winter, and 
 spring. In autumn it will, after sunset, generally be low 
 down in the north-east; in winter, high up in the north, not 
 far from the zenith; and in spring, low down in the north- 
 west. Usually it shines as a faint second-magnitude star: on 
 an accurate scale the magnitude is about 23. But at inter- 
 vals of a little less than three days, it fades out to the fourth 
 magnitude for a few hours, and then resumes its usual splen- 
 dor once more. These changes were first noticed about two 
 
NEW AND VARIABLE STARS. 439. 
 
 centuries ago, but it was not till 1782 that they were accn- 
 rately observed. ‘The period is now known to be 2 days, 20 
 hours, 49 minutes—that is, 8 hours 11 minutes less than three 
 days. It takes about four hours and a half to fade away to 
 its least brilliancy, and four hours more are spent in recover- 
 ing its light; so that there are nine and a half hours during 
 each period in which its light is below the average. But near 
 the beginning and end of the variations, the change is very 
 slow, so that there are not more than five or six hours during 
 which the ordinary eye would see that the star was any smaller 
 than usual. 
 
 The apparent regularity of this variation of light at first 
 suggested, as an explanation of its cause, that a large dark 
 planet was revolving round Algol, and passed over its face 
 at every revolution, thus cutting off a portion of its light. 
 This theory accounts very well for the salient features of 
 the variation. But when the latter came to be studied more 
 closely and carefully, it was found that there were small irreg- 
 ularities in the variation which the theory would not well ac- 
 count for. The period of the variation was found to change a 
 little at different times, while the star does not lose and recover 
 its light in the same time as it would if the passage of a dark 
 body caused the changes. 
 
 Another remarkable variable star, but of an entirely differ- 
 ent type, is o Ceti, or Mira (the Wonderful). It may be found 
 on Map IL., in right ascension 2 hours 12 minutes, declination 
 3° 39’ south. During most of the time this star is entirely 
 invisible to the naked eye, but at intervals of about eleven 
 months it shines forth with the brilliancy of a star of the sec- 
 ond or third magnitude. It is, on the average, about forty 
 days from the time it first becomes visible until it attains its 
 greatest brightness, and it then requires about two months to 
 become invisible; so that it comes into sight more rapidly 
 than it fades away. It is expected to attain its greatest brill- 
 iancy in November, 1877; in October, 1878, and so on, about 
 a month earlier each year; but the period is quite irregular, 
 ranging from ten to twelve months, so that the times of its 
 
AAQ THE STELLAR UNIVERSE. 
 
 appearance cannot be predicted with certainty. Its maximum 
 brilliancy is also variable, being sometimes of the second mag- 
 nitude, and at others only of the third or fourth. 
 
 ” ple ‘gus. —Perhaps the most extraordinary known variable 
 star in the heavens is n Argus, of the southern hemisphere, of 
 which the position is, right ascension, 10 hours 40 minutes; 
 declination, 59° 1’ south. Being so far south of the equator, 
 it cannot be seen in our latitudes, and the discovery and ob- 
 servations of the variations of its light have been generally 
 made by astronomers who have visited the southern hemi- 
 sphere. In 1677, Halley, while at St. Helena, found it to be 
 of the fourth magnitude. In 1751, Lacaille found that it had 
 increased to the second magnitude. From 1828 to 1838 it 
 ranged between the first and second magnitudes. The first 
 careful observations of its variability were made by Sir John 
 Herschel while at the Cape of Good Hope. He says: “It 
 was on the 16th December, 1837, that, resuming the photo- 
 metrical comparisons, my astonishment was excited by the ap- 
 pearance of a new candidate for distinction among the very 
 brightest stars of the first magnitude in a part of the heay- 
 ens with which, being perfectly familiar, I was certain that no 
 such brilliant object had before been seen. After a momen- 
 tary hesitation, the natural consequence of a phenomenon so 
 utterly unexpected, and referring to a map for its configura- 
 tion with other conspicuous stars in the neighborhood, I be- 
 came satisfied of its identity with my old acquaintance, n Ar- 
 gus. Its light, was, however, nearly tripled. While yet low, 
 it equalled Rigel, and, when it attained some altitude, was 
 decidedly greater.”* Sir John states that it continued to in- 
 crease until January 2d, 1838, when it was nearly matched 
 with a Centauri. It then faded a little till the close of his 
 observations in April following, but was still as bright as Al- 
 debaran. but in 1842 and 1843 it blazed up inaiees than 
 ever, and in March of the latter year was second only to 
 Sirius. During the twenty-five years following, it slowly but 
 
 * ** Astronomical Observations at the Cape of Good Hope,” p. 33. 
 
 OS 
 
NEW AND VARIABLE STARS. A4] 
 
 steadily diminished: in 1867 it was barely visible to the naked 
 eye, and the year following it vanished entirely from the un- 
 assisted view, and has not yet begun to recover its brightness. 
 
 When we speak of this star as the most rémarkable of the 
 well-known variables, we refer, not to the mere range of its 
 variations, but to its briliancy when at its maximum. Sev- 
 eral cases of equally great variation are known; but the stars 
 are not so bright, and therefore would not excite so much no- 
 tice. Thus, the star R Andromede varies from the sixth to 
 the thirteenth magnitude in a-pretty regular period of 405 
 days. When at its brightest, it is just visible to the naked 
 eye, while only a large telescope will show it when at its min- 
 imum. <A. number of others range through five or six orders 
 of magnitude, but o Ceti is the only one of these which ever - 
 becomes as bright as the second magnitude. 
 
 The foregoing stars are the only ones the variations of 
 which would strike the ordinary observer. Among the hun- 
 dred remaining ones which astronomers have noticed, (3 Lyre 
 is remarkable for having two maxima and two minima of un- 
 equal brilliancy. If we take it when at its greatest minimum, 
 we find its magnitude to be 43. In the course of three days, 
 it will rise to magnitude 33. In the course of the week fol- 
 lowing, it will first fall to the fourth magnitude, and increase 
 again to magnitude 34. In three days more it will drop 
 again to its minimum of magnitude 44; the period in which 
 it goes through all its changes being thirteen days. This pe- 
 riod is constantly increasing. The changes of this star can 
 best be seen by comparing it with its neighbor, y Lyra. Some- 
 times it will appear equally bright with the latter, and at other 
 times a magnitude smaller.* 
 
 * In 1875, Professor Schonfeld, now director of the observatory at Bonn, pub- 
 lished a complete catalogue of known variable stars, the total number being 143. 
 The following are the more remarkable ones of his list. The positions are re- 
 ferred to the ecliptic and equinox of 1875: 
 
 T-Cassiopeix: right ascension, 0 hours 16 minutes 29 seconds; declination, 55° 
 6’.0 N.—This is a case in which a star, having once been observed, was after- 
 wards found to be missing. Examination showed that it had so far diminished 
 as to be no longer visible without a larger telescope, and continued observations 
 
4492 THE STELLAR UNIVERSE. 
 
 New Stars.—It was once supposed to be no uncommon occur- 
 rence for new stars to come into existence and old ones to dis- 
 appear, the former being looked upon as new creations, and 
 the disappearances as due. to the destruction or annihilation 
 of those stars which had fulfilled their end in the economy of 
 nature. The supposed disappearances of stars are, however, 
 found to have no certain foundation in fact, probably owing 
 their origin to errors in recording the position of stars actu- 
 ally existing. It was explained, in treating of Practical As- 
 tronomy, that the astronomer determines the position of a 
 body in the celestial vault by observing the clock-time at which 
 it passes the meridian, and the position of the circle of his in- 
 
 showed it to range from the seventh to the eleventh magnitude with a regular 
 period of 436 days. 
 
 B Cassiopeix: right ascension, 0 hours 17 minutes 52 seconds; declination, 
 63° 27'.0 N.—This is supposed to be the celebrated star which blazed out in 
 November, 1572, and was so fully described by Tycho Brahe. But the proof of 
 identity can hardly be considered conclusive, especially as no variation has, of re- 
 cent years, been noticed in the star. 
 
 o Ceti: right ascension, 2 hours 13 minutes 1 second; declination, 3° 32’.7 
 S.—We have already described the variations of this star. 
 
 8 Persei, or Algol: right ascension, 3 hours 0 minutes 2 seconds; declina- 
 tion, 40° 28.4 N.—The variations of this star, which is the most regular one 
 known, have just been described. 
 
 R Aurige: right ascension, 5 hours 7 minutes 12 seconds; declination, 53° 
 26’.6 N.—This star is one of very wide and complex variation, changing from the 
 sixth to the thirteenth magnitude in a period of about 465 days. 
 
 R Geminorum: right ascension, 6 hours 59 minutes 49 seconds; declination, 
 22° 53’.8 N.—This star was discovered by Mr. Hind, of England, and ranges be- 
 tween the seventh and the twelfth magnitude in a period of 371 days. 
 
 U Geminorum: right ascension, 7 hours 47 minutes 41 seconds; declination, 
 22° 19.7 N.—An irregular variable, never visible to the naked eye, remarkable 
 for the rapidity with which it sometimes changes. Schonfeld says that in Feb- 
 ruary, 1869, it increased three entire magnitudes in 24 hours. The periods of its 
 greatest brightness have ranged from 75 to 617 days. 
 
 n Argus: right ascension, 10 hours 40 minutes 13 seconds; declination, 59° 
 1’.6 S.—This remarkable object has already been described. 
 
 R Hydre: right ascension, 13 hours 22 minutes 53 seconds; declination, 22° 
 38’.0 S.—The variability of this star was recognized by Maraldi, in 1704. It is 
 generally invisible to the naked eye, but rises to about the fifth magnitude at 
 intervals of about 437 days. Its period seems to be diminishing, having been 
 about 500 days when first discovered. 
 
NEW AND VARIABLE STARS. 443 
 
 strument when his telescope is pointed at the object. If he 
 happens to make a mistake in writing down any of these 
 numbers—if, for example, he gets his clock-time one minute 
 or five minutes wrong, or puts down a wrong number of de- 
 grees for the position of his cirele—he will write down the 
 position of the star where none really exists. Then, some sub- 
 sequent astronomer, looking in this place and seeing no star, 
 may think the star has disappeared, when, in reality, there was, 
 never any star there. Where thousands of numbers have to be 
 written down, such mistakes will sometimes occur; and it is to 
 them that some cases of supposed disappearance of stars are to 
 be attributed. There have, however, been several cases of ap- 
 parently new stars coming suddenly into view, of which we 
 shall describe some of the most remarkable. 
 
 T Coron: right ascension, 15 hours 54 minutes 16 seconds; declination, 26° 
 16'.5 N.—This is the ‘‘new star” which blazed out in the Northern Crown in 
 1866, as hereafter described. Of late years it has remained between the ninth 
 and tenth magnitudes without exhibiting any remarkable variations. 
 
 T Scorpii: right ascension, 16 hours 9 minutes 36 seconds; declination, 22° 
 40’.0 S.—This star was discovered by Auwers, in 1860, in the midst of a well- 
 known cluster. It gradually diminished during the following months, and finally 
 disappeared entirely among the stars by which it is surrounded. 
 
 — Serpentarii: right ascension, 17 hours 23 minutes 9 seconds; declination, 
 21° 22’.4 S.—This is supposed to-be the celebrated ‘‘new star” seen and de- 
 scribed by Kepler in 1604, soon to be described. 
 
 x Cygni: right ascension, 19 hours 45 minutes 46 seconds; declination, 32° 36’.0 
 N.—This star becomes visible to the naked eye at intervals of about 406 days, and 
 then sinks to the twelfth or thirteenth magnitude, so that only large telescopes will 
 show it. Its greatest brightness ranges from the fourth to the sixth magnitude. 
 
 n Aquilz: right ascension, 19 hours 46 minutes 6 seconds; declination, 0° 
 41’.2 N.—This star varies from magnitude 33 to 42%, and is therefore one of 
 those which can readily be observed with the naked eye. Its period is 7 days 4 
 hours 14 minutes 4 seconds. 
 
 P Cygni: right ascension, 20 hours 13 minutes 11 seconds; declination, 37° 
 38’.7 N.—This was supposed to be a new star in 1600, when it was first seen 
 by Janson. During the remainder of the century it varied from the third to the 
 ‘sixth magnitude; but during two centuries which have since elapsed no further 
 variations have been noticed, the star being constantly of the fifth magnitude. 
 
 uw Cephei: right ascension, 21 hours 39 minutes 41 seconds; declination, 58° 
 12’.4 N.—One of the reddest stars visible to the naked eye in the northern hemi- 
 sphere. Its magnitude is found to vary from the fourth to the fifth in a very w- 
 regular manner. 
 
444 THE STELLAR UNIVERSE. 
 
 In 1572 an apparently new star showed itself in Cassiopeia. 
 It was first seen by Tycho Brahe on November 11th, when 
 it had attained the first magnitude. It increased rapidly in 
 brilliancy, soon becoming equal to Venus, so that good eyes 
 could discern it in full daylight. In December it began to 
 grow smaller, and continued gradually to fade away until the 
 following May, when it disappeared entirely. This was forty 
 years before the invention of the telescope. Tycho has left us 
 an extended treatise on this most remarkable star. 
 
 In 1604 a similar phenomenon was seen in the constella- 
 tion Ophinchus. The star was first noticed in October of that 
 year, when it had attained the first magnitude. In the follow- 
 ing winter it began to wane, but remained visible during the 
 whole year 1605. Early in 1606 it faded away entirely, hav- 
 ing been visiblé for more than a year. A very full history of 
 this star has been left to us by Kepler. 
 
 The most striking recent case of this kind was in May, 
 1866, when a star of the second magnitude suddenly appeared 
 in Corona Borealis. On the 11th and 12th of that month it 
 was remarked independently by at least five observers in Eu- 
 rope and America, one of the first being Mr. Farquhar, of the 
 United States Patent-office. Whether it really blazed out as 
 suddenly as this would indicate has not been definitively set- 
 tled. If, as would seem most probable, it was several days 
 attaining its greatest brilliancy, then the only person known 
 to have seen it was Mr. Benjamin Hallowell, a well-known 
 teacher near Washington, whose testimony is of such a nature 
 that it is hard to doubt that the star was visible several days 
 before it was generally known. On the other hand, Schmidt, 
 of Athens, asserts in the most positive manner that the star 
 was not there on May 10th, because he was then scanning 
 that part of the heavens, and would certainly have noticed it. 
 However the fact may have been in this particular case, it is 
 noteworthy that none of the new stars we have described were 
 noticed until they had nearly or quite attained their greatest 
 brilliancy, a fact which gives color-to the view that they have 
 all blazed up with great rapidity. 
 
NEW AND VARIABLE STARS. 445 
 
 In November, 1876, a new star of the third magnitude was 
 noticed by Schmidt, of Athens, in the constellation Cygnus. 
 It soon began to fade away, and disappeared from the unaided 
 vision in a few weeks. ‘The position of the constellation Cyg- 
 nus becomes so unfavorable for observation in November that 
 very few people got a sight of this object. 
 
 The view that these bodies may be new creations, designed 
 to rank permanently among their fellow-stars, is completely 
 refuted by their transient character, if by nothing else. Their 
 apparently ephemeral existence is in striking contrast to the 
 permanency of the stars in general, which endure from age to 
 age without any change whatever. They are now classified 
 by astronomers among the variable stars, their’changes being 
 of a very irregulat and fitful character. There is no serious 
 doubt that they were all in the heavens as very small stars 
 before they blazed forth in this extraordinary manner, and 
 that they are in the same place yet. The position of the star 
 of 1572 was carefully determined by Tycho Brahe; and a 
 small telescopic star now exists within 1’ of the place com- 
 puted from his observations, and is probably the same. The 
 star of 1866 was found to have been recorded as one of the 
 ninth magnitude in Argelander’s great catalogue of the stars 
 of the northern hemisphere, completed several years before. 
 After blazing up in the way we have described, it gradually 
 faded away to its former insignificance, and has shown no 
 further signs of breaking forth again. There is a wide differ- 
 ence between these irregular variations, or breaking-forth of 
 . light, on a single occasion in the course of centuries, and the 
 regular changes of Algol and (3 Lyre. But the careful obser- 
 vations of the industrious astronomers who have devoted them- 
 selves to this subject have resulted in the discovery of stars 
 of nearly every degree of irregularity between these extremes. 
 Some of them change gradually from one magnitude to another, 
 in the course of years, without seeming to follow any law what- 
 ever, while in others some tendency to regularity can be faintly 
 traced. The best connecting link between new and variable stars 
 is, perhaps, afforded by n Argus, which we have just described. 
 
446 THE STELLAR UNIVERSE. 
 
 It is probable that the variations of light of which we have 
 spoken are the result of operations going on in the star itself, 
 which, it must be remembered, is a body of the same order of 
 magnitude and brilliancy with our sun, and that these opera- 
 tions are analogous to those which produce the solar spots. It 
 was shown in the chapter on the sun that the frequency of 
 solar spots shows a period of eleven years, during one portion 
 of which there are frequently no spots at all to be seen, while 
 during another portion they are very numerous. Hence, if 
 an observer so far away in the stellar places as to see our sun 
 like a star, could, from time to time, make exact measures of 
 the amount of light it emitted, he would find it to be a vari- 
 able star, with a period of eleven years, the amount of light 
 being least when we see most spots, and greatest when there 
 are few spots. The variation would, indeed, be so slight that 
 we could not perceive it with any photometric means which 
 we possess, but it would exist nevertheless. Now, the general 
 analogies of the universe, as well as the testimony of the spec- 
 troscope, lead us to believe that the physical constitution of 
 the sun and the stars is of the same general nature. We may 
 therefore expect that, as we see spots on the sun which vary 
 in form, size, and number from day to day, so, if we could 
 take a sufficiently close view of the faces of the stars, we 
 should, at least in some of them, see similar spots. It is also 
 likely that, owing to the varying physical constitution of these 
 bodies, the number and extent of the spots might be found to 
 be very different in different stars. In the cases in which the 
 spots covered the larger portion of the surface, their variations . 
 in number and extent would alone cause the star to vary in 
 light, from time to time. Finally, we have only to suppose 
 the same kind of regularity which we see in the eleven-year 
 eycle of the solar spots, to have a variation in the brightness 
 of a star going through a regular cycle, as in the case of Algol 
 and Mira Ceti. 
 
 The occasional outbursts of stars which we have described, 
 in which their light is rapidly increased a hundred-fold, would 
 seem not to be accounted for on the spot theory, without car: 
 
NEW AND VARIABLE STARS. 447 
 
 rying this theory to an extreme. It would, in fact, if not 
 modified, imply that ninety-nine parts of the surface out of a 
 hundred were ordinarily covered with spots, and that on rare 
 occasions these spots all disappeared. But the spectroscopic 
 observations of the star of 1866 showed an analogy of a little 
 different character with operations going on in our sun, Mr. 
 Huggins found the spectrum of this star to be a continuous 
 one, crossed by bright lines, the position of which indicated 
 that they proceeded partly or wholly from glowing hydrogen. 
 The continuous spectrum was also crossed by dark absorption 
 lines, indicating that the light had passed through an atmos- 
 phere of comparatively cool gas. Mr. Huggins’s interpreta- 
 tion of this is that there was a sudden and extraordinary out- 
 burst of hydrogen gas from the star which, by its own light, 
 as well as by heating up the whole surface of the star, caused 
 the immense accession of brilliancy. Now, we have shown 
 that the red flames seen around the sun during a total eclipse 
 are caused by eruptions of hydrogen from his interior; more- 
 over, these eruptions are generally connected with faculee, or 
 portions of the sun’s disk several times more brilliant than the 
 rest of the photosphere. Hence, it is not unlikely that the 
 blazing-forth of this star arose from an action similar to that 
 which produces the solar flames, only on an immensely larger 
 scale. | 
 
 We have thus in the spots, facule, and protuberances of 
 the sun a few suggestions as to what is probably going on in 
 those stars which exhibit the extraordinary changes of light 
 which we have described. Is there any possibility that our 
 sun may be: subject to such outbursts of light and heat as 
 those we have described in the cases of apparently new and 
 temporary stars? We may almost say that the continued ex- 
 istence of the human race is involved in this question ; for if 
 the heat of the sun should, even for a few days only, be in- 
 creased a hundred-fold, the higher orders of animal and veg- 
 etable life would be destroyed. We can only reply to it that 
 the general analogies of nature lead us to believe that we 
 need not feel any-apprehension of such a catastrophe. Not 
 
 OU 
 
 * 
 
448 : THE STELLAR UNIVERSE. 
 
 the slightest certain variation of the solar heat has been de- 
 tected since the invention of the thermometer, and the gen- 
 eral constancy of the light emitted by ninety-nine stars out of 
 every hundred may inspire us with entire confidence that no 
 sudden and destructive variation need be feared in the casé 
 of our: sun. 
 
 §$ 4. Double Stars. 
 
 Telescopic examination shows that many stars which seem 
 single to the naked eye are really double, or composed of a 
 pair of stars lying side by side. There are in the heavens 
 several pairs of stars the components of which are so close 
 together that, to the naked eye, they seem almost to touch 
 each other. One of the easiest and most beautiful of these 
 is in Taurus, quite near Aldebaran. . Here the two stars 6° 
 Tauri and @ Tauri are each of the fourth magnitude. <An- 
 other such pair is a Capricorni, in which the two pairs are un- 
 equal. ’ Here an ordinary eye has to look pretty carefully to 
 see the smaller star. Yet another pair is ¢ Lyree, the com- 
 ponents of which are so close that only a good eye can dis- 
 tinguish thein. These pairs, however, are not considered as 
 double stars in astronomy, because, althongh to the naked eye 
 they seem so close, yet, when viewed in a telescope of high 
 power, they are so wide apart that they cannot be seen at the 
 same time. The telescopic double stars ‘are formed of com- 
 ponents only a few seconds apart; indeed, in many cases, only 
 a fraction of a second. The large majority of those which 
 are catalogued as doubles range from half a second to fifteen 
 seconds in distance. When they exceed the latter limit, they 
 are no longer objects of special interest, because they may 
 be really withont any connection, and appear together only 
 because they lie in nearly the same straight line from our 
 system. 
 
 The most obvious question which suggests itself here is 
 whether in any case there is any real connection between the 
 two stars of the pair, or whether they do not appear close to- 
 gether, siinply because they chance to lie on nearly the same 
 
DOUBLE STARS. 449. 
 
 straight line from the earth. That some stars do appear dou- 
 ble in this way there is no doubt, and such pairs are called 
 “optically double.” But notwithstanding the immense num- 
 ber of visible stars, the chance of many pairs falling within 
 a few seconds of each other is quite small; and the number 
 of close double stars is so great as to preclude all possibility 
 that they appear together only by chance. If any further 
 proof was wanted that the stars of these pairs are really phys- 
 ically connected, and therefore close together in reality as well 
 as in appearance, it is found in the fact that many of them 
 constitute systems in which one revolves round the other, or, 
 to speak more exactly, in which each revolves round the cen- 
 tre of gravity of the pair. Such pairs are called binary sys- 
 tems, to distinguish them from those in which no such revolu- 
 tion has been observed. The revolution of these binary sys- 
 tems is generally very slow, requiring many centuries for its 
 accomplishment; and the slower the motion, the longer it 
 will take to perceive and determine it. Generally it has been 
 detected by astronomers of one generation comparing their 
 observations with those of their predecessors; for instance, 
 when the elder Struve. compared his observations with those 
 of Herschel, and when Dawes or the younger Struve compared 
 with the elder Struve, a great number of pairs were found to 
 be binary. As every observer is constantly detecting new 
 cases of motion, the number of binary systems known to as- 
 tronomers is constantly increasing. 
 
 A brief account of the manner in which these objects are 
 measured may not be out of place. For the purpose in ques- 
 tion, the eye-piece of the telescope must be provided with a 
 “filar micrometer,” the important part of which consists of a 
 pair of parallel spider-lines, one of which can be moved side- 
 ways by a very fine screw, and can thus be made to pass back 
 and forth over the other. The exact distance apart of the 
 lines can be determined from the position of the screw. The 
 whole micrometer turns round on an axis parallel to the tel- 
 escope, the centre of which is in the centre of the field of 
 view. To get the direction of one star from the other, the ob- 
 
450 THE STELLAR UNIVERSE. 
 
 server turns the micrometer round until the spider-lines are 
 parallel to the line joining the two stars, as shown in Fig. 98, 
 and he then reads the position circle. Knowing what the 
 position circle reads when he turns the wires so that the star 
 shall run along them by its diurnal motion, the difference of 
 the two angles shows the angle which the line joining the 
 two stars makes with the celestial parallel. To obtain the 
 distance apart of the stars, the observer turns the micrometer 
 90° from the position in Fig. 98,and then turns the screw and 
 moves the telescope, until each star is bisected by one of the 
 wires, as shown in Fig. 99. The position of the wires is then 
 interchanged, and the measure is repeated. The mode in 
 
 setae tea em 2 
 
 a 
 .. 
 .. 
 .. 
 Ht 
 
 .. 
 ‘ 
 ‘. 
 
 . 
 . 
 ' 
 ' 
 ’ 
 ' 
 ' 
 1 
 t 
 As t 
 ACE 
 s 
 
 Fra. 100. 
 
 which the direction of one star from another is reckoned is 
 this: Imagine a line, SN, in Fig. 100, drawn due north from 
 the brighter star, and another, SP, drawn through the smaller 
 star. Then the angle NSP which these two lines make with 
 each other, counted from north towards east, is the position 
 angle of the stars, the changes in which show the revolution 
 of one star around the other. 
 
 In a few of the binary systems the period is so short that 
 a complete revolution, or more, of the two stars round each 
 other has been observed. As a general rule, the pairs which 
 have the most rapid motion are very close, and therefore of 
 comparatively recent discovery, and difficult to observe. One 
 or two are suspected to have a period of less than thirty years, 
 but they are very hard to measure. 
 
 Binary Systems of Short Period.—The following table shows 
 
 —— 
 
DOUBLE STARS. 451 
 
 the periods of revolution in the case of those stars which have 
 been observed through a complete revolution, or of which the 
 periods have been well determined : 
 
 NMI esd ase ose .ncoscesasan s 26 years. |= Urses, Majoris....d-sesees000- 63 years. 
 MEE TETCONS.. f05 wccus coaches ceoaces aes is n Coronz Borealis. ............. yay 
 PEIVEs DEAL. ech .sesesedecnene Seer toe a Centatyi,.2.4dcceedidectecis ETO 
 PRU OLONIO Ve. cecesicisdscseneee ye E0P De bie! Ophiichii1t. Sabet Oot 
 Df EE Sin ee meee IPB cr: MeO amnn od ASCODLINCHE,.... cess vet vceetes ct eee OD sen 
 EMOP MICH IS, cc cccissaccesseccseees tee i MMIII SCOLDING >. nds eos eee ase nccers Do cat 
 
 Two or three others are suspected to move very rapidly, but 
 they are so very close and difficult that it is only on favora- 
 ble occasions that they can be seen to be double. One of 
 the most remarkable stars in this list is Sirius, the period of 
 which is calculated, not from the observations of the satel- 
 lite, but from the motion of Sirius itself. It has long been 
 known that the proper motion of this star is subject to cer- 
 tain periodic variations; and, on investigating these varia- 
 tions, it was found by Peters and Auwers that they could be 
 completely represented by supposing that a satellite was re- 
 volving around the planet in a certain orb:t. The elements 
 of this orbit were all determined except the distance of the 
 satellite, which did not admit of determination. Its direction 
 could, however, be computed from time to time almost as ac- 
 curately as if it were actually seen with the telescope. But, 
 before the time of which we speak, no one had ever seen it. 
 Indeed, although many observers must have examined Sirius 
 from time to time with good telescopes, it is not likely that 
 they made a careful search in the predicted direction. 
 
 Such was the state of the question until February, 1862, 
 when Messrs. Alvan Clark & Sons, of Cambridgeport, were 
 completing their eighteen-inch glass for the Chicago Observa- 
 tory. Turning the glass one evening on Sirius, for the pur- 
 pose of trying it, the practised eye of the younger Clark soon 
 detected something unusual. “ Why, father,’ he exclaimed, 
 “the star has a companion!” The father looked, and there 
 was a faint companion due east from the bright star, and dis- 
 tant about 10”. This was exactly the predicted direction for 
 
452 THE STELLAR UNIVERSE. 
 
 that, time, though the discoverers knew nothing of it. As the 
 news went round the world, all the great telescopes were 
 pointed on Sirius, and it was now found that when observers 
 knew where the companion was, many telescopes would show 
 it. It lay in the exact direction which theory had predicted 
 for that time, and it was now observed with the greatest inter- 
 est, in order to see whether it was moving in the direction of the 
 theoretical satellite. Four years’ observation showed that this 
 was really the case, so that hardly any doubt could remain that 
 this almost invisible object was really the body which, by its at- 
 traction and revolution around Sirius, had caused the inequal- 
 ity in its motion. At the same time, the correspondence has 
 not since proved exact, the observed companion having moved 
 about half a degree per annum more rapidly than the theo- 
 retical one. This difference, though larger than was expected, 
 is probably due to the inevitable errors of the very delicate 
 and difficult observations from which the movements of the 
 theoretical companion were computed. 
 
 The visibility of this very interesting and difficult object 
 depends almost as much on the altitude of Sirius and the state 
 of the atmosphere as on the power of the telescope. When 
 the images of the stars are very bad, it cannot be seen even 
 in the great Washington telescope, while there are cases of its 
 being seen under extraordinarily favorable conditions with tel- 
 escopes of six inches aperture or less. These favorable condi- 
 tions are indicated to the naked eye by the absence of twinkling. 
 
 A case of the same kind, except that the disturbing satellite 
 has not been seen, is found in Procyon. Bessel long ago sus- 
 pected that the position of this star was changed by some at- 
 tracting body in its neighborhood, but he did not reach a defi- 
 nite conclusion on the subject. Auwers, having made a care- 
 ful investigation of all the observations since the time of Brad- 
 ley, found that the star moved around an invisible centre 1” 
 distant, which was probably the centre of gravity of the star 
 and an invisible satellite. This satellite has been carefully 
 searched for with great telescopes during the last few years, 
 but without success. 
 
CLUSTERS OF STARS: 453 
 
 Triple and Multiple Stars.— Besides double’ stars, groups 
 of three or more stars are frequently found. Such objects 
 are known as triple, quadruple, etc. They commonly occur 
 through one of the stars of a wide pair being itself a close 
 double star, and very often the duplicity of the component 
 has not been discovered till long after it was known to form 
 one star of a pair. Tor instance, « Herculis was recognized 
 as a double star by Sir W. Herschel, the companion star being 
 about 380” distant, and much smaller than yw itself. In 1856, 
 Mr. Alvan Clark, trying one of his glasses upon it, found that 
 the small companion was itself double, being composed of two 
 nearly equal stars, about 1” apart. This close pair proves to 
 be a binary system of short period, more than half a revolu- 
 tion of the two stars around each other having been made 
 since 1856. Another case of the same kind is y Andromede, 
 which was found by Herschel to have a companion about 10” 
 distant, while Struve found this companion to be itself double. 
 
 Many double and multiple stars are interesting objects for 
 telescopic examination. We give in the Appendix a list of 
 the more interesting or remarkable of them. 
 
 § 5. Clusters of Stars. 
 
 A very little observation with the telescope will show that 
 while the brighter stars are scattered nearly equally over the 
 whole celestial vault, this is not the case with the smaller ones. 
 A number of stars which it is not possible to estimate are 
 found to be aggregated into clusters, in which the separate 
 stars are so small and so numerous that, with insufficient tele- 
 scopic power, they present the appearance of a mass of cloudy 
 light. We find clusters of every degree of aggregation. At 
 one extreme we may place the Pleiades, or “seven stars” 
 which form so well-known an object in our winter sky, in 
 which, however, only six of the stars are plainly visible to the 
 naked eve. There isan old myth that this group originally 
 consisted of seven stars, one of which disappeared from the 
 heavens, leaving but six. But a very good eye can even now 
 see eleven when the air is clear, and the telescope shows from 
 
An4 THE STELLAR UNIVERSE. 
 
 fifty to a hundred more, according to its power. We present a 
 view of this group as it appears through a small telescope. 
 
 No absolute dividing-line can be drawn between such wide- 
 ly extended groups as the Pleiades and the densest clusters. 
 
 Paine eh a 
 ERS Atcyrone Ke. 
 
 Arttas *« 16 
 
 Fig. 101.—Telescopic view of the Pleiades, after Engelmann. The six larger stars are those 
 easily seen by ordinary eyes without a telescope, while the four next in size, having 
 four rays each, can be seen by very good eyes. About an inch from the upper right- 
 hand corner is a pair of small stars which a very Keen eye can see as a single star. 
 
 The cluster Preesepe, in the constellation Cancer (Map IL, 
 right ascension, 8 hours 20 minutes; declination, 20° 10’ N.), 
 is plainly visible to the naked eye on a clear, moonless night, 
 as a nebulous mass of light. Examined with a small tele- 
 
CLUSTERS OF STARS. 455 
 
 scope, it is fonnd to consist of a group of stars, ranging from 
 the seventh or eighth magnitude upwards. For examination 
 with a small telescope, one of the most beautiful groups is in 
 the constellation Perseus (Map L, right ascension, 2 hours 10 
 minutes; declination, 57° N.). It is seen to the best advantage 
 with a low magnifying power, between twenty-five and fifty 
 times, and may easily be recognized by the naked eye as a 
 little patch of light. 
 
 The heavens afford no objects of more interest to the con- 
 templative mind than some of these clusters. Many of them 
 are so distant that the most powerful telescopes ever made 
 show them only as a patch of star-dust, or a mass of light so 
 faint that the separate stars cannot be distinguished. Their 
 distance from us is such that they are beyond, not only all 
 our means of measurement, but all our powers of estimation. 
 Minute as they appear, there is nothing that we know of to 
 prevent our supposing each of them to be the centre of a 
 group of planets as extensive as our own, and each planet to 
 be as full of inhabitants as this one. We may thus think of 
 them as little colonies on the outskirts of creation itself, and 
 as we see all the suns which give them light condensed into 
 one little speck, we might be led to think of the inhabitants 
 of the various systems as holding intercourse with each other. 
 Yet, were we transported to one of these distant clusters, and 
 stationed on a planet circling one of the suns which compose 
 it, instead of finding the neighboring suns in close proximity, 
 we should only see a firmament of stars around us, such as we 
 see from the earth. Probably it would be a brighter firma- 
 nent, in which so many stars would glow with more than the 
 splendor of Sirius, as to make the night far brighter than 
 ours; but the inhabitants of the neighboring worlds would as 
 completely elude telescopic vision as the inhabitants of Mars 
 do here. Consequently, to the inhabitants of every planet in 
 the cluster, the question of the plurality of worlds might be 
 as insolvable as it is to us. 
 
 To give the reader an idea what the more distant of these 
 star clusters looks like, we present two views from Sir John 
 
456 THE STELLAR UNIVERSE. 
 
 Herschiel’s observations at the Cape of Good Tlope. Fig. 102 
 shows the cluster numbered 2822 in Herschel’s catalogue, and 
 known as 47 Toucani. That astronomer describes it as “a 
 most glorious globular cluster, the stars of the fourteenth mag- 
 nitude immensely numerous. It is compressed to a blaze of 
 light at the centre, the diameter of the more compressed part 
 being 80” in right ascension.” Fig. 103 is No. 3504 of Her- 
 schel: “The noble globular cluster w Centauri, beyond all 
 comparison the richest and largest object of the kind in the 
 heavens. The stars are literally innumerable, and as their 
 
 South. 
 
 East. 
 
 West. ° 
 
 North. 
 
 Fig. 102.—Cluster 47 Toucani. Right ascen- Fia. 103.—Cluster » Centauri. Right ascen- 
 sion, 0 hours 18 minutes; declination, sion, 13 hours 20 minutes; declination, 
 {2° 45'S. 46° 52’ S., 
 
 total light when received by the naked eye affects it hardly 
 more than a star of the fifth or fourth to fifth magnitude, the 
 minuteness of each star may be imagined.” 
 
 § 6. Nebule. 
 
 Nebule appear to us as masses of soft diffused light, of 
 greater or less extent. Generally these masses are very ir 
 recular in outline, but a few of them are round and well- 
 defined. These are termed planetary nebule. It may some- 
 times be impossible to distinguish between star clusters and 
 nebula, because when the power of the telescope is so low 
 that the separate stars of a cluster. cannot be distinguished, 
 they will present the appearance of a nebula. To the naked 
 eye the cluster Preesepe, described in the last chapter, looks 
 
NEBULE.. AST 
 
 exactly like’a nebula, though a very small telescope will re- 
 solve it into stars. The early observers with telescopes de- 
 scribed many objects as nebulee which the more powerful in- 
 struments of Herschel showed to be clusters of stars. Thus 
 arose the two classes of resolvable and irresolvable nebule, 
 the first comprising such as could be resolved into stars, and 
 the second such as could not. It is evident, from what we 
 have just said, that this distinction would depend partly on 
 the telescope, since a nebula which was irresolvable in one 
 telescope might be resolvable in another telescope of greater 
 power. This suggests the question whether all nebule: may 
 not really be clusters of stars, those which are irresolvable ap- 
 pearing so merely because their distance is so great that the 
 separate stars which compose them cannot be distinguished 
 with our most powerful telescopes. If this were so, there 
 would be no such thing as a real nebula, and everything 
 which appears as such should be classified as a star cluster. 
 The spectroscope, as we shall presently show, has settled this 
 question, by showing that many of these objects are immense 
 masses of glowing gas, and therefore cannot be stars. 
 
 Classification and Forms of Nebule.—The one object of this 
 class which, more than all others, has occupied the attention 
 of astronomers and excited the wonder of observers, is the 
 great nebula of Orion. It surrounds the middle of the three 
 stars which form the sword of Orion. Its position may be 
 found on Maps II. and IIL, in right ascension 5 hours 28 
 minutes, declination 6° 8. <A good eye will perceive that 
 this star, instead of looking like a bright point, as the other 
 stars do, has an ill-defined, hazy appearance, due to the sur- 
 rounding nebule. This object was first described by Huy- 
 ghens in 1659, as follows: 
 
 “There is one phenomenon among the fixed stars worthy 
 of mention which, so far as I know, has hitherto been noticed 
 by no one, and- indeed cannot be well observed except with 
 large telescopes. In the sword of Orion are three stars quite 
 close together. In 1656, as I chanced to be viewing the mid- 
 dle one of these with the telescope, instead of a single star, 
 
458 THE STELLAR UNIVERSE. 
 
 twelve showed themselves (a not uncommon circumstance). 
 Three of these almost touched each other, and, with four oth- 
 ers, shone through a nebula, so that the space around them 
 seemed far brighter than the rest of the heavens, which was 
 entirely clear, and appeared quite black, the effect being that 
 of an opening in the sky, through which a brighter region 
 was visible.’’* 
 
 Fira. 104.—The great nebula of Orion, as drawn by Trouvelot with the twenty-six-inch 
 Washington telescope. 
 
 Since that time it has been studied with large telescopes 
 by a great number of observers, including Messier, the two 
 
 — 
 
 * Systema Saturnium, p. 8. The last remark of Huyghens seems to have pro- 
 duced the impression that he or some of the early observers considered the nebulz 
 to be real open‘ngs in the firmament, through which they got glimpses of the 
 glory of the empyrean, But it may be doubted whether the old ideas of the firma- 
 ment and the empyrean were entertained by any astronomer after the invention 
 of the telescope, and there is nothing in the remark of Huyghens to indicate that 
 he thought the opening really existed. His words are rather obscure. 
 
NEBULA. 459 
 
 Herschels, Rosse, Struve, and the Bonds. The representation 
 which we give in Fig. 104 is from a drawing made by Mr. 
 Trouvelot with the great Washington telescope. In brilliancy 
 and variety of detail it exceeds any other nebula visible in 
 the northern hemisphere. The central point of interest is oc- 
 cupied by four comparatively bright stars, easily distinguished 
 by a small telescope with a magnifying power of 40 or 50, 
 combined with two small ones, requiring a nine-inch telescope 
 to be well seen. The whole of these form a sextuple group, , 
 included in a space a few seconds square, which alone would 
 be an interesting and remarkable object. Besides these, the 
 nebula is dotted with so many stars that they would almost 
 constitute a cluster by themselves. 
 
 In the winter of 186465, the spectrum of this object was 
 examined independently by Secchi and Huggins, who found 
 that it consisted of three bright lines, and hence concluded 
 that the nebula was composed, not of stars, but of glowing 
 gas. ‘The position of one of the lines was near that of a line 
 of nitrogen, while another seemed to coincide with a hydrogen 
 line. There is, therefore, a certain probability that this object 
 is a mixture of hydrogen and nitrogen gas, though this is a 
 point on which it is impossible to speak with certainty. 
 
 Another brilliant nebula visible to the naked eye is the 
 great one of Andromeda (Maps II. and V., right ascension, 
 0 hours 35 minutes; declination, 40° N.). The observer can 
 see at a glance with the naked eve that this is not a star, but 
 a mass of diffused light. Indeed, untrained observers have 
 sometimes very naturally mistaken it for a comet.* It was 
 first described by Marius, in 1614, who compared its light to 
 that of a candle shining through horn. This gives a very 
 good idea of the singular impression it produces, which is that 
 of an object not self-luminous, but translucent, and illuminated 
 by a very brilliant light behind it. With a small telescope, it 
 
 * A ship-captain who had crossed the Atlantic once visited the Cambridge Ob- 
 servatory, to tell Professor Bond that he had seen a small comet, which remained 
 in sight during his entire voyage. The object proved to be the nebula of An- 
 dromeda. 
 
460 THE STELLAR UNIVERSE. 
 
 is easy to imagine it to be a solid like horn; but with a large 
 one, the effect is much more that of a great mass of matter, 
 like fog or mist, which scatters and reflects the light of a brill- 
 iant body in its midst. That this impression can be correct, 
 it would be hazardous to assert; but the result of a spectrum 
 
 Fig. 105,—The annular nebula in Lyra. Drawn by Professor E. 8. Holden. 
 y y 
 
 analysis of the light of the nebula certainly seems to favor it. 
 Unlike most of the nebulee, its spectrum is a continuous one, 
 similar to the ordinary spectra from heated bodies, thus indi- 
 cating that the light emanates, not from a glowing gas, but 
 from matter in the solid or liquid state. This would suggest 
 
NEBULA. . 461. 
 
 the idea that the object is really an immense star- cluster, so 
 distant that the most powerful telescopes cannot resolve it. 
 Though we cannot positively deny the possibility of this, yet 
 in the most powerful telescopes the light fades away so softly 
 and gradually that no such thing as a resolution into stars 
 seems possible. Indeed, it looks less resolvable and more like 
 a gas in the largest ee: than in those of moderate size. 
 ee it is really a gas, and if the spectrum is continuous through- 
 out the Role extent of the nebula, it would indicate either 
 that it shone by reflected light, or that the gas was subjected 
 to a great pressure almost to its outer limit, w 1ak hardly seems 
 possible. But, granting that the light is weeds ted, we cannot 
 say whether it originates in a single bright star or in a nuin- 
 ber of small ones scattered about through the nebula. 
 
 Another extraordinary object of this class is the annular, or 
 ring-nebula of Lyra, situated in that constellation, about half- 
 way between the stars and y. In the older telescopes it 
 looked like a perfect ring; but the larger ones of modern times 
 show that the opening of the ring is really filled with nebu- 
 lous ight; in fact, that we have here an object of very regular 
 outline, in which the outer portion is brighter than the inte- 
 rior. Its form is neither circular nor exactly elliptic, but ege- 
 shaped, one end being more pointed than the other. A mod- 
 erate-sized telescope will show it, but a large one is required 
 to see it to good advantage. 
 
 It would appear, eben a comparison of drawings Bradt at 
 different dates, that some nebulee are subject to great changes 
 of form. Especially does this hold trne of the nebula sur- 
 rounding the remarkable variable. star » Argus. In many 
 other nébulee changes lave been suspected; but the softness 
 and indistinctness of outline which characterize most.of these 
 objects, and the great difference of their aspect when seen. in 
 telescopes of very different powers, make it difficult to prove a 
 change from mere differences of drawing. One of the strong- 
 est cases in favor of change has been made out by Professor 
 Holden from a study of drawings and descriptions of what is 
 called the “Omega nebula,’ from a resemblance of one of 
 
Fig. 106.—The Omega nebula; Herschel 2008. Right ascension, 1S hours 13 minutes; 
 declination, 16° 14/8. After Holden and Trouvelot. 
 
 its branches to the Greek letter Q. We present a figure of 
 this object as it now appears, from a drawing by Professor 
 Holden and Mr. Trouvelot, with the great Washington tele- 
 scope. It is the branch on the left-hand end of the nebula 
 which was formerly supposed to have the form of Q. 
 
 As illustrative of the fantastic forms which nebule some- 
 times assume, we present Herschel’s views of two more neb- 
 ule. That shown in Fig. 108 he calls the “ looped nebula,” 
 and describes as one of the most extraordinary objects in the 
 heavens. It cannot be seen to advantage except in the south- 
 ern hemisphere. 
 
 Distribution of the Nebule.— A remarkable feature of the 
 distribution of the nebule is that they are most numerous 
 where the stars are least so. While the stars grow thicker as 
 we approach the region of the Milky Way, the nebule dimin- 
 ish in number. Sir John Herschel remarks that one-third of 
 
NEBULZE. 463 
 
 “6/0, 50-410, -20. 210, 1. Of IQ #210 +90 440 4 G10. 4 GI0, + 90 +80 
 
 fo ete —|-- —- ab pe | | [ 
 
 Fig. 107.—Nebula Herschel 3722. Right ascension, 17 hours 56 minutes; declination, 24° 
 21'S. After Sir John Herschel. 
 
 the nebulous contents of the heavens are congregated in a 
 broad, irregular patch occupying about one-eighth the sur- 
 face of the celestial sphere, extending from Ursa Major in the 
 north to Virgo in the south. If, however, we consider, not the 
 true nebule, but star clusters, we find the same tendency to 
 condensation in the Milky Way that.we do in the stars. We 
 thus have a clearly marked dis- 
 tinction between nebule and 
 stars as regards the law of their 
 distribution.. The law in ques- 
 tion can be most easily under- 
 stood by the non-mathematical 
 reader by supposing the starry 
 sphere in such a position that 
 the Milky Way coincides with 
 
 é Fie. 108.—The looped nebula; Herschel 
 the horizon. Then the starsand 9941. Right ascension, 5 hours 40 min- 
 star clusters will be fewest at the tess declination, 69° 6° S. 
 zenith, and will increase in number as we approach the horizon. 
 Also, in the invisible hemisphere the same law will hold, the 
 stars and clusters being fewest under our feet, and will increase 
 as we approach the horizon. But the true nebulz will then 
 
 ol 
 
464 THE STELLAR UNIVERSE. 
 
 be fewest in the horizon, and will increase in number as we ap- 
 proach the zenith, or as, going below the horizon, we approach 
 the nadir. The positions of the nebulee and clusters in Sir John 
 Herschel’s great catalogue have been studied by Mr. Cleve- 
 land Abbe with especial reference to their distance from the 
 galactic circle, and the following numbers show part of his re- 
 sults. Imagine a belt thirty degrees wide extending around 
 the heavens, including the Milky Way, and reaching fifteen 
 degrees on each side of the central circle of the Milky Way. 
 This belt will include nearly one-fourth the surface of the ce- 
 lestial sphere, and if the stars or nebula were equally distrib- 
 uted, nearly one-fourth of them would be found in the belt. 
 Instead, however, of one-fourth, we find nine-tenths of the star 
 clusters, but only one-tenth of the nebule. 
 
 The discovery that the nebulze are probably masses of glow- 
 ing gas is of capital importance as tending to substantiate the 
 view of Sir William Herschel, that these masses are the crude 
 material out of which suns and systems are forming. This 
 view was necessarily an almost purely speculative one on the 
 part of that distinguished astronomer; but unless we suppose 
 that the nebulse are objects of almost miraculous power, there 
 must be some truth in it. A nebulous body, in order to shine 
 by its own light, as it does, must be hot, and must be losing 
 heat through the very radiation by which we see it. As it 
 cools, it must contract, and this contraction cannot cease un- 
 til it becomes either a solid body or a system of such bodies 
 revolving round each other. We shall explain this more fully 
 in treating of cosmical physics and the nebular hypothesis. 
 
 § 7. Proper Motions of the Stars. 
 
 To the unassisted eye, the stars seem to preserve the same 
 relative positions in the celestial sphere generation after gen- 
 eration. If Job, Hipparchus, or Ptolemy should again look 
 upon the heavens, he would, to all appearance, see Aldebaran, 
 Orion, and the Pleiades exactly as he saw them thousands of 
 years ago, withont a single star being moved from its place. 
 But the refined methods of modern astronomy, in which the 
 
PROPER MOTIONS OF THE STARS. 465 
 
 telescope is brought in to measure spaces absolutely invisible 
 to the eye, have shown that this seeming unchangeability is 
 not real, and that the stars are actually in motion, only the 
 rate of change is so slow that the eye would not, in most cases, 
 notice it for thousands of years. In ten thousand years quite 
 a number of stars, especially the brighter ones, would be seen 
 to have moved, while it would take a hundred thousand years 
 to introduce a very noticeable change in the aspect of the con- 
 stellations. 
 
 As a general rule, the brighter stars have the greatest 
 proper motions. But this is a rule to which there are many 
 exceptions. The star which, so far as known, has the greatest 
 proper motion of all—namely, Groombridge 1830—is of the 
 seventh magnitude only. Next in the order of proper motion 
 comes the pair of stars 61 Cygni, each of which is of the sixth 
 magnitude. Next are four or five others of the fourth and 
 fifth magnitudes. The annual motions of these stars are as 
 follows: 
 
 Groombridge 1830........ gi, Lalande 21258 .........006 . 4.4 
 GY Cyanieiiaiides doses caves 5'.2 on ridanize. 63078834. e140 tS | 
 Lalande 21185............. 4.7 p Cassiopeia. .........seeeee 3.8 
 COLTS Repeater Peery AN 5  COntaUi ts toga tases ccceg nu Ee t 
 
 The first of these stars, though it has the greatest proper 
 motion of all, would require 185,000 years to perform the 
 circuit of the heavens, while j Cassiopeize would require near- 
 ly 340,000 years to perform the same circuit. Slow as these 
 motions are, they are very large compared with those of most 
 of the stars of corresponding magnitude. As a general rule, 
 the stars of the fourth, fifth, and sixth magnitudes move only 
 a few seconds in a hundred years, and would therefore re- 
 quire many millions of years to perform the circuit of the 
 heavens. | 
 
 So far as they have yet been observed, and, indeed, so far 
 as they can be observed for many centuries to come, these 
 motions take place in perfectly straight lines. If each star is 
 moving in some orbit, the orbit is so immense that no curva- 
 ture can be perceived in the short are which has been de- 
 
466 THE STELLAR UNIVERSE. 
 
 scribed since accurate determinations of the positions of the 
 stars began to be made. So far as mere observation can in- 
 form us, there is no reason to suppose that the stars are sever- 
 ally moving in definite orbits of any kind. It is true that 
 Midler attempted to show, from an examination of the proper 
 motions of the stars, that the whole stellar universe was revolv- 
 ing around the star Alcyone, of the Pleiades, as a centre—a 
 theory the grandeur of which led to its wide diffusion in popu- 
 lar writings. But not the slightest weight has ever been given 
 it by astronomers, who have always seen it to be an entirely 
 baseless speculation. If the stars were moving in any regular 
 circular orbits whatever having a common centre, we could 
 trace some regularity among their proper motions. But no 
 such regularity can be seen. The stars in all parts of the 
 heavens move in all directions, with all sorts of velocities. It 
 is true that, by averaging the proper motions, as it were, we 
 can trace a certain law in them; but this law indicates, not a 
 particular kind of orbit, but only an apparent proper motion, 
 common to all the stars, which is probably due to a real mo- 
 tion of our sun and solar system. 
 
 The Solar Motion.—As our sun is merely one of the stars, 
 and rather a small star too, it may have a proper motion as 
 well as the other stars. Moreover, when we speak of the 
 proper motion of a star, we mean, not its absolute motion, but 
 only its motion relative to our system. As the sun moves, he 
 earries the earth and all the planets along with him; and if 
 we observe a star at perfect rest while we ourselves are thus 
 moving, the star will appear to move in the opposite direc- 
 tion, as we have already shown in explaining the Copernican 
 system. Hence, from an observation of the motion of a sin- 
 gle star, it is impossible to decide how much of this apparent 
 motion is due to the motion of our system, and how much to 
 the real motion of the star. If, however, we should observe a 
 great number of stars on all sides of us, and find them all ap- 
 parently moving in the same direction, it would be natural to 
 conclude that it was really our system which was moving, and 
 not the stars. Now, when Herschel averaged the proper mo- 
 
PROPER MOTIONS OF THE STARS. 467 
 
 tions of the stars in different regions of the heavens, he found 
 that this was actually the case. In general, the stars moved 
 from the direction of the constellation Hercules, and towards 
 the opposite point of the celestial sphere, near the constella- 
 tion Argus. This would show that, relatively to the general 
 mass of the stars, our sun was moving in the direction of the 
 constellation Hercules. Herschel’s data for this conclusion 
 were, necessarily, rather slender. The subject was afterwards 
 very carefully investigated by Argelander, and then by a num- 
 ber of other astronomers, whose results for the point of the 
 heavens towards which the sun is moving are as follows: 
 
 Right Ascension. Declination. 
 
 257° 49’ 28° 50’ N. 
 261° 22’ 37° 36’ N. 
 252° 24' 14° 26’ N. 
 
 260° 1’ 34° 23' N. 
 261° 38' 39° 54' N. 
 i 262° 29! 28° 58’ N. 
 
 It will be seen that while there is a pretty wide range among 
 the authorities as to the exact point, and, therefore, some un- 
 certainty as to where we should locate it, yet, if we lay the 
 different points down on a star-map, we shall find that they 
 all fall in the constellation Hercules, which was originally as- 
 signed by Herschel as that towards which we were moving. 
 
 As to the amount of the motion, Struve found that if the 
 sun were viewed from the distance of an average star of the 
 first magnitude placed in a direction from us at right angles 
 to that of the solar motion, it would appear to move at the 
 rate of 83.9 per century. Dunkin found the same motion to 
 be 38’.5 or 41’’.0, according to the use he made of stars hay- 
 ing large proper motions. 
 
 Motion of Groups of Stars.—There are in the heavens sev- 
 eral cases of widely extended groups of stars, having a com- 
 mon proper motion entirely different from that of the stars 
 around and among them. Such groups must form connected 
 systems, in the motion of which all the stars are carried along 
 together without any great change in their positions relative 
 
468 THE STELLAR UNIVERSE. 
 
 to each other. The most remarkable case of this kind oc- 
 curs in the constellation Taurus. A large majority of the 
 brighter stars in the region between Aldebaran and the Plei- 
 ades have a common proper motion of about ten seconds per 
 century towards the east. How many stars are included in 
 this group no one knows, as the motions of the brighter ones 
 only have been accurately investigated. Mr. R. A. Proctor 
 has shown that five out of the seven stars which form the 
 Dipper, or Great Bear, are similarly connected. He proposes 
 for this community of proper motions in certain regions the 
 name of Star-drift. Besides those we have mentioned, there 
 are cases of close groups of stars, like the Pleiades, and of 
 pairs of widely separated stars, in which star-drift has been 
 noticed. 
 
 Motion in the Line of Sight.—Until quite recently, the only 
 way in which the proper motion of a star could be detected 
 was by observing its change of direction, or the change of the 
 point in which it is seen on the celestial sphere. It is, how- 
 ever, impossible in this way to decide whether the star is or is 
 not changing its distance from our system. If it be moving 
 directly towards us, or directly away from us, we could not 
 see any motion at all. The complete motion of the stars can- 
 not, therefore, be determined by mere telescopic observations. 
 But there is an ingenious method, founded on the undulatory 
 theory of light, by which this motion may be detected with 
 more or less probability by means of the spectroscope, and 
 which was first successfully applied by Mr. Huggins, of Eng- 
 land. According to the usual theory of light, the luminosity 
 of a heated body is a result of the vibrations communicated 
 by it to the ethereal medium which fills all space ; and if the 
 body be gaseous, it is supposed that a molecule of the gas vi- 
 brates at a certain definite rate, and thus communicates only 
 certain definite vibrations to the ether. The rate of vibration 
 is determined by the position of the bright line in the spec- 
 trum of the gas. Now, if the vibrating body be moving 
 through the ether, the light-waves which it throws behind it 
 will be longer, and those which it throws in front of it will be 
 
PROPER MOTIONS OF THE STARS. ABD 
 
 shorter, than if the body were at rest. The result will be, that 
 in the former case the spectral lines will be less refrangible, 
 or nearer the red end of the spectrum, and in the latter case 
 nearer the blue end. If the line is not a bright one which the 
 gas emits, but the corresponding dark one which it has ab- 
 sorbed from the light of a star passing through it, the result 
 will be the same. If such a known line is found slightly 
 nearer the blue end of the spectrum than it should be, it is 
 — concluded that the star from which it emanates is approach- 
 ing us, while in the contrary case it is receding from us. 
 
 The question may be asked, How can we identify a line as 
 proceeding from a gas, unless it is exactly in the position of 
 the line due to that gas? How do we know but that it may 
 be due to some other gas which emits light of slightly differ- 
 ent refrangibility ? The reply to this must be, that absolute 
 certainty on this point is not attainable; but that, from the 
 examination of a number of stars, the probabilities seem large- 
 ly in favor of the opinion that the displaced lines are really 
 due to the gases near whose lines they fall. If the lines were 
 always displaced in one direction, whatever star was exam: 
 ined, the conclusion in question could not be drawn, because 
 it might be that this line was due to some other unknown sub- 
 stance. But as a matter of fact, when different stars are ex- 
 amined, it is found that the lines in question are sometimes 
 on one side of their normal position and sometimes on the 
 other. This makes it probable that they really all belong to 
 one substance, but are displaced by some cause, and the motion 
 of the star is a cause the existence of which is certain, and the 
 sufficiency of which is probable. 
 
 Mr. Huggins’s system of measurement has been introduced 
 by Professor Airy into the Royal Observatory, Greenwich, 
 where very careful measures have been made during the past 
 two years by Mr. Christie and Mr. Maunder. To show how 
 well the fact of the motion is made out, we give in the tables 
 on the following page the results obtained by Mr. Huggins 
 and by the Greenwich observers for these stars in which the 
 motion is the largest : 
 
470 THE STELLAR UNIVERSE. 
 
 STARS RECEDING FROM US. 
 
 By Mr. Hugyins. By Greenwich. 
 
 25 miles per sec. 
 76 66 66 
 8 Orionis f receding. 
 a Geminorum i 25 miles per sec. 
 a Leonis 20 a 
 
 By Greenwich. 
 
 41 miles per sec. 
 
 a4 
 
 8 Geminorum approaching. 
 a Urse Majoris approaching. 
 
 There are several collateral circumstances which tend to 
 confirm these results. One is that the general amount of+mo- 
 tion indicated is,in a rough way, about what we should expect 
 the stars to have, from their observed proper motions, com- 
 bined with their probable parallaxes. Another is that those 
 stars in the neighborhood of Hercules are mostly found to be 
 approaching the earth, and those which lie in the opposite di- 
 rection to be receding from it, which is exactly the effect which 
 would result from the solar motion just described. Again, the 
 five stars in the Dipper which we have described as having a 
 common proper motion are also found to have a common mo- 
 tion in the line of sight. The results of this wonderful and 
 refined method of determining stellar motion, therefore, seem 
 worthy of being received with some confidence so far as the 
 general direction of the motion is concerned. But the dis- 
 placement of the spectral lines is so slight, and its measure- 
 ment a matter of such difficulty and delicacy, that we are far 
 from being sure of the exact numbers of miles per second 
 given by the observers. The discordances between the results 
 of Greenwich and those of Mr. Huggins show that numerical 
 certainty is not yet attained. 
 
 A necessary result of these motions will be that those stars 
 which are receding from us will, in the course of ages, appear 
 less brilliant, owing to their greater distance, while those which 
 
PROPER MOTIONS OF THE STARS. A471 
 
 are approaching us will, as they come nearer, appear brighter, 
 always supposing that their intrinsic brightness does not vary. 
 But so immense is the distance of the stars, that many thon- 
 sands of years will be required to produce any appreciable 
 change in their brightness from this cause. For instance, 
 from the best determinations which have been made, the dis- 
 tance of Sirius from our system is more than a million radii 
 of the earth’s orbit. With a velocity of twenty miles per sec- 
 ond, it would require more than one hundred and fifty thon- 
 sand years to pass over this distance. 
 
 It will, of course, be understood that the velocities found by 
 the spectroscopic method are not the total velocities with 
 which the stars are moving, but only the rate.at which they 
 are approaching to or receding from the earth, or, to speak 
 mathematically, the component of the velocity in the direc- 
 tion of the line of sight. To find the total velocity, this com- 
 ponent must be combined with the telescopic velocity found 
 from the observed proper motion of the star, which is the ve- 
 locity at right angles to the line of sight. None of the stars 
 are moving exactly towards our system, and it is not likely 
 that any will ever pass very near it. In the preceding list, 
 the star a Cygni is the one which is coming most directly 
 towards us. Its telescopic proper motion is so slight that, 
 though we suppose its distance to be two million radii of the 
 earth’s orbit, yet its velocity at right angles to the line of sight 
 will hardly amount to one-third of a mile per second. If the 
 spectroscopic determination is correct, then, after an interval 
 which will probably fall between one hundred thousand and 
 three hundred thousand years, a Cygni will pass by our sys- 
 tem at something like a hundredth of its present distance, 
 and will, for several thousand years, be many times nearer and 
 brighter than any star is now. 
 
4AT2 THE STELLAR UNIVERSE. 
 
 CHAPTER II. 
 THE STRUCTURE OF THE UNIVERSE. 
 
 Havine in the preceding chapter described those features 
 of the universe which the telescope exhibits to us, we have 
 now, in pursuance of our plan, to inquire what light telescopic 
 discoveries can throw upon the structure of the universe as a 
 whole. Here we necessarily tread upon ground less sure than 
 that which has hitherto supported us, because we are on the 
 very boundaries of human knowledge. Many of our conclu- 
 sions must be more or less hypothetical, and liable to be modi- 
 fied or disproved by subsequent discoveries. We shall en- 
 deavor to avoid all mere guesses, and to state no conclusion 
 which has not some apparent foundation in observation or 
 analogy. The human mind cannot be kept from speculating 
 upon and wondering abont the order of creation in its widest 
 extent, and science will be doing it a service in throwing ev- 
 ery possible light on its path, and preventing it from reaching 
 any conclusion inconsistent with observed facts. 
 
 The first question which we reach in regular order is, How 
 are the forty or fifty millions of stars visible in the most pow- 
 erful telescopes arranged in space? We know, from direct 
 observation, how they are arranged with respect to direction 
 from our system; and we have seen that the vast majority of 
 small stars visible in great telescopes are found in a belt span- 
 ning the heavens, and known as the Milky Way. But this 
 gives us no complete information respecting their absolute po- 
 sition: to determine this, we must know the distance as well 
 as the direction of each star. But beyond the score or so of 
 stars which have a measurable parallax, there is no known 
 way of measuring the stellar distances; so that all we can do 
 
VIEWS OF MODERN ASTRONOMERS. 473 
 
 is to make more or less probable conjectures, founded on the 
 apparent magnitude of the individual stars and the probable 
 laws of their arrangement. If the stars were all of the same 
 intrinsic brightness, we could make a very good estimate of 
 their distance from their apparent magnitude; but we know 
 that such is not the case. Still,in all reasonable probability, 
 the diversity of absolute magnitude is far less than that of the 
 apparent magnitude; so that a judgment founded on the lat- 
 ter is much better than none at all. It was on such consider- 
 ations as these that the conjectures of the first observers with 
 the telescope were founded. 
 
 § 1. Views of Astronomers before Herschel. 
 
 Before the invention of the telescope, any well-founded 
 opinion respecting the structure of the starry system was out 
 of the question. We have seen how strong a hold the idea of 
 a spherical universe had on the minds of men, so that even 
 Copernicus was fully possessed with it, and probably believed 
 the sun to be, in some way, the centre of this sphere. Before 
 any step could be taken towards forming a true conception of 
 the universe, this idea had to be banished from the mind, and 
 the sun had to be recognized as simply one of innumerable 
 stars which made up the universe. The possibility that such 
 might have been the case seems to have first suggested itself 
 to Kepler, though he was deterred from completely accepting 
 the idea by an incorrect estimate of the relative brilliancy of 
 the stars. He reasoned that if the sun were one of a vast 
 number of fixed stars of equal brilliancy scattered uniformly 
 throughont space, there could not be more than twelve which 
 were at the shortest distance from us. We should then have 
 another set at double the distance, another at triple the dis- 
 tance, and so on; and since the more distant they are, the 
 fainter they would appear, we should speedily reach a limit 
 beyond which no stars could be seen. In fact, however, we 
 often see numerous stars.of the same magnitude crowded 
 closely together, as in the belt of Orion, while the total num- 
 ber of visible stars is reckoned by thousands. He therefore 
 
A474 THE STELLAR UNIVERSE. 
 
 concludes that the distances of the individual stars from each 
 other are much less than their distances from our sun, the lat- 
 ter being situated near the centre of a comparatively vacant 
 region. 
 
 Had Kepler known that it would require the light of a hun- 
 dred stars of the sixth magnitude to make that of one of the 
 first magnitude, he would not have reached this conclusion. 
 A simple calculation would have shown him that, with twelve 
 stars at distance unity, there would have been four times that 
 number at the double distance, nine times at the treble dis- 
 tance, and so on, until, within the tenth sphere, there would 
 have been more than four thousand stars. The twelve hun- 
 dred stars on the surface of the tenth sphere would have 
 been, by calculation, of the sixth magnitude, a number near 
 enough to that given by actual count to show him that the 
 hypothesis of a uniform distribution was quite accordant with 
 observations. It is true that, where many bright stars were 
 found crowded together, as in Orion, their distance from each 
 other is probably less than that from our sun. But this ag- 
 glomeration, being quite exceptional, would not indicate a gen- 
 eral crowding together of all the stars, as Kepler seemed to 
 suppose. In justice to Kepler it must be said that he put 
 forth this view, not as a well-founded theory, but only as a 
 surmise, concerning a question in which certainty was not 
 attainable. 
 
 Ideas of Kant.—Those who know of Kant only as a specula- 
 tive philosopher may be surprised to learn that, although he 
 was not a working astronomer, he was the author of a theory 
 of the stellar system which, with some modifications, has been 
 very generally held until the present time. Seeing the Gal- 
 axy encircle the heavens, and knowing it to be produced by 
 the light of innumerable stars too distant to be individually 
 visible, he concluded that the stellar system extended much 
 farther in the direction of the Galaxy than it did elsewhere. 
 In other words, he conceived the stars to be arranged in a 
 comparatively thin, flat layer, or stratum, our sun being some- 
 where near the centre. When we look edgewise along this 
 
VIEWS OF MODERN ASTRONOMERS. 475 
 
 stratum, we see an immense number of stars, but in the per- 
 pendicular direction comparatively few are visible.* 
 
 This thin stratum suggested to Kant the idea of a certain 
 resemblance to the solar system. Owing to the small inclina- 
 tions of the planetary orbits, the bodies which compose this 
 system are spread out in a thin layer, as it were; and we have 
 only to add a great multitude of planets moving around the 
 sun in orbits of varied inclinations to have a-representation in 
 miniature of the stellar system as Kant imagined it to exist. 
 Had the zone of small planets between Mars and Jupiter then 
 been known, it would have afforded a striking confirmation of 
 Kant’s view by showing a yet greater resemblance of the plan- 
 etary system to his supposed stellar system. Were the num- 
 ber of these small planets sufficiently increased, we should see 
 them as a sort of Galaxy around the zodiac, a second Milky 
 Way, belonging to our system, and resolvable with the tele- 
 scope into small planets, just as the Galaxy is resolved into 
 small stars. The conclusion that two systems which were so 
 similar in appearance were really alike in structure would 
 have seemed very well founded in analogy. 
 
 As the planets are kept at: their proper distances, and pre- 
 vented from falling into each other or into thé sun by the 
 centrifugal force generated by their revolutions in their or- 
 bits, so Kant supposed the stars to be kept apart by a revolu- 
 tion around some common centre. The proper motions of 
 the stars were then almost unknown, and the objection was 
 anticipated that the stars were found to occupy the same po- 
 sition in the heavens from generation to generation, and there- 
 fore could not be in motion around a centre. To this Kant’s 
 reply was that the time of revolution was so long, and the 
 motion so slow, that it was not perceptible with the imper- 
 fect means of observation then available. Future genera- 
 tions would, he doubted not, by comparing their observations 
 
 * The original idea of this theory is attributed by Kant to Wright, of Durham, 
 England, a writer whose works are entirely unknown in this country, and whose 
 authorship of the theory has been very generally forgotten. 
 
476 THE STELLAR UNIVERSE. 
 
 with those of their predecessors, find that there actually was a 
 motion among the stars. 
 
 This conjecture of Kant, that the stars would be found to 
 have a proper motion, has, as we have seen, been amply con- 
 firmed; but the motion is not of the kind which his theory 
 would require. On this theory, all the stars ought to move in 
 directions nearly parallel to that of the Milky Way, just as in 
 the planetary system we find them all moving in directions 
 nearly parallel to the ecliptic. But the proper motions actually 
 observed have no common direction, and follow no law what- 
 ever, except that, on the average, there is a preponderance of 
 motions from the constellation Hercules, which is attributed 
 to an actual motion of our sun in that direction. Making al- 
 lowance for this preponderance, we find the stars to be appar- 
 ently moving at random in every direction; and therefore 
 they cannot be moving in any regularly arranged orbits, as 
 Kant supposed. A defender of Kant’s system might indeed 
 maintain that, as it is only in a few of the stars nearest us 
 that any proper motion has been detected, the great cloud of 
 stars which make up the Milky Way might really be moving 
 along in regular order, a view the possibility of which we shall 
 be better prepared to consider hereafter. 
 
 The Kantian theory supposes the system which we have 
 just been describing to be formed of the immense stratum of 
 stars which make up the Galaxy and stud our heavens, and 
 to include all the stars separately visible with our telescopes. 
 But he did not suppose this system, immense though it is, to 
 constitute the whole material universe. In the nebule he 
 saw other similar systems at distances so immense that the 
 combined light of their millions of suns only appeared as a 
 faint cloud in the most powerful telescopes. This idea that 
 the nebulz were other galaxies was more or less in vogue 
 among popular writers until a quite recent period, when it 
 was refuted by the spectroscope, which shows that these ob- 
 jects are for the most part masses of glowing gas. It has, 
 however, not received support among astronomers since the 
 time of Sir William Herschel. 
 
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 477 
 
 System of Lambert.—A. few years after the appearance of 
 Kant’s work, a similar but more elaborate system was sketched 
 out by Lambert. He supposed the universe to be arranged in 
 systems of different orders. The smallest systems which we 
 know are those made up of a planet, with its satellites circu- 
 lating around it as a centre. The next system in order of 
 magnitude is a solar system, in which a number of smaller 
 systems are each carried round the sun. Each individual star 
 which we see is a sun, and has its retinue of planets revolving 
 around it, so that there are as many solar systems as stars. 
 These systems are not, however, scattered at random, but are 
 divided up into greater systems which appear in our telescopes 
 as clusters of stars. An immense number of: these clusters 
 make up our Galaxy, and form the visible universe as seen in 
 our telescopes. There may be yet greater systems, each made 
 up of galaxies, and so on indefinitely, only their distance is so 
 immense as to elude our observation. 
 
 Each of the smaller systems visible to us has its central body, 
 the mass of which is much greater than that of those which 
 revolve around it. This feature Lambert supposed to extend 
 to other systems. As the planets are larger than their satel- 
 lites, and the sun larger than its planets, so he supposed each 
 stellar cluster to have a great central body around which each 
 solar system revolved. As these central bodies are invisible to 
 us, he supposed them to be opaque and dark. All the systems, 
 from the smallest to the greatest, were supposed to be bound 
 together by the one universal law of gravitation. 
 
 As not the slightest evidence favoring the existence of these 
 opaque centres has ever been found, we are bound to say that 
 this sublime idea of Lambert’s has no scientific foundation. 
 Astronomers have handed it over without reservation to the 
 lecturers and essayists. 
 
 § 2. Researches of Herschel and his Successors. 
 
 Herschel was the first who investigated the structure of 
 the stellar system by a long-continued series of observations, 
 executed with a definite end in view. His plan was that of 
 
478 THE STELLAR UNIVERSE. 
 
 “star - gauging,” which meant, in the first place, the simple 
 
 enumeration of all the stars visible with a powerful tele- 
 scope in a given portion of the heavens. He employed a 
 telescope of twenty inches aperture, magnifying one hundred 
 and sixty times, the field of view being a quarter of a degree 
 in diameter. ‘This diameter was about half that of the full 
 moon, so that each count or gauge included all the stars visi- 
 ble in a space having one-fourth the apparent surface of the 
 lunar disk. From the number of stars in any one field of 
 view, he concluded to what relative distance his sight ex- 
 tended, supposing a uniform distribution of the stars through- 
 out all the space included in the cone of sight of the telescope. 
 When an observer looks into a telescope pointed at the heav- 
 ens, his field of vision includes a space which constantly 
 widens out on all sides as the distance becomes greater; and 
 the reader acquainted with geometry will see that this space 
 forms a cone having its point in the focus of the telescope, and 
 its circular base at the extreme distance to which the telescope 
 reaches. The solid contents of this cone will be proportional 
 to the cube of the distance to which it extends; for instance, 
 if the telescope penetrates twice as far, the cone of sight will 
 be not only twice as long, but the base will be twice as wide 
 in each direction, so that the cone will have altogether eight 
 times the contents, and will, on Herschel’s hypothesis, contain 
 eight times as many stars. So, when Herschel found the stars 
 eight times as numerous in one region as in another, he con- 
 cluded that the stellar system extended twice as far in the 
 direction of the first region. 
 
 To count all the stars visible with his telescope, Herschel 
 found to be out of the question. He would have had to point 
 his instrument several hundred thousand times, and count all 
 the visible stars at each pointing. He therefore extended his 
 survey only over a wide belt extending more than half-way 
 round the celestial sphere, and cutting the Galaxy at right 
 angles. In this belt he counted the stars in 8400 telescopic 
 fields. Comparing the average number of stars in different 
 regions with the position of the region relative to the Galaxy, 
 
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 479 
 
 he found that the stars were thinnest at the point most distant 
 from the Galaxy, and that they constantly increased in num- 
 ber as the Galaxy was approached. The following table will 
 give an idea of the rate of increase. It shows the average 
 number of stars in the field of view of the telescope for each 
 of six zones of distance from the Galaxy. 
 
 HUPBt-ZONS 2.8.05. «5s 90°"to 75° from Galaxy... <... 4 stars per field. 
 Second zone ......... Der ee OU aes Bon ae fen eae Beet Aci 
 A hird Zone). os. euc b.GOR FAG RS a8 HD MARA Ree peek SP ota ee sf 
 Fourth zone.......... r Pieper {Vea bat pore cs 2 ts TA Aas? oF 
 Pitth FONG 5. sees acne S07 uli. ers PET Te ANE ere 24 ee oh 
 EXE ZOMG, 6,2 sc1cee LOC ies aU On ins MRIS vce) ¢ Bales: a 
 
 A similar enumeration was made by Sir John Herschel for the 
 corresponding region on the other, or southern, side of the Gal- 
 axy. le used the same telescope, and the same magnifying 
 power. His results were: 
 
 [Baret ZONe accords cas 6 stars per field. | Fourth zone............ 13 stars per field. 
 
 Second ZOMCh see. ¢é ee BUG 2006s ccc worsece 26 ae as 
 Bhd ZONE... sccese eect a as uA Sixth ZOMG Caisse scence 59 es re 
 
 The reader will, perhaps, more readily grasp the significa- 
 tion of these numbers by the mode of representation which 
 was suggested in describing the distribution of the nebulee. 
 Let him imagine himself standing under a clear sky at the 
 time when the Milky Way encircles the horizon. Then, the 
 first zone, as we have defined it, will be around the zenith, ex- 
 tending one-sixth of the way to the horizon on every side; 
 the second zone will be next below and around this circular 
 space, extending one-third of the way to the horizon; and so 
 each one will follow in regular order until we reach the sixth, 
 or galactic, zone, which will encircle the horizon to a height 
 of 15° on every side. The numbers we have given show that 
 in the position of the observer which we have supposed the 
 stars would be thinnest around the zenith, and would con- 
 stantly increase in number as we approached the horizon. 
 The observer being supposed still to occupy the same posi- 
 
 tion, the second table shows the distribution of the stars in the 
 o2 
 
480 THE STELLAR UNIVERSE. 
 
 opposite or invisible hemisphere, which he would see if the 
 earth were removed. In this hemisphere the first, or thinnest, 
 zone would be directly opposite the thinnest zone in the ob- 
 server's zenith; that is, it would be directly under his feet. 
 The successive zones would then be nearer the horizon, the 
 sixth or last encircling it, and extending 15° below it on every 
 side. 
 
 The numbers we have given are only averages, and do not 
 give an adequate idea of the actual inequalities of distribu- 
 tion in special regions of the heavens. Sometimes there was 
 not a solitary star in the field of the telescope, while at oth- 
 ers there were many hundreds. In the circle of the Galaxy 
 itself, the stars are more than twice as thick as in the average 
 of the first zone, which includes not only this circle, but a 
 space of 15° on each side of it. 
 
 Adopting the hypothesis of a uniform distribution of the 
 stars, Herschel concluded from his first researches that the 
 stellar system was of the general form supposed by Kant, ex- 
 tending out on all sides five times as far in the direction of 
 the Galaxy as in the direction perpendicular to it. The most 
 important modification he made was to suppose an immense 
 cleft extending edgewise into the system from its circumfer- 
 ence about half-way to the centre. This cleft corresponded to 
 the division in the Milky Way which commences in the sum- 
 mer constellation Cygnus in the north, and passes through 
 Aguila, the Serpent, and Scorpius far into the southern hemi- 
 sphere. Estimating the distance by the arrangement and ap- 
 parent magnitude of the stars, he was led to estimate the mean 
 thickness of the stellar stratum from top to bottom as 155 
 units, and the diameter as 850 units, the unit being the aver- 
 age distance of a star of the first magnitude. Supposing this 
 distance to be that which light would travel over in 16 years 
 —a supposition which is founded on the received estimate of 
 the mean parallax corresponding to stars of that magnitude— 
 then it would take light nearly 14,000 years to travel across 
 the system from one border to the other, and 7000 years to 
 reach us from the extreme boundary. 
 
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 481 
 
 The foregoing deduction of 
 Herschel was founded on the 
 hypothesis that the stars were 
 equally dense in every part of 
 the stellar system, so that the 
 number of stars in any direc- 
 tion furnished an index to the 
 extent of the stars in that di- 
 rection. Further study show- 
 ed Herschel that this assump- 
 tion might be so far from cor- 
 rect that his conclusions would 
 have to be essentially modi- 
 fied. Binary and other double 
 stars and star clusters evident- 
 ly offered cases in which sev- 
 eral stars were in much closer 
 association than were the stars 
 in general. ‘To show exactly 
 on what considerations this 
 change of view is founded, we 
 remark that if the increase of 
 density in the direction of the 
 Milky Way were quite regu- 
 lar, so that there were no cases 
 of great difference in the thick- 
 ness of the stars in two adjoin- 
 ing regions, then the original 
 view would have been sound 
 so far as it went. But such ir- 
 regularities are very frequent, 
 and it would lead to an obvi- 
 ous absurdity to explain them 
 on Herschel’s first hypothesis ; 
 for instance, when the tele- 
 scope was directed towards 
 
 the Pleiades there would be Fre. 109.—Herschel’s view of the form of the 
 universe. 
 
 * 
 
 KKK 
 eK 
 
 * 
 bad 
 
 Stk 
 
 hbk 
 
482 THE STELLAR UNIVERSE. 
 
 found, probably, six or eight times as many stars as in the ad- 
 joining fields. But supposing the real thickness of the stars 
 the same, the result would be that in this particular direction 
 the stars extended out twice as far as they did in the neigh- 
 boring parts of the sky; that is, we should have a long, nar- 
 row spike of stars pointing directly from us. As there are 
 many such clusters in various parts of the sky, we should have 
 to suppose a great number of such spikes. In other regions, 
 especially around the Milky Way, there are spaces nearly void 
 of stars. To account for these we should have to suppose 
 long narrow chasms reaching through towards our sun. ‘Thus 
 the stellar system would present the form of an exaggerated 
 star-fish with numerous deep openings, a form the existence 
 of which is beyond all probability, especially if we reflect 
 that all the openings and all the arms have to proceed from 
 the direction of our sun. 
 
 The only rational explanation of a group of stars showing 
 itself in a telescope, with a comparatively void space surround- 
 ing it, is that we have here a real star cluster, or a region in 
 which the stars are thicker than elsewhere. Now, one can see 
 with the naked eye that the Milky Way is not a continuous 
 uniform belt, but is, through much of its course, partly made 
 up of a great number of irregular cloud-like masses with com- 
 paratively dark spaces between them. The conclusion is un- 
 avoidable that we have here real aggregations of stars, and 
 not merely a region in which the bounds of the stellar-sys- 
 tem are more widely extended. Whether Herschel clearly saw 
 this may be seriously questioned; but however it may have 
 been, he adopted another method of estimating the relative 
 distances of the stars visible in his gauges. 
 
 This method consisted in judging of the distances to which 
 his telescope penetrated, not by the number of stars it brought 
 into view, but by their brightness. If all the stars were of the 
 same intrinsic brightness, so that the differences of their ap- 
 parent magnitude arose only from their various distances from 
 us, then this method would enable us to fix the distance of 
 each separate star. But as we know that the stars are by no 
 
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 488 
 
 means equal in intrinsic brightness, the method cannot be 
 safely applied to any individual star, a fact which Herschel 
 himself clearly saw. It does not follow, however, that we 
 cannot thus form an idea of the relative distances of whole 
 classes or groups of stars. Although it is quite possible that 
 an individual star of the fifth magnitude may be nearer to us 
 than another of the fourth, yet we cannot doubt that the av- 
 erage distance of all the fifth-magnitude stars is greater than 
 the average of those of the fourth magnitude, and greater, 
 too, in a proportion admitting of a tolerably accurate numeri- 
 cal estimate. Such an estimate Herschel attempted to make, 
 proceeding on the following plan: 
 
 Suppose a sphere to be drawn around our sun as a centre 
 of such size that it shall be 
 equal to the average space ep hs a a 
 occupied by a single one of 
 the stars visible to the naked 
 
 Ae order 
 eye; that is, if we suppose ve 
 that portion of the space of ehardey 
 the stellar system occupied 
 
 by the six thousand bright- | ghordep 
 er stars to be divided into . 
 six thousand parts, then the 
 sphere will be equal to one 
 of these parts. The radius 
 of this sphere will probably 
 not differ much from the dis- 
 tance of the nearest fixed star, 
 a distance we shall take for 
 unity. Then, suppose a series 
 of larger spheres, all drawn “18 star® 
 
 around our sun as a centre, 
 
 and having the radii 8, 5, 7, a 
 9, etc. The contents of the $ 
 spheres being as the cubes Eysseiigiigys °f 87h 
 of their diameters, the first Fig. 110.—Ilustrating Herschel’s orders of dis- 
 sphere willhave8x3x3=27 tance of the stars. 
 
484 THE STELLAR UNIVERSE. 
 
 times the bulk of the unit sphere, and will therefore be large 
 enough to contain 27 stars; the second will have 125 times 
 the bulk, and will therefore contain 125 stars, and so with 
 the successive spheres. Fig. 110 shows a section of portions 
 of these spheres up to that with radius 11. Above the centre 
 are given the various orders of stars which are situated be- 
 tween the several spheres, while in the corresponding spaces 
 below the centre are given the number of stars which the re- 
 gion is large enough to contain; for instance, the sphere of 
 radius 7 has room for 343 stars, but of this space 125 parts 
 belong to the spheres inside of it: there is, therefore, room for 
 218 stars between the spheres of radii 5 and 7. 
 
 Herschel designates the several distances of these layers of 
 stars as orders; the stars between spheres 1 and 3 are of the 
 first order of distance, those between 3 and 5 of the second 
 order, and so on. Comparing the room for stars between the 
 several spheres with the number of stars of the several magni- 
 tudes, he found the result to be as follows: 
 
 Number of Number of 
 
 Order of Stars there Magnitude. | Stars of that 
 
 Distance. 
 
 is room for. magnitude. 
 
 1 26 1 Li 
 2 98 2 57 
 3 218 3 206 
 4 386 4 454 
 5 602 5 1161 
 6 866 6 6103 
 vf 1178 7 6146 
 8 1538 
 
 There is evidently no correspondence between the calculat- 
 ed orders of distance and the magnitudes as estimated on the 
 usual scale. But Herschel found that this was because the 
 magnitudes as usually estimated corresponded to an entirely 
 different scale of distance from that which he adopted. In 
 his scale the several distances increased in arithmetical pro- 
 gression; while in the order of magnitudes the increase is 
 in geometrical progression. In consequence, the stars of the 
 sixth magnitude correspond to the eighth, ninth, or tenth order 
 of distances; that is, we should have to remove a star of the 
 
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 485 
 
 first magnitude to eight, nine, or ten times its actual distance 
 to make it shine as a star of the sixth magnitude. 
 
 Attempting on this system to measure the extent of the 
 Milky Way, Herschel concluded that it was unfathomable 
 with his twenty-foot telescope, which, he calculated, would 
 penetrate to the 900th order of distances, that is, to stars 
 which were 900 times as far as the average of those of the 
 first magnitude. He does not seem to have made any very 
 extended examination with his forty-foot telescope, but con- 
 cluded that it would leave him in the same uncertainty in 
 respect to the extent of the Milky Way as the twenty-foot one 
 did. This unrivalled man, to whom it was given to penetrate 
 farther into creation than man had ever done before him, 
 seems to have rested from his labors without leaving any more 
 definite theory of the boundaries of the stellar system than 
 that they extended, at least in the direction of the Milky Way, 
 beyond the utmost limit to which his telescope could penetrate. 
 If we estimate the time it would require light to come from 
 the utmost limit to which he believed his vision to extend, 
 we shall find it to be about fourteen thousand years, or more 
 than double that deduced from his former gauges. We can 
 say with confidence that the time required for light to reach 
 us from the most distant visible stars is measured by thon- 
 sands of years. But it must be admitted that Herschel’s esti- 
 -mate of the extent of the Milky Way may be far too great, be- 
 cause it rests on the assumption that all stars are of the same 
 absolute brightness. If the smallest stars visible in his tele- 
 scope were, on the average, of the same intrinsic brilliancy as 
 the brighter ones, the conclusion would be well founded. But 
 if we suppose a boundary, it is impossible to decide from Her- 
 schel’s data whether the minuteness of those stars arises from 
 their great distance or from their small magnitude. Notwith- 
 standing this uncertainty, it has been maintained by some, not- 
 ably by Mr. Proctor, that the views of Herschel respecting the 
 constitution of the Milky Way, or stellar system, were radical- 
 ly changed by this second method of star-gauging. I see no 
 evidence of any radical change. Although Herschel does not 
 
A486 THE STELLAR UNIVERSE. 
 
 express himself very definitely on the subject, yet, in his last 
 paper on the distribution of the stars (Philosophical Trans- 
 actions for 1817), there are several remarks which seem to im- 
 ply that he still supposed the stellar system to have the gen- 
 eral form shown in Fig. 109, and that, in accordance with that 
 view, he supposed the clustering of stars to indicate protuber- 
 ant parts of the Milky Way. He did, indeed, apply a differ- 
 ent method of research, but the results to which the new meth- 
 ods led were, in their main features, the same as those of the 
 old method. 
 
 Since the time of Herschel, one of the most eminent of the 
 astronomers who have investigated this subject is Struve the 
 elder, formerly director of the Pulkowa Observatory. His re- 
 searches were founded mainly on the numbers of stars of the 
 several magnitudes found by Bessel in a zone thirty degrees 
 wide extending all round the heavens, fifteen degrees on each 
 side of the equator. With these he combined the gauges of 
 Sir William Herschel. The hypothesis on which he based his 
 theory was similar to that employed by Herschel in his later 
 researches, in so far that he supposed the magnitude of the 
 stars to furnish, on the average, a measure of their relative 
 distances. Supposing, after Herschel, a number of concentric 
 spheres to be drawn around the sun as a centre, the successive 
 spaces between which corresponded to stars of the several 
 magnitudes, he found that the farther out he went, the more 
 the stars were condensed in and near the Milky Way. ‘This 
 conclusion may be drawn at once from the fact we have al- 
 ready mentioned, that the smaller the stars, the more they are 
 condensed in the region of the Galaxy. Struve found that if 
 we take only the stars plainly visible to the naked eye—that 
 is, those down to the fifth magnitude—they are no thicker in 
 the Milky Way than in other parts of the heavens. But those 
 of the sixth magnitude are a little thicker in that region, those 
 of the seventh yet thicker, and so on, the inequality of distri- 
 bution becoming constantly greater as the telescopic power is 
 increased. 
 
 From all this, Struve concluded that the stellar system might 
 
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 487 
 
 be considered as composed of layers of stars of various densi- 
 ties, all parallel to the plane of the Milky Way. The stars are 
 thickest in and near the central layer, which he conceives to 
 be spread out as a wide, thin sheet of stars. Our sun is situ- 
 ated near the middle of this layer. As we pass out of this 
 layer, on either side we find the stars constantly growing thin- 
 ner and thinner, but we do not reach any distinct boundary. 
 As, if we could rise in the atmosphere, we should find the air 
 constantly growing thinner, but at so gradual a rate of prog- 
 ress that we could hardly say where it terminated; so, on 
 Struve’s view, would it be with the stellar system, if we could 
 mount up in a direction perpendicular to the Milky Way. 
 Struve gives the following table of the thickness of the stars 
 on each side of the principal plane, the unit of distance being 
 that of the extreme distance to which Herschel’s telescope 
 could penetrate : 
 
 Mean Distance 
 
 Distance from Principal Plane. Density. between Neigh- 
 boring Stars. 
 In the principal plane........... 1.0000 1.000 
 0.05 from principal plane...... 0.48568 1.272 
 0.10 SG hls heads 0.35288 1.458 
 0.20 % ps ah 0.23895 POLY 
 0.30 Et, Dtenay, bine 0.17980 1.772 
 0.40 ra eee 0.13021 1.973 
 0.50 i. deste. 0.08646 2.261 
 0.60 is srt) ita ent 0.05510 2.628 
 0.70 ee ne sen arene 0.03079 3.190 
 0.80 fe ae OP Talent 0.01414 4.131 
 0.866 ea ee. eel 0.00532 5.729 
 
 This condensation of the stars near the central plane, and 
 the gradual thinning-out on each side of it, are only designed 
 to be the expression of the general or average distribution 
 of those bodies. The probability is that even in the central 
 plane the stars are many times as thick in some regions as in 
 others, and that as we leave the plane, the thinning-out would 
 be found to proceed at very different rates in different re- 
 gions. That there may be a gradual thinning-out cannot be 
 denied ; but Struve’s attempt to form a table of it is open to 
 the serious objection that, like Herschel, he supposed the dif- 
 
488 THE STELLAR UNIVERSE. 
 
 ferences between the magnitudes of the stars to arise entirely 
 from their different distances from us. Although where the 
 scattering of the stars is nearly uniform this supposition may 
 not lead us into serious error, the case will be entirely differ- 
 ent where we have to deal with irregular masses of stars, and 
 especially where our telescopes penetrate to the boundary of 
 the stellar system. In the latter case we cannot possibly dis- 
 tingnish between small stars lying within the boundary and 
 larger ones scattered outside of it, and Struve’s gradual thin- 
 ning-out of the stars may be entirely accounted for by great 
 diversities in the absolute brightness of the stars. 
 
 Among recent researches on this subject, those of Mr. R. 
 A. Proctor are entitled to consideration, from being founded 
 on facts which were not fully known or understood by the 
 investigators whom we have mentioned. The strongest point 
 which he makes is that all views of the arrangement of the 
 stellar system founded upon the theory that the stars are 
 either of similar intrinsic brightness, or approach an equality 
 of distribution in different regions, are entirely illusory. He 
 cites the phenomena of star-drift, described in the last chap- 
 ter,as proving that stars which had been supposed widely sep- 
 arated are really agglomerated into systems; and claims that — 
 the Milky Way may be a collection of such systems, having 
 nothing like the extent assigned it by Herschel. 
 
 How far the considerations brought forward by Mr. Proc- 
 tor should make us modify the views of the subject hitherto 
 held, cannot be determined without further observations on the 
 clustering of stars of different magnitudes. We may, howev- 
 er, safely concede that there is a greater tendency among the 
 stars to be collected into groups than was formerly supposed. 
 A curious result of Mr. J. M. Wilson, of Rugby, England, re- 
 specting the orbits of some binary stars, throws light on this 
 tendency. It was found by Struve that although the great 
 common proper motion of the pair of stars 61 Cygni, cele- 
 brated for the determinations of their parallax, was such as to 
 leave no reasonable doubt that they were physically connect- 
 ed, yet not the slightest deviation in their courses, arising 
 
RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 489 
 
 from their mutual attraction, could be detected. Mr. Wilson 
 has recently confirmed this result by an examination of the 
 whole series of measures on this pair from 1753 to 1874, 
 which do not show the slightest deviation, but. seem to indi- 
 cate that each star of the pair is going on its course indepen- 
 dently of the other. But, as just stated, they move too nearly 
 together to permit of the belief that they are really indepen- 
 dent. The only conclusion open to us is that each of them de- 
 scribes an immense orbit around their common centre of gray- 
 ity, an orbit which may be several degrees in apparent diam- 
 eter, and in which the time of revolution is counted by thou- 
 sands of years. Two thousand years hence they will be so 
 far apart that no connection between them would be sus- 
 pected. 
 
 It is a question whether we have not another instance of 
 the same kind in the double star Castor, or a Geminorum. 
 Mr. Wilson finds the orbit of this binary to be apparently 
 hyperbolic, a state of things which would indicate that the 
 two stars had no physical connection whatever, but that, in 
 pursuing their courses through space, they chanced to come 
 so close together that they were brought for a while within 
 each other’s sphere of attraction. If this be the case, they 
 will gradually separate forever, like two ships meeting on the 
 ocean and parting again. We remark that the course of each 
 star will then be very different from what it would have 
 been if they had not met. We cannot, however, accept the 
 hyperbolic orbit of Mr. Wilson as an established fact, because 
 the case is one in which it is very difficult to distinguish be- 
 tween a large and elongated elliptic orbit and a hyperbolic 
 orbit. The common proper motion of the two objects is such 
 as to lead to the belief that they constitute a pair, the compo- 
 nents of which separate to a great distance. 
 
 Now, these discoveries of pairs of stars moving around a 
 common centre of gravity, in orbits of immense extent, sug- 
 gest the probability that there exist in the heavens great num- 
 bers of pairs, clusters, and systems of this sort, the members 
 of which are so widely separated that they have never been 
 
490 THE STELLAR UNIVERSE. 
 
 suspected to belong together, and the widely scattered groups 
 having a common proper motion may very well be systems of 
 this kind. 
 
 § 3. Probable Arrangement of the Visible Universe. 
 
 The preceding description of the views held by several gen- 
 erations of profound thinkers and observers respecting the 
 arrangement of the visible universe furnishes an example of 
 what we may call the evolution of scientific knowledge. Of 
 no one of the great men whom we have mentioned can it be 
 said that his views were absolutely and unqualifiedly errone- 
 ous, and of none can it be said that he reached the entire 
 truth. Their attempts to solve the mystery which they saw 
 before them were like those of a spectator to make out the ex- 
 act structure of a great building which he sees at a distance 
 in the dim twilight. He first sees that the building is really 
 there, and sketches out what he believes to be its outlines. As 
 the light increases, he finds that his first outline bears but a 
 rude resemblance to what now seems to be the real form, and 
 he corrects it accordingly. In his first attempts to fill in the 
 columns, pilasters, windows, and doors, he mistakes the darker 
 shades between the columns for windows, other lighter shad- 
 ows for doors, and the pilasters for columns. Notwithstand- 
 ing such mistakes, his representation is to a certain extent cor- 
 rect, and he will seldom fall into egregious error. The suc- 
 cessive improvements in his sketch, from the first rough out- 
 line to the finished picture, do not consist in effacing at each 
 step everything he has done, but in correcting it, and filling in 
 the details. 
 
 The progress of our knowledge of nature is generally of this 
 character. But in the case now before us, so great is the dis- 
 tance, so dim the light, and so slender our ideas of the princi- 
 ples on which the vast fabric is constructed, that we cannot 
 pass beyond a few rough outlines. Still there are a few feat- 
 ures which we can describe with a near approach to certainty, 
 and others respecting which, though our knowledge is some- 
 what vague, we can reach a greater or less degree of proba- 
 
PROBABLE ARRANGEMENT OF THE VISIBLE UNIVERSE. 491 
 
 bility. We may include these under the following seven 
 heads: 
 
 1st. Leaving the nebule out of consideration, and confining 
 ourselves to the stellar system, we may say, with moral cer- 
 tainty, that the great mass of the stars which compose this 
 system are spread out on all sides, in or near a widely extend- 
 ed plane passing through the Milky Way. In other words, 
 the large majority of the stars which we can see with the tele- 
 scope are contained in a space having the form of a round, flat 
 disk, the diameter of which is eight or ten times its thickness. 
 This was clearly seen by Kant, and has been confirmed by 
 Herschel and Struve. In fact, it forms the fundamental base 
 of the structures reared by these several investigators. When 
 Kant saw, in this arrangement, a resemblance to the solar 
 system, in which the planets all move round near one central 
 plane, he was correct, so far as he went. The space, then, in 
 which we find most of the stars to be contained is bounded 
 by two parallel planes forming the upper and lower surfaces 
 of the disk we have described, the distance apart of these 
 planes being a small fraction of their extent — probably less 
 than an eighth. 
 
 2d. Within the space we have described the stars are not 
 scattered uniformly, but are for the most part collected into 
 irregular clusters or masses, with comparatively vacant spaces 
 between them. These collections have generally no definite 
 boundaries, but run into each other by insensible gradations. 
 The number of stars in each collection may range from two 
 to many thousands; and larger masses are made up of smaller 
 ones in every proportion, much as the heavy clouds on a sum- 
 mer’s day are piled upon each other. 
 
 3d. Our sun, with its attendant planets, is situated near the 
 centre of the space we have described, so that we see nearly 
 the same number of stars in any two opposite quarters of the 
 heavens. 
 
 Ath. The six or seven thousand stars around us, which are 
 easily seen by the naked eye, are scattered in space with a 
 near approach to uniformity, the only exception being local 
 
492, THE STELLAR UNIVERSE. 
 
 clusters, the component stars of which are few in number and 
 pretty widely separated. Such are the Pleiades, Coma Bere- 
 nices, and perhaps the principal stars of many other constella- 
 tions, which are so widely separated that we do not see any 
 connection among them. 
 
 5th. The disk which we have described does not represent 
 the form of the stellar system, but only the limits within 
 which it is mostly contained. The absence of any definite 
 boundary, either to star clusters or the stellar system, and the 
 number of comparatively vacant regions here and there among 
 the clusters, prevent our assigning any more definite form to 
 the system than we could assign to a cloud of dust. The thin 
 and widely extended space in which the stars are most thickly 
 clustered may, however, be called the galactic region. 
 
 6th. On each side of the galactic region the stars are more 
 evenly and thinly scattered, but probably do not extend out to 
 a distance at all approaching the extent of the galactic region. 
 If they do extend out to an equal distance, they are very few 
 in number. It is, however, impossible to set any definite boun- 
 daries, not only from our ignorance of the exact distance of 
 the smallest stars we can see in the telescope, but because the 
 density of the stars probably diminishes very gradually as we 
 go out towards the boundary. 
 
 7th. On each side of the galactic and stellar region we have 
 a nebular region, in which we find few or no stars, but vast 
 numbers of nebule. The nebule diminish greatly in num- 
 ber as we approach the galactic region, only a very few being 
 found in that region. 
 
 The general arrangement of the stars and nebulee which we 
 have described is seen in Fig. 111, which shows what is prob- 
 ably the general aspect of a section of the visible universe per- 
 pendicular to the Milky Way. In the central part of the fig- 
 ure we have the galactic region, in which the stars are mostly 
 aggregated in large masses. Of the arrangement of these 
 masses nothing certain is known; they are, therefore, put in 
 nearly at random. Indeed, it is still an undecided question 
 whether the aggregations of stars which make up the Milky 
 
PROBABLE ARRANGEMENT OF THE VISIBLE UNIVERSE. 493 
 
 Way extend all the way across the diameter of the galactic 
 region, or whether they are arranged in the form of a ring, 
 with our sun and his surrounding stars in the centre of it. 
 In the latter case, the masses of stars near the centre should 
 be less strongly marked. This central region being that in 
 which our earth is situated, this uncertainty respecting the 
 density of stars in that region implies an uncertainty whether 
 
 FONEBULAE™ 
 
 “REGION. OF NEBUL 
 
 Fig. 111.—Probable arrangement of the stars and nebule visible with the telescope. In 
 the Galaxy the stars are not evenly scattered, but are agglomerated into clusters. 
 the stars visible with the naked eye are part of one of the 
 masses which make up the Galaxy, or whether we are in a 
 comparatively thin region. Although this question is still 
 unsolved, it is one which admits of an answer by telescopic 
 research. When we described Sir William Herschel’s ar- 
 rangement of the stars in concentric spheres, we saw that in 
 the more distant spheres the stars were vastly more dense 
 
494 THE STELLAR UNIVERSE. 
 
 around the galactic belt of each sphere than they were in 
 other parts of it. To answer the question which has been 
 presented, we must compare the densities of the stars at the 
 circumferences of these spheres with the density immediately 
 around us. In other words, the question is, Suppose a human 
 being could dart out in the direction of the Milky Way, and 
 pass through some of the masses of stars composing it, would 
 he find them thicker or thinner than they are in the visible 
 heavens around us ? 
 
 A question still left open is, whether all the celestial objects 
 visible with the telescope are included within the limits of the 
 three regions we have just indicated, or whether the whole 
 Galaxy, with everything which is included within its limits, 
 is simply one of a great number of widely scattered stellar 
 systems. Since any consideration of invisible galaxies and 
 systems would be entirely idle, the question may be reduced 
 to this: Are the most distant star clusters which the telescope 
 shows us situated within the limits of the stellar system or far 
 without them, a great vacant space intervening? ‘The latter 
 alternative is the popular one, first suggested by Kant, it be- 
 ing supposed that the most distant nebule constituted other 
 Milky Ways or stellar systems as extensive as our own. 
 
 Although the possibility that this view is correct cannot be 
 denied, yet the arrangement of the star clusters or resolvable 
 nebulze militates against it. We have shown that the major- 
 ity of the latter lie near the direction of the plane of the 
 Milky Way, comparatively few being seen near the perpen- 
 dicular direction. But if these objects were other galaxies, 
 far outside of the one which surrounds us, they would be as 
 likely to lie in one direction as in another, and the probabil- 
 ity against the great mass of them lying in one plane would 
 be very great. The most probable conclusion, therefore, is 
 that they constitute part of our stellar system. They may, in- 
 deed, be scattered around or outside of the extreme limits with- 
 in which single stars can be seen, but not at distances so great 
 that they should be considered as separate systems. The most 
 probable conclusion, in the present state of our knowledge, 
 
DO THE STARS REALLY FORM A SYSTEM? 495 
 
 seems to be that the scheme shown in Fig. 111 includes the 
 whole visible universe. 
 
 The differences of opinion which now exist respecting the 
 probable arrangement and distance of the stars arise mainly 
 from our uncertainty as to what is the probable range of ab- 
 solute magnitude of the stars, a subject to which we have al- 
 ready several times alluded. The discovery of the parallax 
 of several stars has enabled us not only to form some idea of 
 this question by comparing the brilliancy of these stars with 
 their known distances, but it has enabled us to answer the in- 
 teresting question, How does our sun compare with these stars 
 in brightness? The curious result of this inquiry is, that our 
 sun is really a star less than the average, which. would mod- 
 estly twinkle among the smaller of its fellows if removed 
 to the distance from us at which they are placed. Zéllner 
 found, by comparing the light of the sun with that of Capella, 
 or a Aurigee, that it would have to be removed to 286,000 
 times its present distance to appear equally bright with that 
 star, which we may take as an average star of the first magni- 
 tude. But the greater number of the stars of this magnitude 
 are situated at four or five times this distance; so that if our 
 sun were placed at their average distance, it would probably 
 not exceed the third or fourth magnitude. Still, it would by 
 no means belong among the smallest stars of all, because we 
 do find stars with a measurable parallax which are only of 
 the fifth, sixth, or even the seventh magnitude. Altogether, it 
 appears that the range of absolute brilliancy among the stars 
 extends through eight or ten magnitudes, and that the largest 
 ones emit several thousand times as much light as the small- 
 est. It is this range of magnitude which really forms the 
 greatest obstacle in the way of determining the arrangement 
 of the stars in space. | 
 
 § 4. Do the Stars really form a System ? 
 
 We have described the sublime ideas of Kant and Lam- 
 bert, who, seeing the bodies of our solar system fitted to go 
 
 through their revolutions without permanent change during 
 33 
 
496 THE STELLAR UNIVERSE. 
 
 an indefinite period of time, reasoned by analogy that the 
 stellar universe was constructed on the same general plan, 
 and that each star had its appointed orbit, round which it 
 would run its course during endless ages. This speculation 
 was not followed up by Herschel and Struve, who, proceeding 
 on a more strictly scientific plan, found it necessary to learn 
 how the stars are now situated before attempting to decide 
 in what kinds of orbits they are moving. In the absence of 
 exact knowledge respecting the structure and extent of the 
 stellar systera, it is impossible to say with certainty what will 
 be the state of that system after the lapse of the millions of 
 years which would be necessary for the stars to perform a 
 revolution around one centre. But, as in describing the con- 
 stitution of the stellar system, we found certain features on 
 which we could pronounce with a high degree of probability, 
 so, in respect to the motions and orbits of the stars, there are 
 some propositions which we may sustain with a near approach 
 to certainty. 
 
 Stability of the System.—We may first assert, with a high de- 
 gree of probability, that the stars do not form a stable system 
 in the sense in which we say that the solar system is stable. 
 By a stable system we mean one in which each star moves 
 round and round in an unchanging orbit, every revolution 
 bringing it back to its starting-point, so that the system as a 
 whole shall retain the same general form, dimensions, and 
 arrangement during innumerable revolutions of the bodies 
 which compose it. It is almost necessary to the existence of 
 such a system that it have a great central body, the mass of 
 which should be at least vastly greater than that of the indi- 
 vidual bodies which revolve around it. At least, such a cen- 
 tral body could be dispensed with only by the separate stars 
 having a regularity of motion and arrangement which cer- 
 tainly does not exist in the stellar system as we actually see 
 it. The question, then, reduces itself to this: Are there any 
 immense attracting centres around which the separate collec- 
 tions of stars revolve; or is there any centre around which all 
 the stars which compose the visible universe revolve? In all 
 
DO THE STARS REALLY FORM A SYSTEM? 497 
 
 human probability, these questions must be answered in the 
 negative. All analogy leads us to believe that if there were 
 any such central masses, they would be not only larger than 
 the other stars, but brighter in a yet greater proportion. It 
 is, of course, possible to conceive of immense dark bodies, 
 such as Lambert. supposed to exist, but we cannot but believe 
 the existence of such bodies to be very improbable. Al- 
 though there is, as we have seen, great diversity among the 
 stars in respect to their magnitudes, there are none of them 
 which seem to have that commanding preéminence above 
 their fellows which the sun presents above the planets which 
 surround him. 
 
 But the most conclusive proof that the stars do not revolve 
 round definite attracting centres is found in the variety and 
 irregularity of their proper motions, which we have already 
 described. We have shown (1) that when the motions of 
 great numbers of stars are averaged, there is found a general 
 preponderance of motions from the constellation Hercules, 
 which is supposed to be due to a motion of our sun with his 
 attendant planets in that direction; and (2) that when the 
 motions of stars in the same region are compared, there is 
 often found to be a certain resemblance among them. But 
 this tendency towards a regular law affects only large masses 
 of stars, and does not imply any such regularity in the mo- 
 tions of individual stars as would be apparent if they moved 
 in regular circular orbits, as the planets move round the sun. 
 The motion of each individual star is generally so entirely 
 different from that of its fellows as seemingly to preclude all 
 reasonable probability that these bodies are revolving in defi- 
 nite orbits around great centres of attraction. 
 
 The most extraordinary instances of the irregularities of 
 which we speak are found in the stars of: unusually rapid 
 proper motion, which are moving forward at such a rate that 
 the gravitation of all the known stars cannot stop them until 
 they shall have passed through and beyond the visible uni- 
 verse. ‘The most remarkable of these, so far as we know, is 
 Groombridge 1830, it having the largest apparent proper mo- 
 
498 THE STELLAR UNIVERSE. 
 
 tion of any known star. The most careful determinations of 
 its parallax seem to show that its distance is so immense that 
 the parallax is only about a tenth of a second; that is, a line 
 drawn from the sun to the earth would subtend an angle of 
 only a tenth of a second when viewed from this star. But 
 the apparent motion of the star, as we actually see it, is more 
 than seven seconds per annum, or seventy times its parallax. 
 It follows that the star moves over a space of more than sev- 
 enty times the distance of the sun from us in the space of a 
 year. If, as is likely, the motion of the star is oblique to the 
 line in which we see it, its actual velocity must be yet greater. 
 Leaving this out of account, we see that the star would pass 
 from the earth to the sun in about five days, so that its veloci- 
 ty probably exceeds two hundred miles per second. 
 
 To understand what this enormous velocity may imply, we 
 must advert to the theorem of gravitational astronomy that 
 the velocity which a body can acquire by falling towards an 
 attracting centre is, at each point of its path, limited. or ex- 
 ample, a body falling from an infinite distance to the earth’s 
 surface, and acted on by the attraction of the earth alone, would 
 acquire a velocity of only about seven miles per second. Vice 
 versa, a body projected from the earth with this velocity would 
 never be stopped by the earth’s attraction alone, but’ would 
 describe an elliptic orbit round the sun. If the velocity ex- 
 ceeded twenty-seven miles per second, the attraction of the sun 
 himself could never stop it, and it would wander forever 
 through the stellar spaces. The greater the distance from the 
 sun at which the body is started, the less the velocity which 
 will thus carry it forever away from the sun. At the orbit of 
 Uranus the required velocity would be only six miles per sec- 
 ond; at Neptune, it would be less than five miles per second ; 
 half-way between the sun and a Centauri, it would be a mile 
 in twelve seconds, or a fourth the speed of a cannon-ball. If 
 we knew the masses of each of the stars, and their arrange- 
 ment in space, it would be easy to compute this limiting ve- 
 locity for a body falling from an infinite distance to any point 
 of the stellar system. If the motion of a star were found to 
 
DO THE STARS REALLY FORM A SYSTEM? 499 
 
 exceed this limit, it would show that the star did not belong 
 to the visible universe at all, but was only a visitor flying 
 on a course through infinite space at such a rate that the 
 combined attraction of all the stars could never stop it. 
 
 Let us now see how the case may stand with our flying star, 
 and what relation its velocity may bear to the probable attrac- 
 tion of all the stars which exist within the range of the tel- 
 escope. The number of stars actually visible with the most 
 powerful telescopes probably falls short of fifty millions; but, 
 to take a probable outside limit, we shall suppose that within 
 the regions occupied by the farthest stars which the telescope 
 will show, there are fifty millions more, so small that we cannot 
 see them, making one hundred millions in all. «We shall also 
 suppose that these stars have, on the average, five times the 
 mass of the sun, and that they are spread out in a layer across 
 the diameter of which light would require thirty thousand years 
 to pass. Then,a mathematical computation of the attractive 
 power exerted by such a system of masses shows that a body 
 falling from an infinite distance to the centre of the system 
 would acquire a velocity of twenty-five miles per second. 
 Vice versa, a body projected from the centre of such a system 
 with a velocity of more than twenty-five miles per second in 
 any direction whatever would not only pass entirely through 
 it, but would fly off into infinite space, never to return. If the 
 body were anywhere else than in the centre of the system, the 
 velocity necessary to carry it away would be less than the 
 limit just given. But this calculated limit is only one-eighth 
 the probable velocity of 1880 Groombridge. The force re- - 
 quired to impress a given velocity on a body falling through 
 any distance is proportional to the square of the velocity, four _ 
 times the force being required to give double the velocity, nine 
 times to increase it threefold, and so on. To give eight times 
 the velocity would require sixty-four times the attracting mass. 
 If, then, the star in question belongs to our stellar system, the 
 masses or extent of that system must be many times greater 
 than telescopic observation and astronomical research indicate. 
 We may place the dilemma in a concise form, as follows: 
 
500 THE STELLAR UNIVERSE. 
 
 Either the bodies which compose our universe are vastly 
 more massive and numerous than telescopic examination 
 seems to indicate, or 1830 Groombridge is a runaway star, 
 flying on a boundless course through infinite space with such 
 momentum that the attraction of all the bodies of the universe 
 can never stop it. 
 
 Which of these is the more probable alternative we cannot 
 pretend to say. That the star can neither be stopped, nor bent 
 far from its course until it has passed the extreme limit to 
 which the telescope has ever penetrated, we may consider 
 reasonably certain. ‘To do this will require two or three mill- 
 ions of years. Whether it will then be acted on by attractive 
 forces of which science’ has no knowledge, and thus carried 
 back to where it started, or whether it will continue straight 
 forward forever, it is anata to say. 
 
 Much the same dilemma may be applied to the past uiseeee 
 of this body. If the velocity of two hundred miles or more 
 per second with which it is moving exceeds any that could be 
 produced by the attraction of all the other bodies in the uni- 
 verse, then it must have been flying forward through space 
 from the beginning, and, having come from an infinite dis- 
 tance, must. be now passing dara our system for the first 
 and only time. 
 
 It may be asked whether, in Lambert’s hypothesis of im- 
 mense attracting bodies, invisible on account of their being 
 dark, we have not at once the centres required to give general 
 stability to the stellar system, and to keep the star of which 
 we have spoken in some regular orbit. We answer,no. To 
 secure such stability, stars equally distant from the attracting 
 centres must move with nearly the same velocity. An at- 
 tracting centre sufficiently powerful to bring a body moving 
 two hundred miles per second into a regular orbit would 
 draw most of the other stars moving with small velocities into 
 its immediate neighborhood, and thus subvert the system. We 
 thus meet the double difficulty that we have good reason to 
 doubt the existence of these opaque, dark bodies, and that if 
 they did exist, they would not fulfil our requirements. — 
 
DO THE STARS REALLY FORM A SYSTEM? 501 
 
 The general result of our inquiry is that the stellar uni- 
 verse does not seem to possess that form of unvarying stabil- 
 ity which we see in the solar system, and that the stars move 
 in irregular courses depending on their situation in respect 
 to the surrounding stars, and probably changing as this situa- 
 tion changes. If there were no motion at all among the stars, 
 they would all fall to a common centre, and universal ruin 
 would be the result. But the motions which we actually see 
 are sufficient to prevent this catastrophe, by supplying each 
 star with a reserve of force which will generally keep it from 
 actual collision with its neighbors. If, then, any one star 
 does fall towards any attracting centre, the velocity which it 
 acquires by this fall will carry it away again ‘in some other 
 direction, and thus it may keep up a continuous dance, under 
 the influence of ever-varying forces, as long as the universe 
 shall exist under its present form. 
 
 To those who have been enraptured with the sublime specu- 
 lations of Kant and Lambert, this may seem an unsatisfactory 
 conclusion; while to those who look upon the material uni- 
 verse as something made to last forever, it may seem improba- 
 ble. But when we consider the immense periods which would 
 be required for the mutual gravitation of the stars to effect 
 any great change in the stellar system, we may be led to alter 
 such views as these. We have shown that tens of thousands 
 of years would be required to make any great change in the 
 arrangement of the stars which we see with the naked eye. 
 The time required for all the stars visible with the telescope 
 to fall together by their own attraction is to be counted by 
 millions of years. If the universe had existed in its present 
 state from eternity, and were to exist forever, the immensity 
 of these periods would not be at all to the point, because a 
 million of years is no more a part of eternity than a single 
 day. But all modern science seems to point to the finite 
 duration of our system in its present form, and to carry us 
 back to the time when neither sun nor planet existed, save as 
 a mass of glowing gas. How far back that was, it cannot tell 
 us with certainty; it can only say that the period is counted 
 
502 THE STELLAR UNIVERSE. 
 
 by: millions of years, but probably not by hundreds of mill- 
 ions. It also points forward to the time when the sun and 
 stars shall fade away, and nature shall be enshrouded in dark- 
 ness and death, unless some power now unseen shail uphold 
 or restore her. The time required for this catastrophe cannot 
 be calculated; but it is probably not so great that the stellar 
 system can, in the mean time, be subverted by the mutual 
 gravitation of its members. 
 
 It would thus appear as if those nicely arranged adjust- 
 ments which secure stability and uniformity of motion are 
 not found where they are not necessary to secure the system 
 from subversion during the time it is to last, much as the 
 wheel of an engine which is to make but two or three revo- 
 lutions while the engine endures need not be adjusted to 
 make thousands of revolutions. ‘The bodies which form our 
 solar system are, on the other hand, like wheels which have 
 to make millions of revolutions before they stop. Unless there 
 is a constant balance between the opposing forces under the 
 influence of which they move, there must be a disarrangement 
 of the movement long before the engine wears out. Thus, 
 although the present arrangement of the stars may be studied 
 without any reference to their origin, yet, when we seek to 
 penetrate the laws of their motion, and foresee the changes — 
 of state to which their motions may give rise, we are brought 
 to face the question of their duration, and hence of their be- 
 ginning and end. 
 
THE COSMOGONY. 503 
 
 CHAPTER III. 
 
 THE COSMOGONY. 
 
 Tue idea that the world has not endured forever in the 
 form in which we now see it, but that there was a time when 
 it either did not exist at all, or existed only as a mass “ with- 
 out form, and void,’ is one which we find to have been always 
 held by mankind. The “chaos” of the Greeks—the rude and 
 formless materials, subject to no law, out of which all things 
 were formed by the creative power—corresponds in a striking 
 manner to the nebulous masses of modern astronomy. These 
 old ideas of chaos were expressed by Milton in the second 
 book of “ Paradise Lost,’ before such a thing as a nebula 
 could be said to be known, and he would be a bold astrono- 
 mer who, in giving a description of the primeval nebulous 
 mass, would attempt to improve on the great poet: 
 
 ‘a dark, 
 Tllimitable ocean, without bound, 
 Without dimension, where length, breadth, and height, 
 And time and place, are lost; where eldest Night 
 And Chaos, ancestors of Nature, hold 
 Eternal anarchy amidst the noise 
 Of endless wars, and by confusion stand : 
 For hot, cold, moist, and dry, four champions fierce, 
 Strive here for mastery, and to battle bring 
 Their embryon atoms. 
 
 * * * * * * * 
 
 Chaos umpire sits, 
 
 And by decision more embroils the fray 
 By which he reigns: next him, high arbiter, 
 Chance governs all. Into this wild abyss 
 The womb of Nature, and perhaps her grave, 
 Of neither sea, nor shore, nor air, nor fire, 
 But all these in their pregnant causes mixed 
 Confusedly, and which thus must ever fight, 
 
504 THE STELLAR UNIVERSE. 
 
 Unless the almighty Maker them ordain 
 
 His dark materials to create more worlds— 
 * * * * * * 
 
 Some tumultuous cloud 
 Instinet with fire and nitre.” 
 
 If we classify men’s ideas of the cosmogony according to 
 the data on which they are founded, we shall find them divis- 
 ible into three classes. The first class comprises those formed 
 before the discovery of the theory of gravitation, and which, 
 for this reason, however correct they might have been, had no 
 really scientific foundation. ‘The second are those founded on 
 the doctrine of gravitation, but without a knowledge of the 
 modern theory of the conservation of force; while the third 
 are founded on this theory. It must not be supposed, how- 
 ever, that the ideas of the last-mentioned class are antagonistic 
 to those of the other classes. Kant and Laplace founded the 
 nebular hypothesis on the theory of gravitation alone, the con- 
 servation of force being then entirely unknown. It was, there- 
 fore, incomplete as it came from their hands, but not neces- 
 sarily erroneous in its fundamental conceptions. 
 
 The consideration of the ancient ideas of the origin of the 
 world belongs rather to the history of philosophy than to as- 
 tronomy, for the reason that they were of necessity purely 
 speculative, and reflected rather the mode of thought of the 
 minds in which they originated than any definite system of 
 investigating the operations of nature. The Hindoo concep- 
 tion of Brahma sitting in meditation on a lotus-leaf through 
 long ages, and then producing a golden egg as large as the 
 universe, out of which the latter was slowly evolved, is not 
 founded on even the crudest observation, but is purely a result 
 of the speculative tendency of the Hindoo mind. The Jew- 
 ish cosmogony is the expression of the monotheistic views of 
 that people, and of the identity of their tutelary divinity with 
 the maker of heaven and earth. Hipparchus and Ptolemy 
 showed the scientific turn of their minds by confining them- 
 selves to the examination of the universe as it is, without mak- 
 ing any vain effort to trace its origin. 
 
THE MODERN NEBULAR HYPOTHESIS. 505 
 
 Though the systems to which we refer are essentially un- 
 scientific, it must not be supposed that they were all errone- 
 ous in their results, or that they belong exclusively to ancient 
 times. Thus, the views of Swedenborg, though they belong 
 to the class in question, are remarkably in accordance with 
 recent views of the subject as regards the actual changes which 
 took place during the formation of the planets. A great deal 
 of what is written on the subject at present is to be included 
 in this same ancient class, as being the production of men who 
 are not mathematicians or working astronomers, and who, 
 therefore, cannot judge whether their views are in accordance 
 with mechanical laws and with the facts of observation. Pass- 
 ing over all speculation of ‘this sort, no matter when or by 
 whom produced, we shall consider in historical order the works 
 of those who have actually contributed to placing the laws of 
 cosmogony on a scientific foundation. 
 
 $1. The Modern Nebular Hypothesis. 
 
 From a purely scientific point of view, Kant has probably 
 the best right to be regarded as the founder of the nebular 
 hypothesis, because he based it on an examination of the actual 
 features of the solar system, and on the Newtonian doctrine 
 of the mutual gravitation of all matter. His reasoning is 
 briefly this: Examining the solar system, we find two remark- 
 able features presented to our consideration. One is that six 
 planets and nine satellites (the entire number then known) 
 move around the sun in circles, not only in the same direction 
 in which the sun himself revolves on his axis, but very nearly 
 in the same plane. This common feature of the motion of 
 so many bodies could not, by any reasonable possibility, have 
 been a result of chance; we are, therefore, forced to believe 
 that it must be the result of some common cause originally 
 acting on all the planets. 
 
 On the other hand, when we consider the spaces in which 
 the planets move, we find them entirely void, or as good as 
 void; for if there is any matter in them, it is so rare as to be 
 without effect on the planetary motions. There is, therefore, 
 
506 THE STELLAR UNIVERSE. 
 
 no: material connection now existing between the planets 
 through which they might have been forced to take up a com- 
 mon direction of motion. How, then, are we to reconcile this 
 common motion with the absence of all material connection ? 
 The most natural way is to suppose that there was once some 
 such connection which brought about the uniformity of mo- 
 tion which we observe; that the materials of which the plan- 
 ets are formed once filled the whole space between them. “I 
 assume,” says Kant, “that all the materials out of which the 
 bodies of our solar system were formed were, in the begin- 
 ning of things, resolved in their original elements, and filled all 
 the space of the universe in which these bodies now move.” 
 There was no formation in this chaos, the formation of sepa- 
 rate bodies by the mutual gravitation of parts of the mass be- 
 ing a later occurrence. But, naturally, some parts of the mass 
 would be more dense than others, and would thus gather 
 around them the rare matter which filled the intervening 
 spaces. The larger collections thus formed would draw the 
 smaller ones into them, and this process would continue until 
 a few round bodies had taken the place of the original chaotic 
 mass. 
 
 If we examine the result of this hypothesis by the light of 
 modern science, we shall readily see that all the bodies thus 
 formed would be drawn to a common centre, and thus we 
 should have, not a collection of bodies like the solar system, 
 but a single sun formed by the combination of them all. In 
 attempting to show how the smaller masses would be led to 
 circulate around the larger ones in circular orbits, Kant’s rea- 
 soning ceases to be satisfactory. He seems to think that the 
 motion of rotation could be produced indirectly by the repul- 
 sive forces acting among the rarer masses of the condensing 
 matter, which would give rise to a whirling motion. But the 
 laws of mechanics show that the sum total of rotary motion in 
 a system can never be increased or diminished by the mutual 
 action of its separate parts,so that the present rotary motions 
 of the sun and planets must be the equivalent of that which 
 they had from the beginning. 
 
THE MODERN NEBULAR HYPOTHESIS. 50T 
 
 Herschel’s Hypothesis. —It is remarkable that the idea of 
 the gradual transmutation of nebulee into stars seems to have 
 been suggested to Herschel, not by the relations of the solar 
 system, but by his examinations of the nebule themselves. 
 Many of these bodies seemed to him to be composed of im- 
 mense masses of phosphorescent vapor, and he conceived that 
 these masses must be gradually condensing, each around its 
 own centre, or around those parts where it is most dense, until 
 it should be transmuted into a star or a cluster of stars. On 
 classifying the numerous nebule which he discovered, it 
 seemed to him that he could see each stage of this operation 
 going on before his eyes. There were the large, faint, diffused 
 nebula, in which the process of condensation seemed to have 
 hardly begun; the smaller but brighter ones, which had been 
 so far condensed that the central parts would soon begin to 
 form into stars; yet others, in which stars had actually begun 
 to form ; and, finally, star clusters in which the condensation 
 was complete. As Laplace observes, Herschel followed the 
 condensation of the nebule in much the same way that we 
 can, in a forest, study the growth of the trees by comparing 
 those of the different ages which the forest contains at the 
 same time. The spectroscopic revelations of the gaseous nat- 
 ure of the true nebule tend to strengthen these views of Her- 
 schel, and to confirm us in the opinion that these masses will 
 all at some time condense into stars or clusters of stars. 
 
 Laplace's View of the Nebular Hypothesis—Laplace was led 
 to the nebular hypothesis by considerations very similar to 
 those presented by Kant a few years before. The remarkable 
 uniformity among the directions of rotation of the planets be- 
 ing something which could not have been the result of chance, 
 he sought to investigate its probable cause. This cause, he 
 thought, could be nothing else than the atmosphere of the sun, 
 which once extended so far out as to fill all the space now oc- 
 cupied by the planets. He does not, like Kant, begin with a 
 chaos, out of which order was slowly evolved by the play of 
 attractive and repulsive forces, but with the sun, surrounded 
 by this immense fiery atmosphere. Knowing, from mechan- 
 
508 _ THE STELLAR UNIVERSE. 
 
 ical laws, that the sum total of rotary motion now seen in the 
 planetary system must have been there from the beginning, he 
 conceives the immense vaporous mass forming the sun and 
 his atmosphere to have had a slow rotation on its axis. The 
 mass being intensely hot would slowly cool off, and as it did so 
 would contract towards the centre. As it contracted, its ve- 
 locity of rotation would, in obedience to one of the funda- 
 mental laws of mechanics, constantly increase, so that a time 
 would arrive when, at the outer boundary of the mass, the cen- 
 trifugal force due to the rotation would counterbalance the at- 
 tractive force of the central mass. Then, those outer portions 
 would be left behind as a revolving ring, while the next inner 
 portions would continue to contract until, at their boundary, 
 the centrifugal and attractive forces would be again balanced, 
 when a second ring would be left behind, and so on. Thus, 
 instead of a continuous atmosphere, the sun would be sur- 
 rounded by a series of concentric revolving rings of vapor. 
 Now, how would these rings of vapor behave? As they 
 cooled off, their denser materials would condense first, and 
 thus the ring would be composed of a mixed mass, partly solid 
 and partly vapcrous, the quantity of solid matter constantly 
 increasing, and that of vapor diminishing. If the ring were 
 perfectly uniform, this condensing process would take place 
 equally all around it, and the ring would thus be broken up 
 into a group of small planets, like that which we see between 
 Mars and Jupiter. But we should expect that in general 
 some portions of the ring would be much denser than others, 
 and the denser portions would gradually attract the rarer por- 
 tions around it until, instead of a ring, we should have a sin- 
 gle mass, composed of a nearly solid centre surrounded by an 
 immense atmosphere of fiery vapor. This condensation of the 
 ring of vapor around a single point would have produced no 
 change in the amount of rotary motion originally existing in 
 the ring ; the planet, surrounded by its fiery atmosphere, would 
 therefore be in rotation, and would be, in miniature, a repro- 
 duction of the case of the sun surrounded by his atmosphere 
 with which we set out. In the same way that the solar at- 
 
THE MODERN NEBULAR HYPOTHESIS. 509 
 
 mosphere formed itself first into rings, and then these rings 
 condensed into planets, so, if the planetary atmospheres were 
 sufficiently extensive, they would form themselves into rings, 
 and these rings would condense into satellites. : In the case of 
 Saturn, however, one of the rings was so perfectly uniform 
 that there could be no denser portion to draw the rest of 
 the ring around it, and thus we have the well-known rings 
 of Saturn. 
 
 If, among the materials of the solar atmosphere, there were 
 any so rare and volatile that they would not unite themselves 
 either into a ring or around a planet, they would continue to 
 revolve around the sun, presenting an appearance like that 
 of the zodiacal light. They would offer no appreciable re- 
 sistance to the motion of the planets, not only on account of 
 their extreme rarity, but because their motion would be the 
 same as that of the planets which move among them. 
 
 Such is the celebrated nebular hypothesis of Laplace which 
 has given rise to so much discussion. It commences, not with 
 a purely nebulous mass, but with the sun surrounded by a 
 fiery atmosphere, out of which the planets were formed. On 
 this theory the sun is older than the planets; otherwise it 
 would have been impossible to account for the slow rotation 
 of the sun upon his axis. If his body had been formed of ho- 
 mogeneous matter extending out uniformly to near the orbit 
 of Mercury, it would not have condensed into a globe revolv- 
 ing on its axis in twenty-five days, but into a flat, almost lens- 
 shaped, body, which would have been kept from forming a 
 sphere by the centrifugal force. But the denser materials be- 
 ing condensed first, perhaps into such a body as we described, 
 the friction of the uncondensed atmosphere would have di- 
 minished the rotation of the sun, the rotating energy which he 
 lost being communicated to the embryo planets and throwing 
 them farther away. 
 
 In accordance with the hypothesis of Laplace, it has al- 
 ways been supposed that the outer planets were formed first. 
 There is, however, a weak point in Laplace’s theory of the for- 
 
 mation of rings. He supposed that when the centrifugal and 
 
510 THE STELLAR UNIVERSE. 
 
 centripetal forces balanced each other at the outer limit of 
 the revolving mass, the outer portions were separated from the 
 rest, which continued to drop towards the centre. If the plan- 
 etary rings were formed in this way, then, after each ring was 
 thrown off, the atmosphere must have condensed to nearly 
 half its diameter before another would have been thrown off, 
 because we see that each planet is, on the whole, nearly twice 
 as far as the one next within it. But there being no cohe- 
 sion between particles of vapor, such throwing-off of immense 
 masses of the outside portions of the revolving mass was im- 
 possible. The moment the forces balanced, the outer portions 
 of the mass would, indeed, cease to drop towards the sun, and 
 would partially separate from the portions next to it; then 
 these would separate next, and so on; that is, there would be 
 a constant dropping-off of matter from the outer portions, so 
 that, instead of a series of rings, there would have been a flat 
 disk formed of an infinite number of concentrating rings all 
 joined together. 
 
 If we examine the subject more closely, we shall see that 
 the whole reasoning by which it is supposed that the inner 
 portions of the mass would drop away from the outer ones 
 needs important modifications. In its primeval state, when it 
 extended far beyond the present confines of the solar system, 
 the rare nebulous atmosphere must have been nearly spherical. 
 As it gradually contracted, and the effect of centrifugal force 
 thus became more marked, it would have assnmed the form 
 of an oblate spheroid. When the contraction had gone so 
 far that the centrifugal and attracting forces nearly balanced 
 each other at the outer equatorial limit of the mass, the result 
 would have been that contraction in the direction of the equa- 
 tor would cease entirely,and be confined to the polar regions, 
 each particle dropping, not towards the sun, but towards the 
 plane of the solar equator. Thus, we should have a constant 
 flattening of the spheroidal atmosphere until it was reduced 
 to a thin flat disk. This disk might then separate itself into 
 rings, which would form planets in much the same way that 
 Laplace supposed. But there would probably be no marked 
 
PROGRESSIVE CHANGES IN‘ OUR SYSTEM. 511 
 
 difference in the age of the planets; quite likely the smaller 
 inner rings would condense into planets more rapidly than the 
 wide-spread outer ones. 
 
 Kant and Laplace may be said to have arrived at the neb- 
 ular hypothesis by reasoning forward, and showing how, by 
 supposing that the space now occupied by the solar system 
 was once filled by a chaotic or vaporous mass, from which the 
 planets were formed, the features presented by this system 
 could be accounted for. We are now to show how our mod- 
 ern science reaches a similar result by reasoning backward 
 from actions which we see going on before our eyes. 
 
 § 2. Progresswwe Changes in our System. 
 
 During the short period within which accurate observations 
 have been made, no actual permanent change has been ob- 
 served in our system. The earth, sun, and planets remain of 
 the same magnitude, and present the same appearance as al- 
 ways. The stars retain their brilliancy, and, for the most part, 
 the nebule their form. Not the slightest variation has been 
 detected in the amount of heat received from the sun, or in 
 the average number and extent of the spots on his surface. 
 And yet we have reason to believe that these things are all 
 changing, and that the time will come when the state of the 
 universe will be very different from that in which we now see 
 it. How a change may be inferred when none is actually vis- 
 ible may be shown by a simple example. 
 
 Suppose an inquiring person, walking in what he sup- 
 posed to be a deserted building, to find a clock running. If 
 he is ignorant of mechanics, he will see no reason why it may 
 not have been running just as he now sees it for an indefinite 
 period, and why the pendulum may not continue to vibrate, 
 and the hands to go through their revolutions, so long as the 
 fabric shall stand. He sees a continuous cycle of motions, and 
 can give no reason why they should not have been going on 
 since the clock was erected, and continue to go on till it shall 
 decay. But let him be instructed in the laws of mechanics, 
 
 and let him inquire into the force which keeps the hands and 
 34 
 
519 THE STELLAR UNIVERSE. 
 
 pendulum in motion. He will then find that this force is 
 transmitted to the pendulum through a train of wheels, each 
 of which moves many times slower than that in front of it, 
 and that the first wheel is acted upon by a weight, with which 
 it is connected by a cord. He can see a slow motion in the 
 wheel which acts on the pendulum, and perhaps in the one 
 next behind it, while during the short time he has for exami- 
 nation he can see no motion in the others. But if he sees how 
 the wheels act on each other, he will know that they must all 
 be in motion; and when he traces the motion back to the first 
 wheel, he sees that its motion must be kept up by a gradual 
 falling of the weight, though it seems to remain in the same 
 position. He can then say with entire certainty: “I do not see 
 this weight move, but I know it must be gradually approach- 
 ing the bottom, because I see a system of moving machinery, 
 the progress of which necessarily involves such a slow falling 
 of the weight. Knowing the number of teeth in each wheel 
 and pinion, | can compute how many inches it falls each day ; 
 and seeing how much room it has to fall in, I can tell how 
 many days it will take to reach the bottom. When this is 
 done, I see that the clock must stop, because it is only the fall- 
 ing of the weight that keeps its pendulum in motion. More- 
 over, I see that the weight must have been higher yesterday 
 than it is to-day, and yet higher the day before, so that I can 
 calculate its position backward as well as forward. By this 
 calculation I see backward to a time when the weight was 
 at the top of its course, higher than which it could not be. 
 Thus, although [ see no motion, I see with the eye of reason 
 that the weight is running through a certain course from the 
 top of the clock to the bottom; that some power must have 
 wound it up and started it; and that unless the same power 
 intervenes again, the weight must reach the bottom in a cer- 
 tain number of days, and the clock must then stop.” 
 
 The corresponding progressive change exhibited by the 
 operations of nature consists in a constant transformation of 
 motion into heat, and the constant loss of that heat by radia- 
 tion into space. As Sir William Thomson has expressed it, 
 
PROGRESSIVE CHANGES IN OUR SYSTEM. 513 
 
 a constant “dissipation of energy” is going on in nature. 
 We all know that the sun has been radiating heat into space 
 during the whole course of his existence. A small portion of 
 this heat strikes the earth, and supports life and motion on its 
 surface. All this portion of the sun’s heat, after performing 
 its function, is radiated off into space by the earth itself. The 
 portion of the sun’s radiant heat received by the earth is, how- 
 ever, comparatively insignificant, since our luminary radiates 
 in every direction eqnally, while the earth can receive only a 
 part represented by the ratio which its apparent angular mag- 
 nitude as seen from the sun bears to the whole celestial sphere, 
 which a simple calculation shows to be the ratio of 1 to 
 2,170,000,000. The stars radiate heat as well as the sun. 
 The heat received from them, when condensed in the focus of 
 a telescope, has been rendered sensible by the thermo-multi- 
 plier, and there is every reason to believe that stellar heat and 
 light bear the same proportion to each other that solar heat 
 and light do. Wherever there is white stellar light, there 
 must be stellar heat; and as we have found that the stars in 
 general give more light than the sun, we have reason to be- 
 lieve that they give more heat also. Thus we have a contin- 
 uous radiation from all the visible bodies of the universe, 
 which must have been going on from the beginning. 
 
 Until quite recently, it was not known that this radiation 
 involved the expenditure of a something necessarily limited in 
 supply, and, consequently, it was not known but that it might 
 continue forever without any loss of power on the part of the 
 sun and stars. But it is now known that heat cannot be pro- 
 duced except by the expenditure of force, actual or potential, 
 in some of its forms, and it is also known that the available 
 supply of force is necessarily limited. One of the best-estab- 
 lished doctrines of modern science is that force can no more 
 be produced from nothing than matter can: to find it so pro- 
 duced would be as complete a miracle as to see a globe created 
 from nothing before our eyes. Hence, this radiation cannot 
 go on forever unless the force expended in producing the heat 
 be returned to the sun in some form. That it is not now 
 
514 THE STELLAR UNIVERSE. 
 
 so. returned we may regard as morally certain. ‘There is no 
 known law of radiation, except that it proceeds out in straight 
 lines from the radiating centre. If the heat were returned 
 back to the sun from space, it would have to return to the 
 centre from all directions; the earth would then intercept as_ 
 much of the incoming as of the outgoing heat; that is, we 
 should receive as much heat from the sky at night as from 
 the sun by day. We know very well that this is not the case ; 
 indeed, there is no evidence of any heat at all reaching us from 
 space except what is radiated from the stars. 
 
 Since, then, the solar heat does not now return to the sun, 
 we have to inquire what becomes of it, and whether a com- 
 pensation may not at some time be aretied whereby all the 
 lost heat will be received back again. Now, if we trace the 
 radiated heat into the wilds of space, we may make three pos- 
 sible hypotheses respecting its ultimate destiny : 
 
 1. We may suppose it to be absolutely annihilated, just as it 
 was formerly supposed to be annihilated when it was lost by 
 friction. 
 
 2. It may continue its onward course through space forever. 
 
 . It may, through some agency of which we have no con- 
 Suen be ‘ibook gathered and returned to the sources 
 from which it emanated. 
 
 The first of these hypotheses is one which the scientific 
 thinkers of the present day would not regard as at all philo- 
 sophical. In our scientific philosophy, the doctrine that force 
 cannot be annihilated is coequal with that that it cannot be 
 created ; and the inductive processes on which the latter doc- 
 trine is founded are almost as unimpeachable as those from 
 which we conclude that matter cannot be created. At the 
 same time, it might be maintained that all these doctrines re- 
 specting the uncreatableness and indestructibility of matter 
 and force can have no proper foundation except induction 
 from experiment, and that the absolute truth of a doctrine 
 like this cannot be proved by induction. Especially may this 
 be claimed in respect of force. The most careful measures of 
 force which we can make under all circumstances show that it 
 
PROGRESSIVE CHANGES IN OUR SYSTEM. 51 
 
 Or 
 
 is subject to no sensible loss by either transmission or transfor- 
 mation. But this alone does not prove that it can be subject 
 to no loss in a passage through space requiring hundreds of 
 thousands or millions of years. There is also: this essential 
 difference between force and matter, that we conceive the lat- 
 ter as made up of individual parts which preserve their iden- 
 tity through all the changes of form which they undergo; 
 while force is something in which we do not conceive of any 
 such identity. Thus, when I allow a drop of water to evapo- 
 rate from my hand, I can in imagination trace each molecule 
 of water through the air, into the clouds, and down to the 
 earth again in some particular drop of rain, so that, if I only 
 had the means of actually tracing it, 1 could say, “ This cup 
 contains one, or two, or twenty of the identical molecules 
 which evaporated from my hand a week or a month ago.” 
 It is on this idea of the separate identity of each molecule 
 of matter that our opinion of the indestructibility of matter is 
 founded, because matter cannot be destroyed without destroy- 
 ing individual molecules, and any cause which could destroy a 
 single molecule might equally destroy all the molecules in the 
 universe. 
 
 But neither parts nor identity is possible in force. <A cer- 
 tain amount of heat may be expended in simply raising a 
 weight. Here heat has disappeared, and is replaced by a 
 mere change of position—something which cannot be con- 
 ceived as identical with it. If we let the weight drop, the 
 same amount of heat will be reproduced that was expended 
 in raising the weight; but, though equal in quantity, it can- 
 not be regarded as identical in the way that the water con- 
 densed from steam is identical with that which was evapo- 
 rated to form the steam. If measures showed it to be less 
 in quantity, we could not say there was a destruction of an 
 identical something which previously existed, as we could if 
 the condensed steam were not equal to the water evaporated. 
 Therefore, while the doctrine of the indestructibility of force 
 is universally received as a scientific principle, it can hardly 
 be claimed that induction has established its absolute correct- 
 
516 THE STELLAR UNIVERSE. 
 
 ness; and, in a case like the present, where we see something 
 which transcends scientific explanation, the failure of the 
 widest induction may be considered among the possible alter- 
 natives. 
 
 The second alternative—that the heat radiated from the 
 sun and stars continues its onward course through space for- 
 ever—is the one most in accord with our scientific concep- 
 tions. We actually receive heat from the most distant star 
 visible in our telescopes, and this heat has, according to the 
 best judgment we can form, been travelling thousands of 
 years without any loss whatever. From this point of view, 
 every radiation which has ever emanated from the earth or 
 the sun is still pursuing its course through the stellar spaces, 
 without any other diminution than that which arises from its 
 being spread over a wider area. A very striking presentation 
 of this view is, we believe, due to some modern writer. If 
 an intelligent being had an eye so keen that he could see the 
 smallest object by the faintest light, and a movement so rapid 
 that he could pass from one bound of the stellar system to the 
 other in a few years, then, by viewing the earth from a dis- 
 tance much less than that of the farthest star, he would see it 
 by light which had left it several thousand years before. By 
 simply watching, he would see the whole drama of human his- 
 tory acted over again, except where the actions had been hid- 
 den by clouds, or under other obstacles to the radiation of light. 
 The light from every human action performed under a clear 
 sky is still pursuing its course among the stars, and it needs 
 only the powers we have mentioned to place a being in front 
 of the ray, and let him see the action again. 
 
 If the hypothesis now under consideration be the correct 
 one, then the heat radiated by the sun and stars is forever lost 
 to them. There is no known way by which the heat thus sent 
 off can be returned to the sun. It is all expended in produe- 
 ing vibrations in the ethereal medium which constantly ex- 
 tend out farther and farther into space. 
 
 The third hypothesis, like the first, is a simple conjecture 
 permitted by the necessary imperfection of our knowledge. 
 
THE SOURCES OF THE SUN’S HEAT. HLT 
 
 All the laws of radiation and all our conceptions of space 
 lead to the conclusion that the radiant heat of the sun cau 
 never be returned to it. Such a return can result only from 
 space itself having such a curvature that what seems to us a 
 straight line shall return into itself, as has been imagined by a 
 great German mathematician ;* or from the ethereal medium, 
 the vibrations in which constitute heat being limited in extent ; 
 or, finally, through some agency as yet totally unknown to sci- 
 ence. The first idea is too purely speculative to admit of dis- 
 cussion, while the other two suppositions transcend our science 
 as completely as does that of an actual annihilation of force. 
 
 § 3. The Sources of the Sun’s Heat. 
 
 We may regard it as good as an observed fact that the sun 
 has been radiating heat into void space for thousands or even 
 millions of years, without any apparent diminution of the sup- 
 ply. One of the most difficult questions of cosmical physics— 
 a question the difficulty of which was not seen before the dis- 
 covery of the conservation of force—has been, How is this sup- 
 
 * This idea belongs to that transcendental branch of geometry which, rising 
 above those conceptions of space derived from our experience, investigates what 
 may be possible in the relations of parts of space considered in their widest range. 
 It is now conceded that the supposed a priori necessity of the axioms of geom- 
 etry has no really sound fogical foundation, and that the question of the limita- 
 tions within which they are true is one to be settled by experience. Especially is 
 this true of the theorem of parallels, no really valid demonstration either that two 
 parallel straight lines will never meet or never diverge being possible. By reject- 
 ing the limitations imposed upon our fundamental geometrical conceptions, yet 
 without admitting anything which positively contradicts them, several geometrical 
 systems have been constructed in recent times, which are included under the gen- 
 eral appellation of the non-Euclidian Geometry. The most celebrated and re- 
 markable of these systems is that of Riemann, who showed that although we are 
 obliged to conceive of space as unbounded, since no position is possible which has 
 not space on all sides of it, yet there is no necessity that we shall consider it as 
 infintte. It may return into itself in something the manner of the surface of a 
 sphere, which, though it has no boundary, yet contains only a finite number of 
 square feet, and on which one who travels straight forward indefinitely will finally 
 arrive at his starting-point. Although this idea of the finitude of space transcends 
 our fundamental conceptions, it does not contradict them, and the most that ex- 
 perience can tell us in the matter is that, though space be finite, the whole extent 
 of the visible universe can be but a very small fraction of the sum total of space. 
 
518 THE STELLAR UNIVERSE. 
 
 ply of heat kept up? If we calculate at what rate the tem- 
 perature of the sun would be lowered annually by the radia- 
 tion from its surface, we shall find it to be 24° Fahrenheit per 
 annum, supposing its specific heat to be the same as that of 
 water, and from 5° to 10° per annum, if we suppose it the 
 same as most of the substances which compose our globe. It 
 would, therefore, have entirely cooled off in a few thousand 
 years after its formation if it had no other source of heat 
 than that shown by its temperature. 
 
 That the temperature could be kept up by combustion, as 
 terrestrial fires are kept up, is out of the question, as new fuel 
 would have to be constantly added in quantities which cannot 
 possibly exist in the neighborhood of the sun. But an allied 
 source of heat has been suggested, founded on the law of the 
 mechanical equivalency of heat and force. If a body should 
 fall into the sun from a great height, all the force of its fall 
 would be turned into heat, and the heat thus produced would 
 be enormously greater than any that would arise from the 
 combustion of the falling body. An instance of this law is 
 shown by the passage of shooting-stars and aérolites through 
 our atmosphere, where, though the velocity rarely amounts to 
 more than forty miles a second, nearly all such bodies are con- 
 sumed by the heat generated. Now, the least velocity with 
 which a body could ee the sun (unless it had been merely 
 thrown from the sun and had fallen back) is about 280 miles 
 per second; and if the body fell from a great height, the ve- 
 locity would be over 850 miles per second. The meteoric 
 theory was founded on this law, and is, in substance, that the 
 heat of the sun is kept up by the impact of meteors upon his 
 surface. ‘The fact that the earth in its course around the sun 
 encounters millions of meteoroids every day is shown by the 
 frequency of shooting-stars, and leads to the result that the 
 solar system is, so to speak, crowded with such bodies revoly- 
 ing in all sorts of erratic orbits. It is therefore to be sup- 
 posed that great numbers of them fall into the sun; and the 
 question whether the heat thus produced can be equal to that 
 radiated by the sun is one to be settled by calculation. It is 
 
THE SOURCES OF THE SUN’S HEAT. 519 
 
 thus found that, in order to keep up the solar heat, a mass of 
 matter equal to our planet would have to fall into the sun ev- 
 ery century. 
 
 This quantity of meteoric matter is so far beyond all rea- 
 sonable possibility that it requires little consideration to show 
 that the supply of solar heat cannot be thus accounted for. 
 Only a minute fraction of all the meteoroids or other bodies 
 circulating through space or revolving around the sun could 
 strike that luminary. In order to reach the sun, they would 
 have to drop directly to it from space, or be thrown into it 
 through some disturbance of their orbits produced by planet- 
 ary attraction. If meteors were as thick as this, the earth 
 would be so pelted with them that its whole surface would be 
 made hot by the force of the impact, and all life would be 
 completely destroyed. While, then, the sun may, at some past 
 time, have received a large supply of heat in this way, it is’ 
 impossible that the supply could always be kept up. 
 
 The Contraction Theory.—It is now known that there is 
 really no necessity for supposing the sun to receive heat from 
 any outward source whatever in ‘order to account for the 
 preservation of his temperature through millions of years. 
 As his globe cools off it must contract, and the heat gener- 
 ated by this contraction will suffice to make up almost the en- 
 tire loss. This theory is not only in accordance with the laws 
 of matter, but it admits of accurate mathematical investiga- 
 tion. Knowing the annual amount of energy which the sun 
 radiates in the form of heat, it is easy, from the mechanical 
 equivalent of the heat thus radiated, to find by what amount 
 he must contract to make it up. It is thus found that, with 
 the present magnitude of the sun, his whole diameter need 
 contract but 220 feet a year to produce all the heat which he 
 radiates. This amounts, in round numbers, to a mile in 25 
 years, or four miles in a century. 
 
 The question whether the temperature of the sun will be 
 raised or lowered by contraction depends on whether we sup- 
 pose his interior to be gaseous, on the one hand, or solid or 
 liquid, on the other. A known principle of the contraction of 
 
520 THE STELLAR UNIVERSE. 
 
 gaseous bodies, and one which, at first sight, seems paradox- 
 ical, is that the more heat such a body loses, the hotter it will 
 become. By losing heat it contracts, but the heat generated 
 by the contraction exceeds that which it had to lose in order 
 to produce the contraction.* When the mass of gas is so far 
 contracted that it begins to solidify or liquefy, this action 
 ceases to hold, and further contraction is a cooling process. 
 We cannot yet say whether the sun has or has not begun to 
 solidify or liquefy in his interior, and therefore cannot make 
 an exact estimate of the time his heat will last. A rough 
 estimate may, however, be made from the rate of contraction 
 necessary to keep up the present supply of heat. This rate 
 diminishes as the sun grows smaller at such a rate that in five 
 millions of years the sun will be reduced to one-half his pres- 
 ent volume. If he has not begun to solidify now, it seems 
 likely that he will then, and his heat must soon after begin 
 to diminish. On the whole, it is quite improbable that the 
 sun can continue the radiation of sufficient heat to support 
 life on the earth ten millions of years more. 
 
 The contraction theory enables us to trace the past history 
 of the sun a little more definitely than that of his future. He 
 must have been larger a hundred years ago than he is now by 
 four miles, and yet larger in preceding centuries. Knowing 
 
 * This curious law of cooling masses of gas was discovered by Mr. J. Homer 
 Lane, of Washington. This gentleman’s paper on the theoretical temperature of 
 the sun, in the American Journal of Science for July, 1870, contains the most 
 profound discussion of the subject with which I am acquainted. The principle in 
 question may be readily shown in the following way. Ifa globular gaseous mass 
 is condensed to one-half its primitive diameter, the central attraction upon any 
 part of its mass will be increased fourfold, while the surface upon which this at- 
 traction is exercised will be reduced to one-fourth. Hence, the pressure per unit 
 of surface will be increased sixteen times, while the density will be increased only 
 eight times. Hence, if the elastic and gravitating forces were in equilibrium in 
 the primitive condition of the gaseous mass, its temperature must be doubled in 
 order that they may still be in equilibrium when the diameter is reduced one-half. 
 A similar paradox is found in the theorem of celestial mechanics—that the effect 
 of a resisting medium is to accelerate the motion of a planet or comet through 
 it. The effect of the resistance is to make the body approach the sun, and the 
 velocity generated by the approach exceeds that lost by the resistance, 
 
THE SOURCES OF THE SUN’S HEAT. 5Y1 
 
 the law of his contraction, we can determine his diameter at 
 any past time, just as in the case of the running clock the 
 height of the weight during preceding days can be calculated. 
 We can thus go back to a time when the globe of the sun ex- 
 tended out to the orbit of Mercury, then to the orbit of the 
 earth, and, finally, when it filled the whole space now occupied 
 by the solar system. We are thus led by a backward process 
 to the doctrine of the nebular hypothesis in a form strikingly 
 similar to that in which it was presented by Kant and La- 
 place, although our reasoning is founded on natural laws of 
 which those great thinkers had no knowledge. 
 
 If we take the doctrine of the sun’s contraction as furnish- 
 ing the complete explanation of the solar heat during the whole 
 period of the sun’s existence, we can readily compute the total 
 amount of heat which can be generated by his contraction 
 from any assigned volume. This amount has a limit, however 
 great we may suppose the sun to have been in the beginning: 
 a body falling from an infinite distance would generate only 
 a limited quantity of heat, just as it would acquire only a lim- 
 ited velocity. It is thus found that if the sun had, in the be- 
 ginning, filled all space, the amount of heat generated by his 
 contraction to his present volume would have been sufticient 
 to last 18,000,000 years at his present rate of radiation. We 
 can say with entire certainty that the sun cannot have been 
 radiating heat at the present rate for more than this period un- 
 less he has, in the mean time, received a miraculous accession 
 of energy from some outside source. We use the term “ mi- 
 raculous” to designate any seeming incompatibility with those 
 well-ascertained natural laws which we see in operation 
 around us. These laws teach us that no body can acquire 
 heat except by changes in its own mass akin to contraction of 
 its parts, or by receiving it from some other body hotter than 
 itself. The heat evolved by contraction from an infinite size, 
 or by the falling of all the parts of the sun from an infinite 
 distance, shows the extreme limit of the heat the sun could 
 acquire from internal change, and this quantity, as just stated, 
 would last only 18,000,000 years. In order that the sun 
 
5992 THE STELLAR UNIVERSE. 
 
 should receive heat from another body, it is not merely neces- 
 sary that that body should be hotter than the sun, but it would 
 have to be so much hotter that the small fraction of its radi- 
 ant heat which reached the sun would be greater than all that 
 the sun himself radiated. To give an instance of what this 
 condition requires, we remark that the body must radiate 
 more heat than the sun in the proportion that the entire vis- 
 ible celestial sphere bears to the apparent angular magnitude 
 of the body as seen from the sun. For instance, if its appar- 
 ent diameter were twelve degrees, it would seem to fill about 
 sc00 part of the celestial sphere, and in order to warm the 
 sun at all it would have to radiate more than three thousand 
 times as much heat as the sun did. Moreover, in order to fur- 
 nish sufficient heat to last the sun any given length of time, 
 it would have to stay in the sun’s neighborhood so long that 
 the excess of what the sun received over what he radiated 
 would furnish a supply of heat sufficient for that time. We 
 cannot suppose the sun to have received even a supply of a 
 thousand years of heat in this way without the most extrava- 
 gant assumptions respecting the volume, the temperature, and 
 the motion of the body from which the heat was received— 
 assumptions which, in addition to their extravagance, would 
 involve the complete destruction of the planets by the heat of 
 the body, and the total disarrangement of their orbits by its 
 attraction, if we suppose them to have been in any way pro- 
 tected from this heat. 
 
 The foregoing computation of the limit of time the sun can 
 have been radiating heat is founded on the supposition that 
 _the amount of heat radiated has always been the same. If 
 we suppose this amount to have been less formerly than now, 
 the period of the sun’s existence may have been longer, and 
 in the contrary case it may have been shorter. The amount 
 in question depends on several causes, the effect of which can- 
 not be accurately computed—namely, the magnitude, temper- 
 ature, and condition of the solar globe. Supposing a uniform 
 radiation, the diameter of this globe was twice as great nine 
 millions of years ago as it is now. Its surface was then of 
 
SECULAR COOLING OF THE EARTH. DY8 
 
 four times its present extent, so that, if it was of the same 
 nature and at the same temperature as now, there would have 
 been four times the radiation. but its density would have 
 been only one-eighth as great as at present, and its temper- 
 ature would have been lower. These circumstances would 
 tend to diminish its radiation, so that it is quite possible that 
 the total amount of heat radiated was no greater than at 
 present. The probability would seem to be on the side of a 
 greater total radiation, and this probability is strengthened by 
 geological evidence that the earth was warmer in its earlier 
 ages than now. If we reflect that a diminution of the solar 
 heat by less than one-fourth its amount would probably make 
 our earth so cold that all the water on its» surface would 
 freeze, while an increase by much more than one-half would 
 probably boil the water all away, it must be admitted that the 
 balance of causes which would result in the sun radiating heat 
 just fast enough to preserve the earth in its present state has 
 probably not existed more than 10,000,000 years. This is, 
 therefore, near the extreme limit of time that we can suppose 
 water to have existed on the earth in the fluid state. 
 
 § 4. Secular Cooling of the Earth. 
 
 An instance of a progressive loss of heat, second in impor- 
 tance only to the loss from the sun itself, and, indeed, con- 
 nected with it, is afforded by the secular cooling of the earth. 
 As we have shown in a preceding chapter, the interior of the 
 earth is hotter than the surface, and wherever there is such 
 a difference of temperature as this, there must be a conduc- 
 tion of heat from the hotter to the colder parts. In order 
 that heat may thus be conducted, there must be a supply of 
 heat inside. The increase of heat downwards into the earth 
 cannot, therefore, terminate suddenly, but must extend to a 
 great depth. | 
 
 Whatever view we may take of the question of the earth’s 
 fluidity, it must be admitted that it was hotter in former ages 
 than now. To borrow an illustration from Sir William Thom- 
 son, the case is much the same as if we should find a hot stone 
 
594 THE STELLAR UNIVERSE. 
 
 in a field. We could say, with entire certainty, that the stone 
 had been in the fire, or some other hot place, within a limited 
 period of time. Respecting the origin of this heat, two hy- 
 potheses have prevailed—one, founded on the nebular theory, 
 that the earth was originally condensed as a molten mass, and 
 has not yet cooled off; the other, that it received its heat from 
 some external source. The latter was the view of Poisson, 
 who accounted for the increase of temperature by supposing 
 that the solar system had, at some former period, passed 
 through a hotter region of space than that in which it is now 
 found. This view is, however, now known to be entirely un- 
 tenable, for several reasons. Space itself cannot be warm, 
 and the earth could have derived heat only from passing near 
 a hot body. A star passing near enough to heat up the earth 
 would have totally disarranged the planetary orbits, by its at- 
 traction, and destroyed all life on the surface of the globe by 
 its heat. 
 
 Thus, tracing back the earth’s heat, we are led back to the 
 time when it was white-hot; and then, again, to when it was 
 enveloped in the fiery atmosphere of the sun; and again, when 
 it was itself a mass of fiery vapor. Jespecting the time re- 
 quired for it to cool off, we cannot make any exact calcula- 
 tion, as we have done in the case of the sun, because the cir- 
 cumstances are entirely different. Owing to the solidity of at 
 least the outer crust of the earth, the heat which it loses bears 
 no known relation to its interior temperature. In fact, were 
 we to compute how long the earth might have been able to 
 radiate heat at its present rate, we may find it to be counted 
 by hundreds or thousands of millions of years. The kernel 
 of the difficulty les in the fact that when a solid crust once 
 formed over the molten earth, there was a sudden change in 
 the rate of cooling. As long as the globe was molten, there 
 would be constant currents between its surface and the inte- 
 rior, the cooling superficial portion constantly sinking down, 
 and being replaced by fresh hot matter from the interior. 
 But when a continuous solid crust was once formed, the heat 
 could reach the surface only by conduction through the crust, 
 
SECULAR COOLING OF THE EARTH. 525 
 
 and the latter, though only a few feet thick, would operate as 
 a screen to prevent the further loss of heat. There would, as 
 the crust cooled, be enormous eruptions of molten matter from 
 the interior; but these would rapidly cool, and thus help to 
 thicken the crust. 
 
 A fact not to be lost sight of, and which in some way as- 
 similates the earth to the sun, is that of the heat lost by the 
 earth by far the greater part is made up, not by a lowering 
 of the temperature of the earth, but by its contraction. It is 
 true that there must be some lowering of temperature, but for 
 each degree that the temperature is lowered there will proba- 
 bly be a hundred degrees of heat evolved by the contraction 
 of our globe. Considering only the earth, it is difficult to set 
 an exact limit to the time it may have been cooling since its 
 crust was formed. 
 
 The sudden change produced in the radiation of a molten 
 body by the formation of a solid crust over its surface may 
 afford us some clue to the probable termination of the heat- 
 giving powers of the sun. Whenever the latter so far cools 
 off that a continuous solid crust is formed over its surface, it 
 will rapidly cease to radiate the heat necessary to support life 
 on the globe. At its present rate of radiation, the sun will be 
 as dense as the earth in about 12,000,000 years; and it is 
 quite likely to be long before that time that we are to expect 
 the permanent formation of such a crust. 
 
 The general cosmical theory which we have been consider- 
 ing accounts for the supposed physical constitution of Jupiter, 
 which has been described in treating of that planet. On the 
 nebular hypothesis, as we have set it forth, the ages of the 
 several planets do not greatly differ. The smaller planets 
 would, therefore, cool off sooner than the larger ones. It is 
 possible that, owing to the great masses of Jupiter and Saturn, 
 their rate of cooling has been so slow that no solid crust is yet 
 formed over them. In this case they would appear self-lumi- 
 nous, were they not surrounded by immense atmospheres, filled 
 with clouds and vapors, which shut off a great part of the 
 internal heat, and thus delay the cooling process. 
 
THE STELLAR UNIVERSE. 
 
 Or 
 bo 
 or) 
 
 ~§ 5. General Conclusions respecting the Nebular ETypothesis. 
 
 It would seem from what has been said that the widest in- 
 ductions of modern science agree with the speculations of 
 thinking minds in past ages, in presenting the creation of the 
 material universe to our view as a process rather than act. 
 This process began when the present material universe was a 
 mass of fiery vapor, filling the stellar spaces; it is still going 
 on in its inevitable course, and it will end when sun and stars 
 are reduced to dark and cold masses of dead matter. The 
 thinking reader will, at this stage of the inquiry, very natu- 
 rally inquire whether this view of the cosmogony is to be 
 received as an established scientific fact, or only as a result 
 which science makes more or less probable, but of the validity 
 of which opinions may reasonably differ. We consider that 
 the latter is the more correct view. All scientific conclusions 
 necessarily rest on the postulate that the laws of nature are 
 absolutely unchangeable, and that their operations have never 
 been interfered with by the action of any supernatural cause ; 
 that is, by any cause not now in operation in nature, or op- 
 erating in any way different from that in which it has always 
 done. The question of the correctness of this postulate is one 
 of philosophy and common-sense rather than of science; and 
 all we can say in its favor is that, as a general rule, the bet- 
 ter men understand it, the more difficulty they find in doubting 
 it. And all we can say in favor of the nebular hypothesis 
 amounts to this: that the operations of nature, in their widest 
 range, when we trace them back, seem to lead us to it, as 
 the mode of running of the clock leads to the conclusion that 
 it was once wound up. 
 
 Helmholtz, Thomson, and others have, as we have explain- 
 ed, made it evident that by tracing back the cooling processes 
 we now see going forward in nature, we are led to a time 
 when the planets were enveloped in the fiery atmosphere of 
 the sun, and were therefore themselves in a molten or vapor- 
 ous form. ut the reverse problem, to show that a nebulous 
 mass would or might condense into a system possessing the 
 
CONCLUSIONS RESPECTING THE NEBULAR HYPOTHESIS. 527 
 
 wonderful symmetry of our solar system—the planets revolv- 
 ing round the sun, and the satellites round their primaries 
 in nearly circular orbits—has not been solved in a manner at 
 all satisfactory. We have seen that Kant’s ideas were in some 
 respects at variance with the laws of mechanics which have 
 since been discovered. lLaplace’s explanation of how the 
 planets might have been formed from the atmosphere of the 
 sun is not mathematical enough to be conclusive. In the ab- 
 sence of a mathematical investigation of the subject, it seems 
 more likely that the solar atmosphere would, under the cond1- 
 tions supposed by Laplace, condense into a swarm of small 
 bodies like the asteroids, filing the whole space now occupied 
 by the planets. Again, when we examine the actual nebule, 
 we find very few of them to present that symmetry of outline 
 which would lead to their condensation into a system so sym- 
 metrical as that to which our planet belongs. The donble 
 stars, revolving in orbits of every degree of eccentricity, and 
 the rings of Saturn, composed apparently of a swarm of small 
 particles, offer better examples of what we should expect from 
 the nebular hypothesis than do the planets and satellites of our 
 system. 
 
 These difficulties may not be insurmountable. The greatest 
 of them, perhaps, is to show how a ring of vapor surrounding 
 the sun could condense into a single planet encircled by satel- 
 lites. The conditions under which such a result is possible 
 require to be investigated mathematically. At the present 
 time we can only say that the nebular hypothesis is indicated 
 by the general tendencies of the laws of nature; that it has 
 not been proved to be inconsistent with any fact; that it is 
 almost a necessary consequence of the only theory by which 
 we can account for the origin and conservation of the sun’s 
 heat; but that it rests on the assumption that this conservation 
 is to be explained by the laws of nature, as we now see them 
 in operation. Should any one be sceptical as to the sufficiency 
 of these laws to account for the present state of things, science 
 can furnish no evidence strong enough to overthrow his doubts 
 
 until the sun shall be found growing smaller by actual meas- 
 30 
 
528 THE STELLAR UNIVERSE. 
 
 urement, or the nebulee be actually seen to condense into stars 
 and systems. 
 
 < 
 
 § 6. The Pluralty of Worlds. 
 
 When we contemplate the planets as worlds like our own, 
 and the stars as suns, each, perhaps, with its retinue of attend- 
 ant planets, the idea naturally suggests itself that other planets 
 as well as this may be the abode of intelligent beings. The 
 question whether other planets are, as a general rule, thus 
 peopled, is one of the highest interest to us, not only as in- 
 volving our place in creation, but as showing us what is really 
 greatest in the universe. Many thinking people regard the 
 discovery of evidences of life in other worlds as the great ul- 
 timate object of telescope research. It is, therefore, extreme- 
 ly disappointing to learn that the attainment of any direct 
 evidence of such life seems entirely hopeless—so hopeless, 
 indeed, that it has almost ceased to occupy the attention of 
 astronomers. The spirit of modern science is wholly adverse 
 to speculation on questions for the solution of which no scien- 
 tific evidence is attainable, and the common answer of astron- 
 omers to all questions respecting life in other worlds would 
 be that they knew no more on the subject than any one else, 
 and, having no data to reason from, had not even an opinion 
 to express. Still, in spite of this, many minds will speculate ; 
 - and although science cannot answer the great question for us, 
 she may yet guide and limit our speculations. It may, there- 
 fore, not be unprofitable to show within what limits specula- 
 tion may not be discordant with the generalizations of science. 
 
 First, we see moving round our sun eight large planets, on 
 one of which we live. Our telescopes show us other suns, in 
 such numbers that they defy count, amounting certainly to 
 many millions. Are these suns, like our own, centres of plan- 
 etary systems? If our telescopes could be made powerful 
 enough to show such planets at distances so immense as those 
 of the fixed stars, the question would at once be settled; but 
 all the planets of our system would disappear entirely from 
 the reach of the most powerful telescopes we can ever hope to 
 
THE PLURALITY OF WORLDS. 529 
 
 make at a distance far less than that which separates us from 
 the nearest fixed star. Observation can, therefore, afford us 
 no information on the subject. We must have recourse to 
 cosmological considerations, and these may lead to the con- 
 clusion that if the whole universe condensed from a nebulous 
 mass, the same cause which led our sun to be surrounded by 
 planets would operate in the case of other suns. But we have 
 just shown that the symmetry of form and arrangement seen 
 in our system is something we could rarely expect to result 
 from the condensation of masses so irregular as those which 
 make up the large majority of the nebulse, while the irreg- 
 ular orbits of the double stars show us what we should rather 
 expect to be the rule. It is, therefore, quite possible that reti- 
 nues of planets revolving in circular orbits may be rare excep- 
 tions, rather than the rule, among the stars. 
 
 Next, granting the existence of planets without number, 
 what indications can we have of their habitability? There 
 is one planet besides our own for which the telescope settles 
 this point—namely, the moon. This body has neither air nor 
 water, and, consequently, nothing on which organic life can 
 be supported. The speculations sometimes indulged in re- 
 specting the possible habitability of the other side of the 
 moon, which we can never see, are nothing more than plays 
 of the imagination. The primary planets are all too distant 
 to enable us to form any certain judgment of the nature of 
 their surfaces, and the little we can see indicates that their 
 constitution is extremely varied. Mars has every appearance 
 of being like our earth in many particulars, and is, therefore, 
 the planet which we should most expect to find inhabited. 
 Most of the other planets give indications of being surround- 
 ed by immense atmospheres, filled with clouds and vapors, 
 through which sight cannot penetrate, and we can reach no 
 certain knowledge of what may be under these clouds. On 
 the whole, we may consider the chances to be decidedly 
 against the idea that any considerable fraction of the heav- 
 enly bodies are fitted to be the abode of such animals as we 
 have on the earth, and that the number of them which have 
 
530 THE STELLAR UNIVERSE. 
 
 the requisites for supporting civilization is a very small frac- 
 tion indeed of the whole. 
 
 This conclusion rests on the assumption that the conditions 
 of life are the same in other worlds as in our own. This as- 
 sumption may be contested, on the ground that we can set no 
 limits to the power of the Creator in adapting life to the con- 
 ditions which surround it, and that the immense range of adap- 
 tation on our globe—some animals living where others are im- 
 mediately destroyed—makes all inferences founded on the im- 
 possibility of our earthly animals living in the planets entirely 
 inconclusive. The only scientific way of meeting this argu- 
 ment is to see whether, on our earth, there are any limits to 
 the adaptability in question. A cursory examination shows 
 that while there are no well-defined limits to what may be 
 considered as life, the higher forms of animal life are very 
 far from existing equally under all conditions, and the high- 
 er the form, the more restricted the conditions. We know 
 that no animal giving evidence of self-consciousness is devel- 
 oped except under the joint influence of air and water, and 
 between certain narrow limits of temperature; that only forms 
 of life which are intellectually very low are developed in the 
 ocean; that there is no adapting power exercised by nature on 
 our globe whereby man can maintain a high degree of intel- 
 lectual or bodily vigor in the polar regions; that the heats of 
 the torrid zone also impose restrictions upon the development 
 of our race. The conclusion which we may draw from this 
 is that, if great changes should occur on the surface of our 
 globe, if it should be cooled down to the temperature of the 
 poles, or heated up to that of the equator, or gradually be cov- 
 ered with water, or deprived of its atmosphere, the higher pres- 
 ent forms of animal life would refuse to adapt themselves to 
 the new state of things, and no new forms of life of equal ele- 
 vation would take the place of those destroyed by the change. 
 There is not the slightest reason for believing that anything 
 more intelligent than a fish would ever live under water, or 
 anything more intellectual than the Esquimanx ever be sup- 
 ported in regions as cold as the poles. If we apply this con- 
 
THE PLURALITY OF WORLDS. 531 
 
 sideration to the question which now occupies us, we are led 
 to the conclusion that, in view of the immense diversity of 
 conditions which probably prevails in the universe, it would 
 be only in a few favored spots that we should expect to find 
 any very interesting development of life. 
 
 An allied acneiqemtien will lead us to nearly the same con- 
 clusion. Enthusiastic writers not only sometimes people the 
 planets with inhabitants, but calculate the possible population 
 by the number of square miles of surface, and throw in a lib- 
 eral supply of astronomers who scan our earth with powerful 
 telescopes. The possibility of this it would be presumption 
 to deny; but that it is extremely improbable, at least in the 
 case of any one planet, may be seen by reflecting on the brev- 
 ity of civilization on our globe, when compared with the exist- 
 ence of the globe itself as a planet. The latter has probably 
 been revolving in its orbit ten millions of years; man has 
 probably existed on it less than ten thousand years; civiliza- 
 tion less than four thousand ; telescopes little more than two 
 hundred. Had an angel visited it at intervals of ten thousand 
 years to seek for thinking beings, he would have been disap- 
 pointed a thousand times or more. Reasoning from analogy, 
 we are led to believe that the same disappointments might 
 await him who should now travel from planet to planet, and 
 from system to system, on a similar search, until he had exam- 
 ined many thousand planets. 
 
 It seems, therefore, so far as we can reason from analogy, 
 that the probabilities are in favor of only a very small frac- 
 tion of the planets being peopled with intelligent beings. 
 But when we reflect that ie possible number fe the planets 
 is counted by hundreds of millions, this small fraction may 
 be really a very large number, and among this number many 
 may be peopled by “peat meen higher on ourselves in the 
 intellectual scale. Here we may give free rein to our imagi- 
 nation, with the moral certainty that science will supply nai 
 ing tending either to prove or to disprove any of its fancies. 
 
Nae be EN Tee 
 
 i 
 
 LIST OF THE PRINCIPAL GREAT TELESCOPES OF THE WORLD. 
 A. feeflecting Telescopes. 
 
 Owner, and Place. Construction.* Aperture. | When built, and by whom. 
 
 The Earl of Rosse, Farsonstown, Newtonian. | 6 feet. | Earl of R., 1844. 
 
 Rnglands. 2.30 sae liye wes ote Culver. 
 The Observatory of Melbourne, Cassegr. | 4 feet. | Mr. Grubb, 1870. 
 AMIS R Tia aa lene g sie ete «ae ea : 
 ( M. Martin and M. 
 
 Mr. A. A. Common, Esq., Ealing, New. 46.1 37 in The owner and Mr. 
 as. G. ; 
 
 The Observatory of Paris........ Newt., 8. G. | 47 in. ) Eichens, 1875 
 ; ; 
 The Earl of Rosse, Parsonstown, Ne ELOnIAT Sl fcotae She caer 
 Lrelaret si. oa. «chet Werte ot oie ; : : 
 Professor Henry Draper, Dobbs : 
 Berry New Yorks em ohn. Cass., 8. G. | 28 in. | The owner. 
 The Observatory of Toulouse, ae! she Oe Noucdult 
 
 Wane sia ean tis. er aces es oe \ 
 The Observatory of Marseilles, } 4 M. Foucault and M. 
 Wrancen ss tyilc oak ware nee j Pat eee Kichens. 
 
 Newtonian. | 2 feet. | The owner. 
 
 B. Refracting Telescopes. 
 
 Owner, and Place. Aperture. Maker, and Date. 
 The Imperial Observatory, Pulkowa, Russiaf...| 30 in. atte AOC 
 The Imperial Observatory, Vienna............ 27 in. | Mr. Grubb, 1881. 
 U.S. Naval Observatory, Washington......... 26 in. * ce SUNG 
 The University of Virginia...........-.-.0.. 26 in. AE RDS aan 
 Mr. R.S. Newall, Gateshead, England......... | 25 in. | ie Fa Sales: 
 The Observatory of Strasburg, Germany....... 19 in. | Merz and Mahler. 
 The Observatory of Chicago. . sabe ten ith BOLO CLL tee pe es 
 Mr. Van der Zee, Buffalo, New York. 18 in. Mr. Fitz, of N. Y. 
 The Observatory of Harvard College, ‘Cam- dV 15 in. Merz and Mahler, 
 bridge; Miss) tome netsh clots. ie).dc eros J 1848. 
 
 *Tn this column, ‘‘ Cassegr.” signifies the Cassegrainian construction, described on page 
 126. 8S. G. signifies that the mirror is of silvered glass. 
 + This telescope, of which the object-glass only is by the Clarks, is still unfinished. 
 
534 APPENDIX. 
 
 Owner, and Place. Aperture. Maker, and Date. 
 The Royal Observatory, Pulkowa, Russia.......| 15 in. 1 ies ae Me 
 Mr. William Huggins, London, England*...... 15 in. Mr. Grubb. 
 Lord Lindsay, Aberdeen, Scotland............ 15 in. | Mr. Grubb. 
 The Observatory of Lisbon, Portugal.......... 14.8 in. | Merz and Mahler. 
 The Observatory, Markree Castle, England. .... 14 in, | seen oes 
 Hamilton College, Clinton, New York.......... 13.5 in. | Mr. Spencer. 
 The Paris Observatory} .!.<. sesemerae ores. . = 13 in. | M. Eichens. 
 The Allegheny Observatory, Pennsylvania..... 13 Jas Bees ees 
 Mr. 1. M: Rutherfurd, News) orkeper-. =... > 13 in. The owner. 
 
 The Dudley Observatory, Albany, New York....| 13 in. | Mr. Fitz, of N. Y. 
 (Merz and Sons, 
 
 The Royal Observatory, Greenwich, Eng- ores 1860. 
 ange Cue eRe REE eerie arbres | rao and 
 ‘ Simms. 
 Michigan University, Ann Arbor............. 12.5 in. | Mr. Fitz, of N. Y. 
 Vassar College, Poughkeepsie, New York 12.8 in. | ee 
 s ge, Poughkeepsie, NeW YOrK...... .o 10, f A. Clark and Sons. 
 
 The Physical Observatory, Oxford, England....} 12.2 in. | Mr. Grubb. 
 
 The Imperial Observatory, Vienna............ 12 in. ze er ess 
 The Cambridge Observatory, England......... 12 in. M. Cauchoix. 
 The Royal Observatory, Dublin............... 12 in. M. Cauchoix. 
 Professor Henry Draper, Dobbs Ferry, New / | 49 ;, ( A. Clark and Sons, 
 York: aie. Soe et ee eee j sap Sa ho bs 
 
 | The Pritchett Institute, Glasgow, Missouri..... 12 in. ae gene 
 Mr. 8. V. White, Brooklyn, New York......... 12 in. | A. Clark and Sons. 
 The Radcliffe Observatory, Oxford, England... .| 12 in. M. Cauchoix. 
 
 _'The Lick Observatory, San José, California....] 12 in. | A.Clark and Sons. 
 
 | The Observatory, Bothkamp, Germany........ 11.7 in. | Schroeder. 
 
 | The Observatory, Cordova, South America..... 11.2 in. | Mr. Fitz, of N. Y. 
 The Observatory, Munich, Germany...........{ 11 in. | Merz. 
 The Observatory, Copenhagen, Denmark.......| ll in. | Merz. 
 The Observatory of Cincinnati, Ohio.......... 11 in. Merz. 
 Middletown University, Connecticut........... ll in. | A. Clark and Sons. 
 
 Besides these, the following three telescopes are projected: A great re- 
 fractor of 33 inches for the Lick Observatory, California, to be made by 
 A. Clark and Sons; a great refractor for the Paris Observatory, to be fig- 
 ured by the brothers Henry, of Paris; a refractor of 28 inches for Yale Col- 
 lege, by A. Clark and Sons. 
 
 * This telescope belongs to the Royal Society, but is in possession of Mr. Huggins, 
 + The object-glass is an old one, but the mounting is new, by Eichens. 
 ¢ The object-glass is by Merz, of Munich, the mounting by Troughton and Simms. 
 
LIST OF THE MORE REMARKABLE DOUBLE STALKS. 535d 
 
 Name. 
 
 Jub 
 
 LIST OF THE MORE REMARKABLE DOUBLE STARS. 
 
 COMPILED BY 8S. W. BURNHAM. 
 
 Right Ascen. | Declination|Positi’n 
 
 é Sculptoris... 
 @ Piscuun 2.35 
 
 y Andromede. 
 
 c Trianguli.... 
 « Cassiopee.. . 
 
 e Persei 
 39 Eridani.... 
 ¢ Tauri 
 p Orionis 
 (c§ 
 ce 
 
 238 
 
 cs 
 
 eee eee 
 
 Z Orionis 
 
 eee eee 
 
 1880. 1880. agi! Distance.| Magnitudes. 
 ba hil Gh : id 2 Me 
 8 47| 8 9/149.8] 11.53/6.2 7.8 
 11 13] 8 12/287.6] 4.59/7.0 8.0 
 16 13] 12 49/838.0] 29.73/6.8 “10.7 
 26 12} 6 18| 82.3) 27.4215.0 9.0 
 33 36] 20 47/192.7| 6.8715.0 8.2 
 41 43] 57 11/140.0] 5.86/4.0 7.6 
 48 32] 22 591358.9| 1.3416.2 6.8 
 1 7 14] 23 57|227.5| 7.9814.7 10.1 
 Re hha 138 41} —1 81351.4! 1.25/62 7.2 
 bearer 13 45} 88 40/210.1| 18.27/2.0 9.0 
 40 1|—25 39] 69.6] 5.53/6.0 10.0 
 55 60] 2 11/322.2] 3.1212.8 3.9 
 56 32] 41 45] 62.4] 10.33/3.0 ° 5.0 
 2 6 25) 29 45] 80.5! 3.68/5.0 6.4 
 19 10) 66 52/265.1} 2.0114.2 7.1 
 Ma FLOR St 7.6212 Sit 
 So ngs 35 4| —1 12/824.47] 4.63160 9.2 
 37 5] 2 44/289.2|) 2.67/13.0 6.8 
 Pat. 52 21) 20 52/201.9] 1.2615.7. 6.0 
 ss 3 46 35} 81 32/207.6| 12.47/2.7 9.8 
 eee 49 48] 39 40] 9.2] 8.81/3.1 8.38 
 4 8 41/—10 38]153.7| 6.26/60 9.1 
 Bens: 12 58] 27 4/245.5| 53.78|5.0 8.0 
 a Seay lie, © 21431068: Abie 7.05427 16 8.6 
 ie 8 46] —8 20/198.8] 9.14]1.0 8.0 
 SK 3 16 32} 8 26] 28.1] 31.7115.0 7.0 
 eee 18 27| —2 30] 83.8] 1.11140 5.0 
 es 28 32| 9 51) 40.8] 4.23/4.0 6.0 
 Re hin: 90°98) --5 28)... a 
 mI 32 43] —2 40/236.5] 11.00/4.1 10.3 
 ake eh Fi 84:51112,86e) “7.5 
 aa 34 42] —2 0/151.8} 2.55/2.0 5.7 
 6 23 0| —6 57/130.0| 7.25/5.0. 5.5 
 ree eee 1017) 246|"*. 6.0 
 35 88! 59 341153.7] 1.53/5.2 6.1 
 304.2] 8.67] 7.4 
 
 Notes. | 
 
 ( White, ©. Pale-white: 
 ) violet, Smyth. 
 Yellow: blue-green, 
 Herschel. 
 White: ashy. 
 Yellow: deep - red, 
 Dembowski. 
 Yellow: purple. 
 
 Binary, 349.1 years. 
 White: blue. 
 
 8|Pale-white : lilac. 
 
 White: dull red. 
 Yellow: blue. B 
 1 again double, 0.5. 
 Yellow: blue. 
 A and B. 
 A and C. 
 Yellow: ashy. 
 Yellow: blue. 
 Binary. 
 Light - green: ashy. 
 Other small stars 
 in the field. 
 
 Yellow: blue. 
 Red: bluish. - 
 Yellow: blue. 
 
 Discovered by Dawes. 
 Yellow : purple. 
 Sextuple. In the great 
 1 nebula of Orion. 
 A and B. 
 A and C. 
 Yellow : light-purple. 
 A and B. 
 B and C. 
 A and B. 
 A and C. 
 
fe 
 
 536 APPENDIX. 
 
 Name. ple, aa ee hee: Distance.| Magnitudes. Note: | 
 HEM, 48.1 20 9e 4s ” 
 56 Aurige.... 38 5| 48 42] 17.1) 55.88/6.0 9.0|White: blue. 
 p Canis Maj... 50 86)/—138 53/348.5} 3.22/4.7 8.0 
 6 Geminorum .| 7 12 57| 22 12/196.9] 7.14/8.2 8.2 
 UVAStOI cen 26 57) 32 9/239.8) 5.49/2.7 3.7 
 SIN AVES Se ase 42 19|—11 54) 17.5) 3.82/5.38 7.4 
 Caneri,.5 7.21.8 5 19) “1S Untson 0, 7415.0. 5.7 asandes. 
 ares Mee vane EO2.0).. 5.48). 6.5. -1Asand:G, 
 88 Lyncis.....| » 11 23] 87 19/240.2) 2.69/4.0 6.7 
 y Leonis ..... 10 13 20} 20 27/111.2} 3.18/2.0 3.5/Yellow: greenish. 
 35 Sextantis. . 37 7] 65 23/240.5) 6.72/6.1 7.2)Yellow: blue. 
 & Urse Maj. ..j11 11 48) 82 13/317.6} 1.09/4.0 4.9/Binary. 
 65 Urse Maj. . 48 51} 47 9} 36.4) 38.71|6.0 8.3/Yellow: blue. 
 ¥ Come. ii...) 58 8) 22 8/240.6} 3.73/6.0 7.5 _ eS 
 2h art. Giles 12 29° 6) 19 2/271.9) 20.42/4.7, 6.2) © ss 
 y Virginis.... 35 36} —O 47|159.3| 4.77/38.0 © 3.0/Binary. 
 35 Come..... 47 23) 21 54] 25.3) 1.48/5.0 7.8/A and B. 
 aelaoe tA 2 .... |124,7) 28.60 9.0 .j}A and C. 
 84 Virginis.../13 37 2) 4 9/285.3) 3.39|5.8  8.2)Yellow: blue. 
 ¢ Bodtis..2 2. 14 35 25] 14 15/303.2) 1.02)3.5 3.9 
 Ay Ne Or ea 39 45} 27 35/320.6| 2.63/3.0  6.3/Yellow: blue or green. 
 Beem (ck sitiok 45 51} 19 36|801.6} 5.44/4.7  6.6/Yellow: reddish purple. 
 CNR ps a aes aes 59 51) 48 17/239.8| 4.80|5.2  6.1/Yellowish: bluish. 
 Pa aa le tea 15 19 58) 87 48/171.9|108.46| 4.0 |A and B. ) Binary 
 Oar 13 fave .... {141.9} 0.69/6.7  7.8/B and C. 
 6 Serpentis... 29 5} 10 56/196.9| 2.56/3.0 4.0/Binary. 
 EVLIDP ss, 57 46/—11 8)173.1) 1.06/4.9 5.2/A and B. Pa 
 ahs Po pe ae LOS e O0U ake ly ea Ce 
 Antares:...628 16 22 2)—26 10/268.7) 3.46)1.0 7.0|/Red: green. 
 36 Ophiuchi ../17 7 59|/—26 25/227.3) 5.55/6.0 6.0 
 a Herculis.... 9 10) 14 82)118.5| 4.65/38.0 6.1/Yellow: emerald. 
 p abides 19 33) 87 15/307.2| 3.60/4.0 5.1 
 70 Ophiuchi . . 59 23) 2 33) 83.7) 3.48|4.1  6.1/Yellow: purple. Binary. 
 SLIVER «cree 18 40 22) 39 33] 26.0! 3.03/4.6 6.8 
 Fitts 4 aaah 40 24) 39 29/155.2) 2.57/49 5.2 
 Ay ee ML Ber 40 38) 87 29|149.7| 48.71|4.2 5.5 
 B Oygni....../19 25 53] 27 42] 55.7] 84.29/3.0 5.8|Golden yellow: blue. 
 é Sagitte.....) 48 39] 18 51/312.8| 8.49|5.7 8.8|Light-green: blue. 
 € Draconis.... 48 34} 69 58/354.5| 2.79|4.0 7.6/Yellow: blue. 
 6 Sagitte...../20 4 39) 20 83/826.7/ 11.40|/6.0 8.8 
 49 Cygni..... 36 11] 381 53} 49.4) 2.74/60 8.1/Yellow: blue. 
 e Equulei..... 53 6 3 50/283.9| 0.06|5.2  6.2/A and B. 
 a Al ores «oe of 010.4| LO Sap 4 leet A, ob, and:O, | 
 12 Aquarii.... 57 44] —6 18/189.6| 2.66/5.6 7.7|Yellowish: blue. 
 61 Cygni...../21 1 14) 38 8/115.6] 19.55)5.38 5.9 
 B Cephei..... 27 6) 70 2/250.0) 13.57/3.0  8.0|Light-green: blue. 
 41 Aquarii....)22 7 40)/—21 40/119.4| 4.08/6.0 8.5)Yellow: blue. 
 53 ee Sy 20 38/—17 21/304.5) 8.20/6.0 6.3)White: yellow. 
 g Oy ore 22 39) —O 38/334,5| 3.40/4.0  4.1/Binary. 
 ~p “4... ./28 9 85) —9 44/312.2) 49.63/4.5  8.5/Yellow: blue. 
 o Cassiopee .. 52 56) 55 5/323.4) 3.01|/5.4 7.5)White: blue. 
 
 Norr.—The sign minus (—) before declinations means south; without the sign, it is 
 north. 
 
LIST OF NEBULA! AND STAR CLUSTERS: eye 
 
 ELE 
 
 LIST OF THE MORE INTERESTING AND REMARKABLE NEBUL.Z AND 
 STAR CLUSTERS. 
 
 Object. R. A. 1880. Dec. 1880. 
 
 H. M. oe: 
 Met LOUCATECHISECE, na wa oar Sit eae eda hg a cress 0 19 72 45S. 
 Great nebula or Andromeda aa) pare ee eats 2 0 386 40 387 N 
 IND GIA wis. as ales ae ain GIs cae 0 42 25. 57S. 
 iy NaMpAME: SURG PL Io ra ae ee 3 29 36. 32.8. 
 Tempel’s variable nebula............. 3 39 23 23 N 
 Hind’s variable nebula....... 4 15 19 14 N 
 Globular cluster........ 5 9 68 55S. 
 i: SE gl BONE eg 5 Mp tad SE ay AKG 40 11S. 
 Great nebula Ob Orlotiw. san sand eee: wee kc a see 5 29 5. 29 8S. 
 Chacornac’s variable nebula... 5 380 Di Oa 
 NODULE TOUTE OTiOlies bute setae en entieel ge ster aye 5 380 BREvGAS: 
 Poopeds NEbuUla ay fan! wks twee wbceta Pacem eee fhebels, 2 5 39 69 105. 
 Cluster and nebula Mess. 46.05. 6....5 0.0 0000046 7 36 LA eS 205, 
 PREC CIUSLOD a) A ace eae aeet Massed Gere arlene cat 7 48 388 13S. 
 s < MPR GO ies. sceye <3 8 45 TZ SUN 
 PA DCEREY NENW, 010 cogs. s eee. om eA oars, = 9-11 36 7S. 
 s eae SE MeY ernie LAO trea Ok ar ae eT ae 9 18 57 47S. 
 Nevula........ 9 45 69 38 N 
 
 PEI PORYE LIC UG. soc on ¢ 4) eshte oalaaeia chee chats ec 2) tele et GLU A 39 515. 
 
 o CSU Ete See GE pS Cea ia Ree CES 10 19 LSet S: 
 = BM Re Ca sU890 Go Aaa ad Wie et tee Pe ae eel ahs ll 8 55 40 N. 
 GU ee Pa, So. os we ere a sveal ee Gey Ophalere 12 138 15 5 N. 
 4 PEs he eis cha siete mthelta. Seles Bike ne ay 16-29 N. 
 NOU MN es ss aces ec cals dvs acto tals ba 84) | 10878. 
 CO beth, «As ie He oi a A eC 12 36 338 12 N. 
 LRG ce RN Tass Goes oes chet wekbeeees | AS) 7 18 48 N, 
 PSU CIE ee PMN 5 cos se a'niayee avd dulesd ewes 1318 49, 23'S. 
 Gluster Sroundren COMtAUil co. 6 os cc ces oe ere tbe oe ees 13 20 46 415. 
 Spiral OF Mle Menuet ee yeaa ses sacle ses [> 1325.0 | 147 49 N: 
 DS DIFa TENA eee Pes alae dah cle cycle ss 13 30 2916.8: 
 yi Pe rae rem tse ates ate dele a de + 138 32 Mel Gs 
 Ghuster; 922) are ey ae een eR te tre oe vial Swe « 13 37 28 59 N. 
 
38 APPENDIX. 
 
 7 Object. R. A. 1880. Dec. 1880. 
 
 H. M. ae 
 
 Claater. jo Ges aes Pesce og es ee 2 33.N., 
 Me i bh aig gre alate aos ie aOR 0S. ee 87 23 8. 
 Resolvable-hebula:/0,. ./. 05. eeeree it ceca cals 16 10 22 4158. 
 Great Cluster of Hercules: eeu reer cs. sacs eee | eee 36 42 N. 
 luster shan 0 ace at. ohare ee Bey, Sas Od Seg a 1 445. 
 ena hie Pe kes Pe ME Se Ee a Se ee, ee te. 38 548. 
 Be) OR ra ee oe: os cls ce ee 44 298. 
 Oe pe Dice ee ae mt Sy koa ec ear ee 29 568. 
 Srnallannular nebulet-peey eee. of. cs Bcc eee ee 388 215. 
 * x Seren ocd °C a earner Pl ft Fa 23 39S. 
 Clusters, . WAR ERIE tes ces. 240s eee enema tee 3 108. 
 Trifid nebulaeee ie eels. <i. oo) ol eee 17 65 |" 28 2-8. 
 Nébulous elistere ee fen Oo. cies hic ge Oe ne ee 24 21S. 
 Gobel Sietiirlas sete eet hs os aosie ecb yin a pitote RnR and rec 16 138. 
 BILE hehe At etic Ne ON ee RR ue As 6, lon ee ke 18 29 24 OS. 
 Annular nebula Of Uyra-os5 ¢.4.,0.4.5 eas Cees oe Lee 382 53 .N, 
 Variablemetula ey 45. lee ticaise Ge Oe ee 19 5 0 50 N. 
 Dumb-bell mebulas, 7500. ees oc ie eee ee ae ak ae 22 24 .N. 
 Smallannularmebula. sc se ee eee St Aah 20 11 30 12 N. 
 Planetary riebula kote ee cee sak ae ee ee 20 17 19 44 .N. 
 Nebula around ik: Cygml. ob.) ac seks el iis ae ee 20 40 30 17 N. 
 Planetary nebula). 32), aie foe > Pott ai ner 20 58 11 50S. 
 Glisten. nl cc aay, See et alee are reek Cade enna ee 1523 5. 
 ial BE ange nee ie Wie, Ait aricain i. 57 Pathe, Odell, 2 21 34 2D 43 5. 
 Blue planetary nebula..............-.: On Gian sane 23 20 41 53 .N. 
 
 L— 
 
 To facilitate the finding of the above nebule and clusters, their posi- 
 tions are marked on the star-maps with small circles, 
 
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 APPENDIX. 
 
 VL. 
 
 ELEMENTS OF THE SMALL PLANHETS. 
 
 COMPILED BY D. P. TODD. 
 
 ay AK A i * & =) a 2 s 4 
 35 Sole3 | ee lee] S | 8S | sa pes jaa s 
 Sign and Name. 3 8 Discoverer. § 3 3 & 3 = 25 = £3 Ey, a 5 & 
 f 3 sa |iz| Ss e"| 8 | BE | es eee 
 
 A = ee Be, Pe = 
 
 “ Yrs, ° ° ° 
 ()PCeresy. nc. sc. TSO ela zZ ie. meas 2.98 | 2.56 | 770.2 | 4.61 | 0.077 | 150.0 | 80.8 | 10.6 | 2.769 
 (2) = Pallas cnn te 1802 | Olbers......... 8.43 | 2.11 | 768.9 | 4.62 | 0.238 | 122.0 | 172.8 | 34.7 | 2.771 
 (3) PUI One cloceteters 1804 | Harding....... 3.35 | 1.98 | 814.1 | 4.36 | 0.257 | 54.9 | 170.9 | 13.0} 2.668 
 jay SV GSt0... oe 1807 | Olbers......... 2.57 | 2.15 | 977.8] 3.63 | 0.089 | 250.9 | 103.5) 7.1] 2.361 
 (6) Astreea...... 1845 | Hencke........ 3.06 | 2.10 | 856.9 | 4.14} 0.186 | 134.9 | 141.5] 5.3] 2.579 
 (6) Hebes....u... 1847 | Hencke........ 2.92 | 1.93 | 939.9 | 3.78 | 0.203 | 15.2 | 138.7 | 14.8 | 2.424 
 CU) RTS eee hier TS47 Gina yes elervels 2.94 | 1.83 | 962.6 | 3.69 | 0.231 | 41.4 | 259.8] 5.5 | 2.386 
 (8) sEloraseemesre S477) Eline ae 2.55 | 1.86 |1086.3 | 3.27 | 0.156 | 32.9 | 110.3} 5.9} 2.201 
 (9) Metis........ 1848 | Graham....... 2.68 | 2.09 | 962.3 | 3.69] 0.123 | 71.1] 68.5] 5.6) 2.387 
 (10) Hygeia...... 1849 | Gasparis....... 3.49 | 2.80 | 636.4] 5.58 | 0.109 | 238.3 | 285.5] 3.8 | 3.144 
 (11) Parthenope .| 1850 | Gasparis....... 2.70 | 2.21 | 924.0] 3.84 | 0.100 | 317.9 | 125.2] 4.6 | 2.452 
 (12) Victoria..... S503 En Ceaser 2.84 | 1.82 | 994.8 | 3.57 | 0.219 | 301.7 | 235.6} 8.4 | 2.3384 
 (13) Egeria ...... 1850 | Gasparis....... 2.80 | 2.35 | $57.9 | 4.14 | 0.087 | 120.2 | 43.2 | 16.5 | 2.577 
 Ci) Men Cs eure ater LAST Ein dS epyeae eb 3.01 | 2.17 | 851.0} 4.17 | 0.163 | 180.3] 86.8] 9.1 | 2.591 
 (15) Eunomia....} 1851 | Gasparis....... 3.14 | 2.15 | 825.4 | 4.30] 0.187 | 27.9 | 293.9 | 11.7 | 2.644 
 (1G)PPSY Chest... 1852 | Gasparis....... 3.33 | 2.52 | 710.8} 4.99 | 0.189 | 15.1 | 150.6 | 3.1] 2.921 
 (1) Dhetis.... 1852 | Luther......... 2.79 | 2.15 | 912.4] 3.89 | 0.129 | 261.3 | 125.4] 5.6) 2.473 
 (18) Melpomene..| 1852 | Hind.......... 2.80 | 1.80 |1020.1 | 3.48] 0.218 | 15.1 | 150.1 | 10.2 | 2.296 
 (19) Fortuna..... LSO2H Hind racet es eee 2.83 | 2.05 | 930.1 | 3.82 | 0.159 | 31.1 | 211.5] 1.5 | 2.449 
 (20) Massalia ....| 1852 | Gasparis....... 2.75 | 2.06 | 948.9 | 3.74 | 0.143 | 99.1 | 206.6 | 0.7 | 2.409 
 (21) Lutetia...... 1852 | Goldschmidt.. .| 2.83 | 2.04] 933.6 | 3.80 | 0.162 | 327.1] 80.5} 3.1} 2.435 
 (22) Calliope..... 1852 | Hind .:2.23 %.% 8.20 | 2.62 | 715.2| 4.96] 0.101 | 59.9] 66.6 | 13.7 | 2.909 
 (23) Thaliaveans AS624) Hind :. sca 5 3.24 | 2.02 | 832.4] 4.27 | 0:231 | 123.8] 67.7 | 10.2 | 2.629 
 (24) Themis...... 1853 | Gasparis....... 3.52 | 2.75 | 639.0 | 5.56 | 0.124 | 144.1 | 35.8] 0.8] 3.136 
 (25) Phocea......| 1853 | Chacornac..... 3.01 | 1.79 | 954.2 | 3.72 | 0.255 | 302.8 | 214.2 | 21.6 | 2.400 
 (26) Proserpine ..| 1853 | Luther......... 2.89 | 2.42 | 819.7 | 4.33 | 0.087 | 236.4] 45.9] 3.6] 2.656 
 (2T) Euterpe..... PODS | WELUO Gets sies e's 5 = 2.76 | 1.94] 986.7 | 3.60 | 0.174] 88.0] 93.9] 1.6 | 2.347 
 (28) Bellona..... 1854 | Luther......... 3.20 | 2.35 | 766.6 | 4.63 | 0.153 | 122.4 | 144.7] 9.4] 2.777 
 (29) Amphitrite..| 1854 | Marth........, 2.71 | 2.34 | $69.0} 4.09 | 0.074 | 56.4 | 856.7 | 6.1 | 2.525 
 
 (80) Urania...... AS54 (SLING Sone wee ees 2.66 | 2.06 | 975.4] 3.64 | 0.127 | 32.1] 30S.1} 2.1 | 2.365 
 
Sign and Name. 
 
 (81) Euphrosyne. 
 (32) Pomona 
 
 (33) Polyhymnia. 
 (34) Circe 
 
 (35) Leucothea... 
 
 (36) Atalanta .... 
 (8T) Fides 
 
 (88) Leda 
 
 (39) Leetitia 
 
 (40) Harmonia... 
 
 (41) Daphne 
 
 (42) Isis 
 
 (43) Ariadne 
 
 (44) Nysa......:. 
 (45) Eugenia 
 
 (46) Hestia 
 (47) Aglaia 
 (48) Doris 
 (49) Pales 
 (50) Virginia 
 
 (51) Nemausa.... 
 (52) Europa 
 
 (53) Calypso 
 
 (54) Alexandra... 
 (55) Pandora 
 
 (56) Melete 
 
 (57) Mnemosyne. 
 (58) Concordia... 
 (59) Elpis 
 
 (60) Echo 
 
 (61) Danaé 
 
 (62) Erato 
 
 (63) Ausonia 
 
 (64) Angelina.... 
 -| (65) Cybele 
 
 (66) Maia 
 
 (67) Asia 
 
 (68) Leto 
 
 (69) Hesperia... 
 (70) Panopea.. 
 
 (71) Niobe 
 
 (72) Feronia 
 
 (73) Clytia 
 
 (74) Galatea 
 
 (75) Eurydice.... 
 
 ELEMENTS OF THE SMALL PLANETS. 
 
 Discovery. 
 
 Discoverer. 
 
 Ferguson 
 
 Goldschmidt... 
 
 Chacornac 
 Chacornac 
 Luther 
 
 Goldschmidt .. 
 
 Luther 
 Chacornac 
 Chacornac 
 
 Goldschmidt... 
 
 Goldschmidt.. 
 
 Goldschmidt... 
 Goldschmidt... 
 
 Pogson 
 Luther 
 
 Goldschmidt... 
 Goldschmidt. . 
 
 Ferguson 
 
 Laurent 
 
 Goldschmidt... 
 
 Luther. 
 
 Goldschmidt... 
 
 Searle 
 
 Goldschmidt... 
 
 Luther 
 Luther 
 Chacornac 
 Ferguson 
 
 Goldschmidt... 
 
 Foerster 
 
 Schiaparelli.... 
 Goldschmidt... 
 
 Luther. 
 Peters 
 
 Petersits soko 
 
 Greatest 
 Distance. 
 
 3.49 
 3.09 
 
 3.49 
 
 Distance. 
 
 Periodic 
 
 | Eccentricity. 
 
 Longitude of 
 Perihelion. 
 Longitude 
 
 of Node 
 
 8.6 | 197.9 
 335.5 | 359.9 
 
 Inclination. 
 
 543 
 
 Mean 
 Distance. 
 
544 
 
 0 
 Sign and Name. 3 S 
 hr 
 
 (76) Freia....... 1862 
 (1) Frigga..... 1862 
 (78) Diana...... 1863 
 (79) EKurynome,.| 1863 
 (80) Sappho..... 1864 
 (81) Terpsichore| 1864 
 (82) Alemene ...| 1864 
 (83) Beatrix..... 1865 
 (84) Clio........ 1865 
 (Sb)in Lowe eats. 1865 
 (86) Semele..... 1866 
 (87) Sylvia...... 1866 
 (88) Thisbe.....| 1866 
 
 (89) Julia.......} 1866 
 
 (90) Antiope....| 1866 
 (91) ASgina..... 1866 
 (92) Undina..... 1867 
 (93) Minerva....| 1867 
 (94) Aurora..... 1867 
 (95) Arethusa...| 1867 
 (96) Aigle....... 1868 
 (97) Clotho..... 1868 
 (98) Ianthe..... 1868 
 9S) SDike.\.2vene 1868 
 (100) Hekate..... 1868 
 (101) Helena..... 1868 
 (102) Miriam..... 1868 
 CEOS ELGra (aces 1868 
 (104) Clymene ...| 1868 
 (105) Artemis....| 1868 
 
 (106) Dione...... 1868 
 (107) Camilla ....| 1868 
 (108) Hecuba..... 1869 
 (109) Felicitas ...} 1869 
 @i0)sLydia\.ta.-. 1870 
 
 (UTD) RA COR: sees state 1870 
 (112) Iphigenia ..| 1870 
 (118) Amalthea ..} 1871 
 
 (114) Cassandra..}| 1871 
 (115) Thyra...... 
 
 (116) Sirona...... 1871 
 dit) Lomia. 2 1871 
 (118) Peitho...... 1872 
 (119) Altheea..... 1872 
 
 (120) Lachesis.... 
 
 APPENDIX. 
 
 Sie 3 
 
 Discoverer. 3s Le: z3 
 cal Bes 
 
 // 
 
 IDVArresteent ier 4.00 | 2.82 | 563.7 
 Peters. i.e... 3.03 | 2.31 | 812.2 
 Luther eee 3.16 | 2.08 | 835.3 
 Watson....... 2.92 | 1.97 | 928.9 
 POPsOn i y.cel 2.76 | 1.84 |1019.8 
 Tempel. {622M 3.45 | 2.25 | 736.2 
 Lutherie eee 3.388 | 2.15 | 771.4 
 Gasparis....... 2.64 | 2.22 | 936.7 
 Iutherstee ee 2.92 | 1.80} 976.9 
 Peters. Je... 3.16 | 2.15 | 820.7 
 Tietjen US. .4.% 3.76 | 2.46 | 646.3 
 Pogsonise cs ve: 3.76 | 3.21 | 546.0 
 Parere, 1405i.. 3.21 | 2.82 | 770.2 
 Stephan....... 3.01 | 2.09 | 870.8 
 Uther Sy. ees 3.68 | 2.61 | 636.2 
 Stephan....... 2.87 | 2.31} 851.8 
 eters: 27 35 so: 8.51 | 2.86 | 623.7 
 Watson........ 3.14 | 2.37 | 776.5 
 WiatSOn sees «see 8.441 2.89 | 630.7 
 ibuther, freee 8.52 | 2.63 | 657.7 
 Cogcia at. J. 3.48 | 2.62 | 666.2 
 Tempatse.s. mas 3.36 | 1.98 | 814.2 
 IPetersiiee cect 8.20 | 2.18 | 804.5 
 iBorellyseprasas 8.46 | 2.13 | 758.7 
 Walsoniceesce 3.60 | 2.58 | 652.5 
 WiathOD eee 2.94 | 2.23 | 854.2 
 Peters 24.4; 25 3.47 | 1.86 | 817.0 
 Watson’, ce aa 2.92 | 2.48 | 799.1 
 iW atSONnIe.eeces 3.70 | 2.60 | 635.0 
 Watsons 1 sck 2.79 | 1.96 | 970.1 
 IWATSOMES weenie 8.73 | 2.59 | 631.6 
 POSSOn Weauses 4.00 | 3.12 | 528.2 
 Lhutheriseceeae. 8.54 | 2.88 | 616.4 
 IPELEKS oe. eeeten 3.50 | 1.89 | 802.0 
 Borelly Reece 2.94 | 2.52 | 785.4 
 Peters! teste nc 2.86 | 2.32 | 849.9 
 IPEtOES. ob slorecteg 2.74 | 2.12 | 934.7 
 Tihs 0\:) Meee Serie 2.58 | 2.17 | 968.8 
 -CLCIBine + <icterelos 3.05 | 2.30 | 810.6 
 Witt SOD or ote austere 2.84 | 1.92 | 966.9 
 PPOLeLR IEE era =k 3.16 | 2.37 | 770.9 
 Borel yc isn aa 3.06 | 2.92 | 686.0 
 Luther vk. 7s 2.83 | 2.05 | 931.9 
 Watson........| 2.79 | 2.36 | 855.0 
 Borelly ts 22... 3.27 | 2.97 | 643.5 
 
 Periodic 
 Time. 
 
 Eccentricity. 
 
 ee ee ey | ees ee eee ee 
 
 S a1 36 5 3 
 Be lee] 283 
 Sta | 4 
 ° ° ° 
 92.8 | 212.2} 2.0] 3.409 
 60.4 2.0] 2.5} 2.672 
 121.3 | 334.1] 8.6] 2.623 
 44.4 | 206.7 | 4.6| 2.444 
 355.3 | 218.7 | 8.6] 2.296 
 48.7 2.7 | 7.9 | 2.853 
 132.4 | 27.0] 2.9] 2.766 
 191.8 | 27.5] 5.0} 2.430 
 339.3 | 327.5 | 9.4 | 2.363 
 322.6 | 203.9 | 11.9 | 2.654 
 29.7 | 88.1] 4.8 | 3.112 
 335.4 | 76.1 | 10.9 | 3.482 
 309.3 | 277.6 | 5.2 | 2.769 
 353.4 | 311.7 | 16.2 | 2.551 
 301.1] 71.4] 2.3) 3.145 
 80.3 | 11.1] 2.1 | 2.589 
 330.8 | 102.9 | 9.9 | 3.187 
 274.7 5.1 | 8.6 | 2.754 
 46.0 4.6 | 8.1 | 3.163 
 31.2 | 244.3 | 12.9 | 3.076 
 163.2 | 322.8 | 16.1 | 3.050 
 65.6 | 160.7 | 11.8 | 2.668 
 147.6 | 354.4 | 15.6 | 2.689 
 240.6 | 41.7 | 13.9 | 2.797 
 307.7 | 128.2 | 6.4} 3.092 
 327.4 | 343.7 
 354.6 | 212.0 
 321.0 | 136.3 
 58.2} 44.0 
 242.8 | 188.0 
 27.0 | 63.4 
 112.8 | 175.7 
 173.5 | 852.4 
 56.0 4.9 
 336.8 | 57.2 
 
 204.0 
 342.9 
 
+™ 
 
 Sign and Name. 
 
 (121) Hermione.. 
 (122) Gerda...... 
 (123) Brunhilda.. 
 (124) Alceste..... 
 (125) Liberatrix. . 
 
 (126) Velleda..... 
 (127) Johanna.... 
 (128) Nemesis.... 
 (129) Antigone... 
 (130) Electra..... 
 
 GEST) AVAL. eeate:c 
 (132) Althra...... 
 (133) Cyrene. .... 
 (134) Sophrosyne. 
 (135) Hertha..... 
 
 (136) Austria..... 
 (187) Melibea.... 
 (138) Tolosa...... 
 (139) Juewa...... 
 (140) Siwa.......- 
 
 (141) Lumen..... 
 (142) Polana..... 
 (148) Adria....... 
 (144) Vibilia...... 
 (145) Adeona.... 
 
 (146) Lucina..... 
 (147) Protogeneia 
 (148) Gallia...... 
 (149) Medusa.... 
 (150) Nuwa...... 
 
 (151) Abundantia. 
 (152) Atala... 3... 
 (253) PHI ake 6. « 
 (154) Bertha...... 
 (155) Sceyllaie. sn 
 
 (156) Xanthippe.. 
 (157) Dejanira.... 
 (158) Coronis.... 
 (159) Atmilia... . 
 (160) Wintabarerstee 
 
 (161) *AthOr sn. 
 (162) Laurentia.. 
 (163) Erigone.... 
 (164) Eva........ 
 (165) Loreley .... 
 
 ELEMENTS OF THE SMALL 
 
 Year of 
 Discovery. 
 
 Greatest 
 Distance. 
 
 Least 
 Distance. 
 
 Periodic 
 Time 
 
 1875 
 1875 
 1875 
 1875 
 1875 
 
 1875 
 1875 
 1876 
 1876 
 1876 
 
 1876 
 1876 
 1876 
 1876 
 1876 
 
 Discoverer. 
 Watsond.e.s<: 3.89 
 Peterss.ieteterce 3.34 
 Peters ands oc 3.02 
 Petersaecenes- 2.83 
 Prosper Henry. | 2.96 
 Paul Henry....| 2.70 
 Prosper Henry.| 2.94 
 Watson.).0.....) 5.10 
 Peters teas. 300 3.47 
 PBtErs 35 Go. oe ore Onl 
 Peters.....- 2.62 
 WatsOn cc. 3 ot 3.59 
 Watson.......> 3.48 
 ISHED os onopad 2.87 
 IPOUCTS elacva ater ole 2.93 
 PALIBA te crete se ote 2.48 
 FeO onan. 3.78 
 Perrotinte-a. 9.85 
 WAESOM Saisiea'sicre 8.27 
 Palisa) fetetes\s, <2 3.32 
 Paul Henry... .| 3.28 
 Palisa acieste ss 9.74 
 Palisa sean te 2.96 
 Petersyaacaae se 8.27 
 POleraiieras. oe 3.00 
 Borelly. 202.05. 2.91 
 Schulhof....... 3.22 
 Prosper Henry.| 3.28 
 Perrotinas. +c 2.39 
 Watson..... Teese 
 Palisa.ie. s: scale 2.68 
 Paul Henry....| 3.41 
 Palisa ierccscs oo 4.63 
 Prosper Henry.| 3.46 
 Palisa tvcie<t os 3.66 
 RALISS Hevacrarets of 3.94. 
 Borel yirwces/acie Sele 
 HEMOTIOsciee ce ste 3.02 
 Paul Henry... .| 3.45 
 Peters 2..3..64 .\s 2.90 
 NALS OM cera ate one 2.69 
 Prosper Henry.| 3.56 
 Pervo tines: 9.72 
 Paul Henry....| 3.85 
 Pelersine Sey te 3.36 
 
 931.0 
 775.3 
 T1T.5 
 727.2 
 642.9 
 
 942.3 
 846.4 
 663.6 
 864.6 
 938.1 
 
 9 |1026.4 
 
 641.9 
 926.0 
 765.8 
 786.1 
 
 814.5 
 942.9 
 773.0 
 821.3 
 815.4 
 
 789.9 
 638.7 
 769.5 
 1139.2 
 689.3 
 
 850.7 
 639.0 
 451.6 
 622.4 
 713.8 
 
 670.2 
 854.8 
 730.6 
 647.7 
 787.2 
 
 970.0 
 673.1 
 981.1 
 829.7 
 642.1 
 
 Eccentricity. 
 
 0.125 
 0.040 
 0.122 
 0.077 
 0.077 
 
 0.107 
 0.067 
 0.128 
 0.208 
 0.208 
 
 0.081 
 0.383 
 0.140 
 0.118 
 0.205 
 
 0.084 
 0.208 
 0.162 
 0.177 
 0.217 
 
 0.211 
 0.132 
 0.073 
 0.235 
 0.126 
 
 0.070 
 0.026 
 0.185 
 OnLT9 
 0.131 
 
 0.036 
 0.087 
 0.172 
 0.084 
 0.256 
 
 0.264 
 0.211 
 0.053 
 0.110 
 0.062 
 
 0.136 
 0.177 
 0.156 
 0.347 
 0.076 
 
 PLANETS. 
 
 ty 
 aS 
 Hel 
 o 
 =| 
 im 
 ) 
 Ay 
 
 Longitude of 
 
 ° 
 358.6 
 204.5 
 
 70.0 
 244.8 
 272.9 
 
 347.8 
 120.0 
 16.8 
 241.8 
 20.5 
 
 257.9 
 152.6 
 247.2 
 
 67.5 
 319.9 
 
 316.1 
 308.0 
 311. 4 
 164.6 
 300.3 
 
 13.9 
 219.9 
 222.5 
 
 7.2 
 118.5 
 
 216.1 
 26.0 
 36.1 
 
 246.7 
 
 857.1 
 
 167.3 
 84.9 
 285.8 
 184.4 
 82.0 
 
 156.0 
 107.4 
 58.0 
 101.3 
 56.0 
 
 313.3 
 145.8 
 
 93.8 
 359.6 
 
 Longitude 
 of Node 
 
 3 
 76.8 
 178.7 
 308.5 
 188.4 
 169.5 
 
 23.1 
 31.8 
 76.5 
 187.9 
 146.0 
 
 65.3 
 259.7 
 321.1 
 346.4 
 343.9 
 
 186.1 
 204.4 
 54.8 
 2.4 
 107.1 
 
 319.1 
 292.3 
 333.7 
 76.8 
 07 
 
 84,2 
 251.2 
 145.2 
 160.1 
 
 207.6 
 
 38.9 
 41.6 
 228.3 
 37.7 
 42.9 
 
 246.2 
 62.5 
 281.2 
 135.2 
 9.4 
 
 18.6 
 38.2 
 159.1 
 17.5 
 
 545 
 
 Inclination. 
 
 ° 
 
 24.4 
 
 277.0 | 304.1 | 11.2 
 
 Mean 
 Distance. 
 
 3.459 
 3.215 
 2.695 
 2.630 
 2.744 
 
 2.440 
 2.756 
 2.751 
 2.876 
 3.123 
 
 2.420 
 2.600 
 3.058 
 2.563 
 2.428 
 
 2.286 
 3.126 
 2.449 
 2.779 
 2.731 
 
 2.667 
 2.419 
 2.762 
 2.653 
 2.665 
 
 2.722 
 3.137 
 2.770 
 2.133 
 2.981 
 
 2.591 
 3.136 
 3.952 
 3.191 
 2.913 
 
 3.038 
 2.583 
 2.868 
 3.107 
 2.729 
 
 2.374 
 3.029 
 2.356 
 2.635 
 3.126 
 
546 APPENDIX. 
 
 Bs A ; B/s_|s d : 
 : Bad Ae gilegledigs| £ /24]22/ 4]! 
 Sign and Name. ag Discoverer. SS8/¢8) eo 28 4 24 |2%3 s o 8 
 a SA) aq te”) cee te | ate 
 
 A = 4 fi 
 
 rE <0 8) Gaui. ed ee neers cae ° ° ° 
 (166) Rhodope.....| 1876| Peters........ 3.27 | 2.12] 803.0} 4.42] 0.214 | 30.9 | 129.6 | 12.0 | 2.693 
 (167) Urda........ 1876 Peters...5.5-s 4.22 | 2.22] 614.5) 5.77) 0.312 | 82.7] 170.1] 1.7] 3.219 
 (168) Sibylla...... 1876| Watson....... 3.62 | 3.14] 570.0 | 6.22] 0.071 | 13.0 | 209.8} 4.5] 3.384 
 (169) Zelia. on 5 ee. 1876 | Prosper Henry| 2.67 | 2.05} 978.5) 3.63} 0.131 | 326.9 | 354.6 | 5.5] 2.360 
 (100) Mariasey.y.. . DSi) Perrotiniees sc 2.72 | 2.39 | 868.8 | 4.08] 0.064 | 95.8 | 301.3 | 14.4] 2.555 
 (171) Ophelia..... 1877 j, Borelly tees 3.51 | 2.79 | 635.5] 5.58] 0.118 | 143.6 | 101.2 | 2.6) 3.147 
 (172) Baucis....... 1877} Borelly 2.32.5 2.65| 2.11] 966.4] 3.67} 0.114 | 328.6 | 331.9 | 10.0} 2.380 
 @UG)) NO ba sachio6 6 1877 | Borelly.cc3..> 3.31 | 2.18] 780.2 | 4.55] 0.205 | 13.6 | 148.6 | 14.2] 2.745 
 (74) Pheedra..... 1877 | Watson....... 3.29] 2.43 | 732.1! 4.85} 0.150 | 253.4 | 328.9 | 12.2] 2.864 
 (175) Andromache.| 1877 | Watson....... 4.72 | 2.28 | 541.0] 6.56 | 0.348 | 293.2 | 23.6] 3.8] 3.504 
 (176) Idunna...... 187 Retereteens.. .t 3.71] 2.67} 622.6] 5.70} 0.164 | 20.8 | 201.2 | 22.5} 3.190 
 77) time ceesese 1877 | Paul Henry...| 3.40 | 2.12| 774.7 | 4.55] 0.233 | 25.2 | 349.0 | 1.4] 2.758 
 (178) Belisana..... STG UISA teces tote 2.60 | 2.32 | 920.1 | 3.86] 0.058 | 268.2 | 50.7] 1.9] 2.459 
 (179) Clytemnestra| 1877 | Watson....... 3.30 | 2.65 | 692.2) 5.13] 0.109 | 354.9 | 253.3 | 7.8] 2.973 
 (180) Garumna..../1878| Perrotin...... 3.19 | 2.26] 787.4 | 4.51] 0.170 | 126.6 | 315.0 | 0.9) 2.728 
 (181) Eucharis ....| 1878} Cottenot...... 3.81] 2.43 | 644.0] 5.51] 0.220 | 95.8 | 144.8 | 18.6] 3.119 
 SZ) MHS trys eect. WSS) Palisa cece. ee 2.87] 1.97} 944.0] 3.76] 0.186 | 54.6 | 106.5} 2.0] 2.417 
 (183)PISETIO. Ve eiee « 1878} Palisa........ 3.79 | 1.82 | 756.4 | 4.69] 0.352 | 45.0 | 142.8 | 26.5) 2.802 
 (184) Deiopea..... 1878} Palisa ........| 3.42] 2.96] 623.3 | 5.69) 0.073 | 169.4 | 336.3 | 1.2} 3.188 
 (185) Eunice...... 1878 | Peters: 2a). 2.1 3.09 | 2.39 | 783.1) 4.53] 0.127 | 15.8 | 153.8 | 23.3 | 2.738 
 (186) Celuta...... 1878 | Prosper Henry} 2.72] 2.01] 977.1} 3.63] 0.151 | 327.2 | 14.6 | 13.2] 2.363 
 (187) Lamberta ...|1878 | Coggia ....... 3.38 | 2.10} 782.4 | 4.53 | 0.235 | 213.6 |. 22.3 | 10.7 | 2.740 
 (188) Menippe ....| 1878] Peters........ 3.43 | 2.21} 748.8 | 4.74] 0.217 | 309.7 | 241.8 | 11.4] 2.821 
 (189) Phthia...... 1878 | Peters..-....: 2.54 | 2.36 | 925.0} 3.84] 0.0386 | 6.8 | 203.4 | 5.2} 2.450 
 (190) Ismene...... 1878) Peterse ae. ee 4.57 | 3.30 | 454.1] 7.81] 0.161 | 105.3 | 177.0 | 6.1] 3.938 
 (191) Colga....... 1878 | Peters.......: 3.13 | 2.65] 722.5 | 4.91} 0.082 | 16.4 | 159.9 | 11.5 | 2.889 
 (192) Nausicaa..../ 1879} Palisa........ 2.99 | 1.81] 952.6 | 3.72] 0.246 | 10.6 | 343.3 | 6.9 | 2.403 
 (193) Ambrosia....|1879 | Coggia....... 8.31 | 1.84] 858.3} 4.13] 0.285 | 70.9 | 851.2 | 11.6} 2.576 
 (194) Prokne...... SiO [Peters see see 3.24 | 2.00 | 836.9 | 4.24] 0.237 | 319.7 | 159.4 | 18.4 | 2.619 
 (195) Euryclea....|1879| Palisa........ 3.14] 2.61] 728.9 | 4.87] 0.092 | 106.8} 84] 7.3] 2.872 
 (196) Philomela...|1879| Peters........ 3.10 | 3.07] 653.8 | 5.43 | 0.005 | 352.3 | 73.5 | 7.3) 3.088 
 (107) Arete... .:...}1879] Palisa $2 2...5% 3.20 | 2.29] 781.0) 4.54] 0.165 | 324.8 | 82.1] 8.8] 2.743 
 (198) Ampella..... 1879| Borelly....... 3.01 | 1.90] 922.9 | 3.84] 0.226 | 354.8 | 268.8 | 9.3] 2.454 
 (199) Byblis....... 1879'\ Petets.25s.2.,. 3.72 | 2.69| 618.2 | 5.74 | 0.162 | 260.8 | 90.4 | 15.3] 3.206 
 (200) Dynamene ..| 1879| Peters........ 3.10 | 2.87] 783.3 | 4.53 | 0.183 | 46.6 | 825.4 | 69] 2.738 
 
 (201) Penelope....| 1879} Palisa ........ 3.16 | 2.19] 809.9] 4.38] 0.182 | 334.6 | 157.1 | 5.7] 2.677 
 (202) Chryseis ....|1879| Peters........ 3.38 | 2.79 | 655.0 | 5.42 | 0.097 | 127.7 | 187.8 | 8.8] 3.084 
 (203) Pompeia ....| 1879} Peters........ 2.90 | 2.58] 782.8} 4.53] 0.059 | 43.4 | 348.6 | 3.2] 2.739 
 (204) Callisto...... 1879 | Palisa ........| 3.14] 2.20} 812.0) 4.37] 0.176 | 257.5 | 205.7 | 8.3| 2.673 
 (205) DSTO AAlISA emis «5s 2.88 | 2.68] 766.7 | 4.63 | 0.035 | 21.9 | 212.2 | 10.7 | 2.777 
 
 (206) Hersilia...... 1879) Peters vetescis 4 PPB Pil Bey Steet Phra ae weil gbisicrd |) dreretemell ese gtetelen Mameats | nee 
 (207) 1879 |) Palisawwex a... 2.35 | 2.22 |1027.4 | 3.45] 0.030 | 217.7 | 28.9] 8.8] 2.285 
 (208) 1879 | Palisa-:73....: 3.02 | 2.72 | 729.1) 4.87 | 0.051 | 233.2 7.8 | 2.0] 2.872 
 (209) DIGG: epee. ss 1879 | Peters........ 3.35 | 2.93 | 637.1] 5.57] 0.067 | 259.3 2:0) F221) 3.242 
 
 (210) 1879)) Palisa sees 3.12) 2.37 
 
ELEMENTS OF THE SMALL PLANETS. 547 
 
 3 & €8j/e8] na 18 3 3 & Bae g a 
 
 Sign and Name 8 8 Discoverer. § § 3 5 E 3 Z E £ 2 3 Ee q é § 
 
 ae Ee Sa"a| CR AN) 8 | RE |e bel ee is ote 
 
 IT Yrs ° ° ° 
 
 (211) USTO) | Palisersrrets sets 3.51 | 2.58 | 667.3 | 5.32 | 0.153 | 74.2 | 265.5 | 3.8] 3.046 
 
 (212) 1880) }, Palisa... 3.41 | 2.82 | 644.9 | 5.50) 0.094 | 62.4] 315.0| 4.2] 3.116 
 
 (213) Lileea.......| 1880 | Peters......... 3.14 | 2.35] 779.8 | 4.55 | 0.144 | 284.3 | 122.6 | 6.8] 2.746 
 
 (214) SSO! | PAlSA) surest 2.69 | 2.58) 840.9 | 4.22; 0.031 | 115.9 ; 342.5 | 3.4] 2.611 
 
 (215) Ginone..... T8805) Kenorrel reece": 2.88 | 2.66 | T70.5 | 4.60 | 0.039 | 346.4} 25.4] 1.7 | 2.768 
 
 (216) 1880) | Palisade cee: 3.60 | 1.99 | 759.7 | 4.67| 0.257 | 35.9 | 214.9 | 13.8] 2.794 
 
 (217) Eudora..... 1880 | Coggia........ 4.09 | 2.01 | 665.8 | 5.33 | 0.340 | 307.2 | 164.1 | 11.1) 3.051 
 
 (218) LSSOU Paligaitrscte: eter 2.95 | 2.37] S17.3 | 4.34] 0.108 | 228.7 | 171.0 | 15.1] 2.661 
 
 | (219) TSSO}| Palisa srsrstolste rs. 2.94 | 1.83 | 965.4 | 3.68 | 0.230 | 339.0 | 200.8 | 11.1 | 2.382 
 } (220) 1881 
 
 REMARKS ON THE PRECEDING ELEMENTS OF THE PLANETS. 
 
 Masses.—The masses of many of the planets are still very uncertain, 
 because exact observations have not yet been made long enough to per- 
 mit of their satisfactory determination. The mass of Mercury may be 
 estimated as uncertain by $ of its entire amount; that of Mars by 73 
 that of Venus by 5; those of: the Earth, Uranus, and Neptune by 435; 
 while those of Jupiter and Saturn are probably correct to ziy5. 
 
 The value of the earth’s mass which we have given does not include 
 that of the moon. The mass of the latter is estimated at gz444 that of 
 the earth. 
 
 The masses of Jupiter, Saturn, Uranus, and Neptune which we have 
 cited are all derived from observations of the satellites of these planets. 
 The masses derived from the perturbations of the planets do not differ 
 from them by amounts exceeding the uncertainty of the determinations. 
 The most noteworthy deviation is in the case of Saturn, of which Lever- 
 rier has found the mass to be x345-q, a result entirely incompatible with 
 the observations of the satellites. ae 
 
 Diameters.—These are also uncertain in many cases, especially in those 
 of the outer planets, Uranus and Neptune. The densities which we have 
 assigned to these last-mentioned planets, depending on their masses and 
 diameters, must be regarded as uncertain by half their entire amounts. 
 
 Elliptic Elements.—Of these it may be said that in general they are very 
 accurate for the planets nearest the sun, but diminish in precision as we 
 go outward, those of Neptune being doubtful by one or more minutes. 
 
 Elements of the Small Planets —These are only given approximately, in 
 order that the reader may see the relations of the group at a glance. 
 They are mostly taken from the Berliner Astronomisches Jahrbuch, which 
 gives annually the latest elements known. The elements of the twenty 
 or thirty last ones are very uncertain. 
 
548 APPENDIX. 
 
 VI. 
 
 DETERMINATIONS OF STELLAR PARALLAX. 
 
 TuHE following is a list of the stars the parallaxes of which are known 
 to be investigated, with the results obtained by the different investiga- 
 tors. The years are generally those in which the observations are sup- 
 posed to have been made, but in the case of one or two of the earlier 
 determinations they may be those of the publication of results. In the 
 references the following abbreviations are used : 
 
 A.G. Publicationen der Astronomischen Gesellschaft. 
 
 A.N. Astronomische Nachrichten. 
 
 B. M. Monatsbericht (of the Berlin Academy of Sciences). 
 
 C.R. Comptes Rendus (of the French Academy of Sciences). 
 
 D. O. Astronomical Observation, etc., at Dunsinsk, by Francis Briinnow. 
 2 Parts. Dublin, 1870 and 1874. 
 
 Mel. Mélanges Mathématiques et Astronomiques, Académie de St. Péters- 
 bourg. 
 
 M.N. Monthly Notices of the Royal Astronomical Society. 
 
 M.R.A.S. Memoirs of the Royal Astronomical Society. 
 
 M. P. Mémoires de l’ Académie de Sciences de St. Pétersbourg. 
 
 P.M. Recueil des Mémoires des Astronomes de Poulkowa, publié par W. 
 Struve. St. Pétersbourg, 1853, vol. i. 
 
 R.O. Radcliffe Observations, Oxford. 
 
 Probable 
 
 Star’s Name. Astronomer, and Date. Parallax. Reference. 
 
 Groombridge sei from heliometer mente 
 
 INO. 3406.2. 1863665054. ocicics lest = cle eet oer 
 Pole Star...... Lindenau, from R. A.’s, 1750-1816..... 0.144 seco [UP pnb: 
 W.. Struve, Dorpat, 181821. 7... ... 0.075 veces) sf. y oeleaamepeters 
 
 Struveand Preuss, from R.A.’s,1822-’38] 0.172 pr tattoo 
 Lundahl, from Dorpat declinations...| 0.147 | +.030| ~~ .......- 
 
 Peters, from declinations, 1842—44....| 0.067 ise Melee Le Dales 
 
 Linda eerie chet: areata clei oceiere ler 0.025 | +.018 | P. M., p. 264 
 Capella........ Peters, from declinations, 1842........ 0.046 | +.20 | P. M., p. 136. 
 
 Struve, with Pulkowa equat., 1855....| 0.305 | +.043 | Mel., IL., p. 400. 
 
 DITIUS pe eee Hendersonsi83saencrancce rc ese 0.34 Art og BAO agli go patie &. 
 
DETERMINATIONS OF STELLAR PARALLAX. 549 
 
 Star’s Name. Astronomer, and Date. Parallax. prerare Reference. 
 
 Maclear, 1837 
 ie esea cee from his own and oe M.R.A.S.,xi.,248. 
 lear’s observations 
 
 Gyldén, from Maclear’s obs., 1836~37.| 0.193 ; Mel., ITI., 595. 
 
 Abbe, from Cape obs., 1856-63 0.273 ; M.N., xxviii., p.2. 
 Johnson, with Oxford heliometer, : ; 
 
 i 185455 t 0.210 4 Rs Ov, xvieg Do (Xl) 
 
 Peters, from declinations, 1842 0.133 -106 | P. M., p. 136. 
 
 Winnecke, with heliometer, 1857~"68..| 0.501 ; A. G., No. xi. 
 
 Auwers, 1860-62 0.271 : A. N., No. 1411. 
 
 Kruegersl S62: (hy er nacmateticcernss «oss 0.260 M.N., xxiii., 173. 
 
 Groombridge } wee 
 
 cl g 0.226 . . M., p. : 
 
 No. 1830... § Peters, from declinations, 1842 P. M., p. 136 
 
 Faye, at the Paris Observatory 1.08* o@s | CO) R., xxiii. 
 Wichman, from Schliiter’s observa- 
 
 Ost808 iets. .N. , .29, 
 
 | tions, 1842-"43 PN TRE AR 
 
 eee tb, p. 33. 
 
 Struve, 1847-49 0.034 : P. M., p. 291. 
 
 Re OF SVs Ds 
 (xxii). 
 
 Auwers, from Johnson’s obs. ........ 0.023 ; B. M., 1874. 
 
 Briinnow, 1870-71 0.09 : DO, IE; ps 23. 
 
 Wichmann, from his own obs., 1801 
 
 Johnson, with heliometer, 1854~55....| 0.033 : | 
 
 Oeltzen Arg. : 3 
 N., No. 17415 Krueger, 1862 (?) 0.247 : Me INS xki., 273. 
 
 6 Centauri Moesta, from declinations, 1860~64...| 0.213 : A. N., 1688. 
 Peters, from declinations, 1842 0.127 z P. M., p. 136. 
 
 Johnson, Oxford heliometer, 1845-’55.| 0.138 : ae ae 
 1 (xxiii). 
 
 Henderson, from his meridian obs. 
 
 | at the Cape of Good Hope, 1832~’33. 
 
 a! Centauri, from right ascensions ... 
 
 a! Centauri, from direct declinations. 
 
 a! Centauri, from reflected decs. ..... 
 
 a? Centauri, from right ascensions.... 
 
 a? Centauri, from direct declinations. 
 
 a? Centauri, from reflected decs. ..... 
 
 Mean of all for both stars 
 
 Peters, from the same obs., finds 
 Henderson, from Maclear’s observa- } 
 
 i tions, 1839-’40 
 
 Peters, from the same observations .. 
 
 Maclear, from decs., 1842~"44 and 1848. 
 
 Moesta, from declinations, 1860-64... 
 
 p Ophiuchi Krueger, 1858~’59 
 
 * This result is probably erroneous. 
 
 + These results of Wichmann are parallaxes relative to the mean of certain stars of com- 
 parison. He concluded that one of the latter had a large parallax which made the paral- 
 lax of 1830 Gr. 0’’.72; but this view was afterwards proved wrong. 
 
550 
 
 . Star’s Name. 
 
 p Ophiuchi.... 
 a Lyre ..... ntets 
 
 fe MVR DU pate cn 
 61 Cygni 
 
 APPENDIX. 
 
 Astronomer, and Date. Parallax. 
 
 Krueger, 1858~’62 
 
 Airy, Troughton’s circle, 1836 
 Airy, Jones's circle, 1836..2..6..+-+ | — 0.102 
 Struve, 1837-’40 
 
 Peters, from declinations, 1842 
 Struve, 1851-53 
 
 Johnson, 185455 
 
 Brinnow, 1868-69 
 
 Briinnow, 1870 
 
 Peters, from declinations, 1842 
 Palehat with Koénigsberg ere 
 
 ter, 183S vada 
 
 Bessel, from subsequent obs., 1840....] 0.348 
 Peters, from declinations, 1842 0.349 
 ee with Oxford pees 
 
 0.392 
 
 Auwers, from Johnson’s obs. ........ 0.42 
 Struve, 1852~53 0.506 
 Auwers, from Koénigsberg heliometer.} 0.564 
 
 Probable 
 
 Reference. 
 Error. 
 
 ” 
 
 ct .00T 
 
 IDSOF Parti. 
 D. O., Part II. 
 
 M. P., VII., I., 45. 
 A. N., 141116. 
 
SYNOPSIS OF PAPERS ON SOLAR PARALLAX, 1854~78. 551 
 
 ELLE 
 SYNOPSIS OF PAPERS ON THE SOLAR PARALLAX, 1854~78. 
 
 The following is believed to be a nearly complete list of the determi- 
 nations of the solar parallax which have appeared since the discovery of 
 the error of the old parallax in 1854. No papers have been included ex- 
 cept those which relate immediately to the determination in question. 
 
 1. HANSEN, 1854—WM.N. BR. A. S., xv., p. 9. 
 
 Statement that he finds the coefficient of the parallactic equation of the 
 moon to be 125”.705—a value greater than that deduced from the solar 
 parallax as given by the transits of Venus. 
 
 2. LEVERRIER, 1858—Annales de V Observatoire de Paris, iv., p. 101. ¢ 
 Discussion of solar parallax from lunar equation of the earth, giving 
 8”.95. (In this paper Mr. Stone has found two small numerical errors: 
 correcting them, there results 8’’.85. There is also a doubt about the 
 theory, which might allow the result 8’’.78.) 
 
 3. FOUCAULT, 1862— Comptes Rendus, lv., p. 501. 
 
 Experimental determination of the velocity of light, leading to the value 
 of the solar parallax, 8’’.86. aa 
 
 4. HALL, 1863— Washington Observations for 1863, p. lx. 
 
 Solar parallax, deduced from observations of Mars with equatorial in- 
 struments, in 1862: result, 8.8415. 
 
 5. FERGUSON, 1863— Washington Observations for 1863, p. lxv. 
 
 Solar parallax, deduced from observations with meridian instruments at - 
 Washington, Albany, and Santiago. Results various and discordant, ow- 
 ing to incompleteness of the work. 
 
 6. STONE, 1863—M. N. R. A. S., xxiii., p. 183; Mem. R. A. S., xxxiii., p. 97. 
 
 Discussion of fifty-eight corresponding observations of Mars (twenty-one 
 pairs) at Greenwich, Cape, and Williamstown, leading to 8.943. 
 
552 APPENDIX. 
 
 7. HANSEN, 1863—WM. N. R. A. S., xxiii., p. 243, 
 Deduction of the value 8”.97 from the parallactic inequality of the moon. 
 
 - 
 
 8. HANSEN, 1863—M. N. R. A. S., xxiv., p. 8. 
 A more accurate computation from the same data gives 8’’.9159. 
 
 9. WINNECKE, 1863—Astr. Nachr., lix., col. 261. 
 
 Comparison of twenty-six corresponding observations (thirteen pairs) at 
 Pulkowa and the Cape of Good Hope. Parallax, 8’’.964. 
 
 10. PowaLky, 1864—Doctoral Dissertation, translated in Connaissance des 
 Temps, 1867. 
 
 Discussion of the transit of Venus, 1769. Result, 8’’.832, or 8.86 when 
 the longitude of Chappe’s station is left arbitrary. 
 
 11. STONE, 1867—WM. N. &. A. S., xXxvii., p. 239. 
 
 Attention directed to a slight lack of precision in Hansen’s first paper 
 (No.7). Deduction also from its data of the result 8”.916—agreeing with 
 that from Hansen’s second paper. 
 
 12. STonz, 1867—W. N. R. A. S., xxvii, p. 241. 
 
 Correction of one of the numerical errors in Leverrier’s determination. 
 Result, 8/’.91. 
 
 13. STONE, 1867—M. N. R. A. S., xxvii, p. 271. 
 
 Determination of the parallactic inequality of the moon from 2075 ob- 
 _ servations at Greenwich. Inequality, 125”.36. Solar parallax, 8’’.85. 
 
 14. NEWCoMB, 1867— Washington Observations, 1865, Appendix II. 
 Discussion of the principal methods employed in determining the solar 
 
 parallax, and of all the meridian observations of Mars during the opposi- 
 tion of 1862. Result, 8.848. 
 
 15. STONE, 1867—M. N. R. A. S., xxviii, p. 21. 
 Comparison of Newcomb’s and Leverrier’s determinations of the solar 
 parallax, leading to the detection of another small error in the latter. 
 
 16. STONE, 1868—M. N. R. A. S., xxviii., p. 255. 
 
 Rediscussion of the observations of the transit of Venus, 1769. Only 
 observations of ingress and egress at the same station are used, and certain 
 alterations are made in the usual interpretation of the observations by 
 Chappe in California, and Captain Cook and his companions at Otaheite. 
 The result of these alterations is that the parallax is increased to 8.91. 
 
SYNOPSIS OF PAPERS ON SOLAR PARALLAX, 1854~7%8. 5538 
 
 17. Newcomp, 1868—M. N. R. A. S., xxix., p. 6. 
 
 Criticism of Mr. Stone’s interpretation of Chappe’s dbservation of egress 
 in 1769. 
 
 18. STONE, 1868—W. N. R.A. S., xxix., p. 8. 
 Reply to the preceding paper. 
 
 19. FAYE, 1869—Comptes Rendus, Ixviii., p. 42. 
 
 Examination of the observations and interpretations in Mr. Stone’s 
 paper, concluding that all that we can decide from these observations is 
 that the solar parallax is between 8”.7 and 8’.9. 
 
 20. STONE, 1869—WM. N. R. A. S., xxix., p. 236. 
 
 Reply to Faye, criticism of Powalky’s paper, and further discussions hay- 
 ing for their object to show that the results of his paper agree with the 
 scattered observations of ingress aud egress in Europe and America. 
 
 21. ANONYMOUS, 1869— Vierteljahrsschrift der Astr. Gesel., iv., p. 190. 
 
 General review of recent papers on the solar parallax, dealing more 
 especially with the work of Stone and Powalky. 
 
 22. PowALky, 1870-——Astr. Nachr., lxxvi., col. 161. 
 
 From a second discussion of the transit of Venus, 1769, he deduces 
 8’”.7869. 
 
 23. PoWALKY, 1871—Astr. Nachr., lxxix., col. 25. 
 
 From the mass of the earth as given by the motion of the node of Venus, 
 8'.77. But the adopted mass of Venus enters into the result in such a way 
 as to make it decidedly uncertain. 
 
 24. LEVERRIER, 1872—Comptes Rendus, 1xxv., p. 165. 
 
 Determination of the solar parallax from the mass of the earth as derived 
 from ‘he motions of the planets, and the diminution of the obliquity of the 
 ecliptic. Result, 8.86. (The distinguished author of this paper does not 
 distinctly state in what way he has allowed for the fact that it is the com- 
 bined mass of the earth and moon which is derived from the perturbations 
 of the planets, while it is the mass of the earth alone which enters into the 
 formula for the solar parallax. His presentation of the formule seems to 
 need a slight correction, which will diminish the parallax to 8’.83.) : 
 
 25. CoRNU, 1874-'76— Annales de V Observatoire de Paris, xiii. 
 
 Redetermination of the velocity of light, leading to the parallax 8.794, 
 it Struvé’s constant of aberration (20’. 445) is used. 
 
554 APPENDIX. 
 
 26. GALLE, 1875— Breslau, Maruschke § Berendt. 
 
 “Ueber eine Bestimmung der Sonnen Parallaxe aus correspondirenden 
 Beobachtungen des Planeten Flora, im October und November 1873.” Dis- 
 cussion of observations made at nine northern observatories, and the Cape, 
 Cordoba, and Melbourne, in the southern hemisphere. Result, 8.873. 
 
 27. PUISEUX, 1875—Comptes Rendus, 1xxx., p. 933. 
 
 Computation of four contact observations of the transit of Venus in 1874, 
 made at Peking and St. Paul’s Island. Result, 8’’.879. 
 
 28. Linpsay and GILL, 1877—M. N. Rf. A. S., xxxvii., p. 308. 
 
 Reduction of observations of Juno with a heliometer at Mauritius, in 
 1874. The result is 8’.765; or 8.815 when a discordant observation is 
 rejected. 
 
 29. LINDSAY and GILL, 1877—Dunecht Observatory Publications, ii. 
 
 Observations and discussion from which the preceding result is derived 
 given in full. 
 
 30. Arry, 1877— Government Report on the Telescopic Observations of the 
 _ Transit of Venus. 
 Observations of contacts made by the British expeditions, and prelimi- 
 nary computation of the results for the solar parallax. The results given 
 on page 7 are: 
 
 From all the observations of ingress...............+.. n—8".739 Wt.=10.46 
 From all thesobservations of egress.........0..0<- +s m=8"'.847 Wt.=2.53 
 Combined result. soe sciswiewia ster /sisteis «cle selina wists Seretete lure a=8'’,760 
 
 31. Airy, 1877—WM. N. R. A. S., xxxviii., p. 11. 
 
 More complete discussion of the British observations leading to the 
 mean result, 8’’.754. 
 
 32. STONE, 1878—WM. N. RB. A. S., XXxviil., p. 279. 
 
 Another discussion of the observations contained in Airy’s report (No. 
 30) leading to the following entirely different results: 
 
 From observations of ingress ......c6uasssee~s af ve sear « m=8/’,860--0/’.136 Xe 
 From observations of egress... S.. copes e ek gee ee oan a—8!".979+-0/.279 Xe 
 From all the observations......2....0 +. gaatets banal tla'e m=8/’.884+-0/.123 xe 
 
 33. CAPTAIN G. L. TUPMAN, R. M. A.—WM.. N. &. A. S., xxxviii., p. 334. 
 
 Statement that the treatment of ingress, as exhibited in the Parliament- 
 ary Report, seemed unsatisfactory. The following are his final results: 
 
 Brom:observations Ofineresay. cs cas nsms occ siset'siowe sss. m=8"" 857-E0'’.040 
 LOM ODSENVAUIONN OL COLCSSie cad sche sic sso icv 5is's cine «o/s ie ot ar=8'/,792+0"'.027 
 Brom all ithe Goservatlonss wae icc colts sce + cos «ces cece m=S"".813-40’.933 
 
 Notr.—In the preceding list the abbreviation M. N. R. A. S. represents the Monthly 
 Notices of the Royal Astronomical Society of London, 
 
LIST OF ASTRONOMICAL WORKS. 
 
 Or 
 Or 
 Or 
 
 [X. 
 
 LIST OF ASTRONOMICAL WORKS, MOST OF WHICH HAVE BEEN CON- 
 SULTED AS AUTHORITIES IN THE PREPARATION OF THE PRESENT 
 WORK. 
 
 The following comprises: 1. A few of the leading works of the great 
 astronomers of the past, and of the investigators of the present, arranged 
 nearly in the order of time. In the case of works before 1800, the sup- 
 posed date of composition, or the years within which the author flour- 
 ished, are given. The list is presented for the benefit of those teachers 
 and students who wish to be acquainted with these authorities, and can- 
 not refer to such works as the Bibliographie Astronomique of Lalande, or 
 the Pulkowa Catalogus Librorum. 
 
 2. Modern telescopic researches upon the physical aspects of the planets 
 which have been employed in the preparation of Part III. of the present 
 work. 
 
 3. Recent works on special departments of astronomy, which may be 
 useful to those who wish to pursue special subjects with greater fulness 
 than that with which they are treated in elementary works. 
 
 In the first two classes the selection is, for the most part, limited to 
 works which have been consulted as authorities in the preparation of this 
 treatise. In the case of Hevelius, however, some writings are added 
 which I have not used, nor even seen, with the object of makiif® the list 
 of his larger works complete. Writings which have appeared in period- 
 icals and the transactions of learned societies are necessarily omitted from 
 the list, owing to their great number. S 
 
 The prices given for some of the older books are those for which they 
 are commonly sold by antiquarian dealers in Germany. 
 
 B.o. 250. ARISTARCHUS: De Magnitudinibus et Distantiis Solis et Lune. Pisa, 
 1572. $1. 
 
 A.p. 150. ProLemy, CLAUDE: MEFAAHS SYNTAZEQ®S BIBA. ID, common- 
 ly called The Almagest. 
 
 The most recent edition is by the Abbé Halma, in Greek, with French 
 eueeidta Two vols., 4to. Paris, 1818~16. Commonly sells for 
 8 to ; 
 
556 : APPENDIX. Lo 
 
 880. ALBATEGNIUS: De Scientia Stellarum Liber. Bonn, 1645. 
 
 1543. CopERNICUS: De Revolutionibus Orbium Celestium. 
 
 The first edition of the great work of Copernicus is rare. The second 
 (Basel, 1566) sells for $4. Two fine editions have been published in 
 Germany in recent times. Price $7 to $10. 
 
 1597. TycHo BRAHE: Astronomiew Instaurate Mechanica. Noriberg, 
 1602. $3. 
 
 Contains description of Tycho’s instruments and methods of observing. 
 Astronomie Instaurate Progymnasmata. 
 De Mundi Attherei Recentioribus Phenomenis. Frank- 
 
 fort, 1610. 
 
 These two volumes generally go under the title of the former. A later 
 edition (1648) was issued under the misleading title Opera Omnia. The 
 selling price is $6 for the two. 
 
 1596- KEPLER, JOHANNES: Opera Omnia. Edidit Dr. Ch. Frisch. 8 
 1630. vols., 8vo. Frankfort, 1858~’71. 
 
 A recent and complete edition of Kepler’s voluminous writings. Price 
 
 from $25 to $30. Generally cheaper at second-hand. 
 
 1590- GALILEO GALILEI: Opere. 13 vols., 8vo. Milan, 1811. Price 
 1636. about $10. 
 
 A much better edition, published in 4to, about 1845, is more expensive. 
 Galileo wrote almost entirely in Italian. 
 
 1603. BAYER, JOHANNES: Uranometria. 
 
 Bayer’s celebrated star-charts, in which the stars were first named with 
 Greek letters. Three or more editions were published, the second be- 
 ing in 1648, the third in 1661. $2 50. 
 
 RiccioLtus: Almagestum Novum. 2 vols. in one, folio. Bonn, 1651. 
 
 Astronomia Reformata. Folio. Bonn, 1665. 
 
 Two ambitious works, remarkable rather for their voluminousness than 
 for their value. The author being an ecclesiastic, had to profess a dis- 
 belief in the Copernican system. 
 
 1630. BULLIALDUS: Astronomia Philolaica. Folio. Paris, 1645. 
 
 The last three works are cited as probably the most voluminous com- 
 pendiums of astronomy of the seventeenth century. They can all be 
 purchased for $3 or $4 each. 
 
 1611. Fasritit, J.: De Maculis in Sole Observatis. 
 
 1655. BorELLi: De Vero Telescopii Inventore. Hague, 1655. $1. 
 
 1647—- 
 
 1690 HEVELIUS, J.: Selenographia, sive Lunw Descriptio. Folio. 
 
 ‘The earliest great work on the geography of the moon and the aspects 
 of the planets. Profusely illustrated. $4 to $5. 
 
1659. 
 
 1687. 
 
 1720. 
 
 1728. 
 
 1740. 
 1741. 
 
 LIST OF ASTRONOMICAL WORKS. 55 
 
 aI 
 
 HEVELIUS, J.: Mercurius in Sole Visus. Folio, 1662. $1. 
 
 Contains also Horrox’s observation of the transit of Venus in 1639. 
 Cometographia. Folio, 1668. 
 
 The first great modern treatise on the subject of comets. 
 
 — Machina Celestis, Pars Prior. Folio, 1673. 
 
 Contains descriptions of his instruments, and a disquisition on the prac- 
 tical astronomy of his time. 
 
 Machina Celestis, Pars Posterior. Folio, 1679. 
 
 A very rare book, almost the entire edition having been destroyed by 
 fire. A copy was sold for $50 in 1872, 
 
 Annus Climactericus. Dantzic, 1685. 
 
 Prodromus Astronomie. Dantzic, 1690. 
 Firmamentum Sobiescianum. Dantzic, 1690. 
 These works comprise star-catalogues, star-maps, etc. $3 50. 
 
 HUYGHENS: Systema Saturnium. Hague, 1659. 
 Horologium Oscillatorium. Paris, 1673. 
 
 The latter work contains the theory of the pendulum clock. These two 
 and most of the other important works of Huyghens were published 
 in Leiden in 1751, under the title of Opera Mechanica, Geometrica, As- 
 tronomica et Miscellanea, nominally in four volumes, but the paging is 
 continuous throughout the series, the total number of pages being 
 776. Leiden, 1751. $5. 
 
 NEWTON, Isaac: Philosophie Naturalis Principia Mathematica. Ato. 
 London, 1687. 
 
 A number of editions of Newton’s Principia have appeared. One of the 
 most common is that of Le Seur and Jacquier, 3 vols. in 4. Geneva, 
 1739. It is accompanied by an extended commentary. Sells for about 
 $4. A very fine edition was issued in 1871, by Sir William Thomson, in 
 Glasgow. There is also an English translation by Motte, which has 
 gone through several editions in England and one in America. 
 
 BREWSTER, Sir D.: Memoirs of the Life, Writings, and Discoveries 
 of Sir Isaac Newton. 2 vols.,8vo. Edinburgh, 1855. 
 
 FLAMSTEED, J.: Historia Celestis Britannica. 3 vols., folio. Lon- 
 don, 1725. $10. 
 
 Contains Flamsteed’s observations and star-catalogue. 
 
 BLANCHINI, F.: Hesperi et Phosphori nova Phanomena sive Observa- 
 tiones circa Planetam Veneris. Folio. Rome, 1728. 
 
 Cassini: Elémens d’Astronomie. 4to. Paris, 1740. $1. 
 
 WEIDLER, Jo.: Historia Astronomiew. Small 4to. Wittemberg, 
 1741. $2. 
 
 BERNOUILLI, JOHN: Opera Omnia. 4 vols., 4to. Lausanne, 1742. 
 
 $o. 
 
558 APPENDIX. 
 
 Lr MonnierR: La Théorie des Cométes. 1 vol., 8vo. Paris, 1743. 
 
 $1. 
 
 1760. KANT, IMMANUEL: Schriften zur Physischen Geographie. 8vo. 
 Leipzig, 1839. 
 
 1780. PINGRE: Cométographie; ou Traité Historique et Théorique des Co- 
 méetes. 2 vols.,4to. Paris, 1783. 
 The most complete historical and general treatise on comets which has 
 appeared. 
 1780— ? BaILLy: Histoire de V Astronomie Ancienne depuis son Origine jusqua 
 1790. UV Etablissement de V Ecole d’ Alexandrie. 1vol.,4to. Paris, 1781. $10. 
 
 Histoire de UVAstronomie Moderne depuis la Fondation de 
 UEcole d@ Aleaandrie, jusqwa U Epoque de MDCCXXX. 3 vols., Ato. 
 Paris, 1779. $6. 
 
 Traité de VAstronomie Indienne et Orientale. 1 vol., Ato. 
 Paris, 1787. 
 
 These histories by Bailly are considered very unsound, the author hay- 
 ing a greatly exaggerated opinion of the knowledge of the ancients. 
 
 1800. LALANDE, J. DE: Bibliographie Astronomique; avec U Histoire de 
 UV Astronomie depuis 1781 jusqu’a 1802. 4to. Paris, 1803. $3. 
 
 1817. Lapuace, P.8.: Traité de Mécanique Céleste. 4 vols., 4to. Paris, 
 1799-1805. $60. 
 
 This work is now expensive, all the editions being exhausted. A new 
 edition is soon to be issued. 
 
 Exposition du Systéme du Monde. 1 vol., 4to. $2. 
 
 The latter work gives a very clear popular exposition of the laws of the 
 celestial motions. 
 
 DELAMBRE: Histoire de U Astronomie Ancienne. 2 vols.,4to. Paris, 
 
 1817. $4. 
 Histoire de UV Astronomie du Moyen Age. 1vol.,4to. Paris, 
 1819. $3. 
 
 Histoire de VAstronomie Moderne. 2 vols., 4to. Paris, 
 1821. $5. . 
 
 Histoire de V Astronomie au dix -huitiéme Siecle. 1 vol.,4to. Paris, 
 1827. $3. 
 
 These histories by Delambre consist principally of abstracts of the writ- 
 ings of all eminent astronomers, accompanied by a running commen- 
 tary, but without any attempt at logical arrangement. Each work is 
 taken up and passed through in regular order, but it is only in the in- 
 Pao. essays that general views of the progress of the science are 
 
 ound. 
 
LIST OF ASTRONOMICAL WORKS. 559 
 
 ENCKE, J. F.: Die Entfernung der Sonne von der Erde aus dem Ve- 
 nusdurchgange von 1761 hergeleitet. 12mo. Gotha, 1822. 
 
 Der Venusdurchgang von 1769. 12mo. Gotha, 1824. 
 
 These two little books contain Encke’s researches on the solar parallax 
 leading to the result 8”.5776, and the distance of the sun 95,300,000 
 miles. 
 
 IDELER, Dr. LuDwia: Handbuch der Mathematischen und Technischen 
 Chronologie. 2 vols.,8vo. Berlin, 1825. 
 
 An exhaustive and commendable work on the measures of time adopted 
 in various countries, especially in ancient times. 
 
 ‘WHEWELL, Wo.: History of the Inductive Sciences. London. 
 
 HERSCHEL, Sir JOHN: Results of Astronomical Observations made 
 during the Years 1834, ’5, ’6, ’7, 8, at the Cape of Good Hope. 1 
 vol., 4to. London, 1847. 
 
 STRUVE, F.G.W.: Etudes d Astronomie Stellaire. St. Petersburg, 
 1847. 
 
 GRANT, RoBERT: History of Physical Astronomy, from the Earliest 
 Ages to the Middle of the Nineteenth Century. 8vo. London, 1852. 
 
 Biot, J. B.: Etudes sur VAstronomie Indienne et Chinoise.  8vo. 
 Paris, 1862. : 
 
 LOVERING, JOSEPH: On the Periodicity of the Aurora. Memoirs 
 of the American Academy of Arts and Sciences. Boston, 1859 
 and 1865. 
 
 OLBERS, W., and GALLE, J. G.: Die leichtste und bequemste Methode 
 die Bahn eines Cometen zu berechnen. 8vo. Leipzig, 1864. 
 
 This work contains a table of all orbits of comets computed, brcught up 
 to the end of 1863. 
 
 ZOLLNER, DR. J. C. F.: Ueber die Natur der Kometen. 8vo. Leipzig, 
 1872. 
 
 DwHRING, Dr. E.: Kritische Geschichte der Principien der Mechanik. 
 8vo. Berlin, 1873. 
 
 TODHUNTER, I.: History of the Mathematical Theories of Attraction 
 and the Figure of the Earth, from the Time of Newton to that of La 
 Place. 2vols.,8vo. London, 1873. 
 
 IIl.—WORKS ON THE PHYSICAL ASPECTS OF THE PLANETS. 
 
 SCHROETER, J. H.: Beitrdge zu den Neuesten Astronomischen Ent- 
 deckungen. Herausgegeben von Bode. 3 vols., 8vo. Berlin, 1788— 
 1800. $5. 
 
 37 
 
560 
 
 APPENDIX. 
 
 SCHROETER, J. H.: Selenotopographische Fragmente zur genauern 
 Kenntniss der Mondfltiche. Ato. Lilienthal, 1791. $3. 
 Aphroditographische Fragmente zur genauern Kenntniss des 
 Planeten Venus. Ato. Helmstedt, 1796. $6. 
 
 Schroeter’s style was intolerably prolix and diffuse, so that a clear idea 
 of the results he really attained involves no small labor. 
 
 BEER, W., and MADLER, J. H.: Physische Beobachtungen des Mars 
 bei seiner Opposition im September 1830. 12mo. Berlin, 1830. 
 
 Der Mond nach seinen kosmischen und individuellen Ver- 
 hdltnissen, oder Allgemeine vergleichende Selenographie. 4to. Berlin, 
 1837. $7. 
 
 This volume is accompanied by a large map of the moon, and is the 
 most complete and celebrated work on selenography which has yet 
 appeared. 
 
 BEER, W., and MADLER, J. H.: Beitrdge zur physischen Kenntniss 
 der himmlischen Kérper im Sonnensysteme. 4to. Weimar, 1841. 
 
 ZOLLNER: Photometrische Untersuchungen mit besonderer Riicksicht 
 auf die physische Beschaffenheit der Himmelskérper. 8vo. Leip- 
 zig, 1865. 
 
 ENGELMANN: Ueber die Helligkeitsverhdltnisse der Jupiterstrabanten. 
 8vo. Leipzig, 1871. 
 
 VoGEL, H. C., and Louse: Beobachtungen angestellt auf der Stern- 
 warte des Kammerherrn von Biilow zu Bothkamp. 3 pts.,4to. Leip- 
 zig, 1872-75. 
 
 II] L.—RECENT TREATISES ON SPECIAL SUBJECTS. 
 THE SUN. 
 
 Proctor, R. A.: The Sun: Ruler, Fire, Light, and Life of the Plan- 
 etary System. 8vo. London, 1871. 
 
 LOCKYER, J. N.: Contributions to Solar Physics. 8vo, London, 1874. 
 
 Sreccul, A.: Le Soleil. 2 -vols., 8vo, with Atlas. Paris, 1875-77. 
 The latter is the most complete and beautifully illustrated treatise on 
 the sun which has yet appeared. 
 
 THE Moon. 
 NASMYTH and CARPENTER: The Moon. London, 1874. 
 Contains very beautiful illustrations of lunar scenery. 
 
 Proctor, R. A.: The Moon: Her Motions, Aspects, Scenery, and 
 Physical Condition. 8vo. London, 1873. 
 This work is illustrated with several of Mr. Rutherfurd’s photographs. 
 
LIST OF ASTRONOMICAL WORKS. 561 
 
 NEISON, EDMUND: The Moon, and the Condition and Configurations 
 of its Surface. Wlustrated. 8vo. London, 1876. 
 Principally devoted to selenography. 
 
 TRANSITS OF VENUS. 
 FORBES, GEORGE: Transits of Venus. London, 1874. 
 
 Proctor, R. A.: Transits of Venus. A Popular Account of Past 
 and Coming Transits. 8vo. London, 1875. 
 
 THEORETICAL AND PRACTICAL ASTRONOMY. 
 
 Loomis, Ex1as: An Introduction to Practical Astronomy, with a Col- 
 lection of Astronomical. Tables. 8vo. New York, 1855. 
 
 Contains much information for the amateur astronomer. 
 
 SawitcH: Abriss der Practischen Astronomie. 2 vols., 8vo. Ham- 
 burg, 1850. 
 
 BrUNNow, F.: Practical and Spherical Astronomy. 8vo. London 
 and New York, 1865. 
 
 CHAUVENET, W.: Manual of Spherical and Practical Astronomy. 2 
 vols.,8vo. Philadelphia, 1863. 
 
 The most complete and exhaustive treatise on the subject which has yet 
 appeared. 
 
 WATSON, J.C.: Theoretical Astronomy. 8vo. Philadelphia, 1868. 
 
562 APPENDIX. 
 
 XxX. 
 
 GLOSSARY OF TECHNICAL TERMS OF FREQUENT OCCURRENCE IN 
 ASTRONOMICAL WORKS. 
 
 The following list is believed to include all the technical terms used in 
 the present work, as well as a number of others which the reader of as- 
 tronomical literature will frequently meet with. The words in parenthe- 
 
 ses which sometimes follow a term express its literal signification. 
 
 Aberration (a wandering-away). Generally applied to a real or apparent 
 deviation of the course of a ray of light. Especially (1) an apparent 
 displacement of a star, owing to the progressive motion of ight com- 
 bined with that of the earth in its orbit, p. 211; (2) the defects of action of 
 a lens in not bringing all rays to the same focus. The spherical aberration 
 of a lens results in the rays which pass through the glass near its edge 
 coming to a shorter focus than those which pass near its centre, while 
 the chromatic aberration is the separation of the light of different colors. 
 
 Achromatic (without color). Applied to an object-glass in which rays of 
 different colors are brought to the same focus. See p. 114. 
 
 Aerolite. A meteoric stone or other body falling from the celestial spaces. 
 
 Albedo. Degree of whiteness, or proportion of incident light reflected by 
 a non-luminous body. When the albedo of a body is said to be 0.6, it 
 means that it reflects 55 of the incident light. 
 
 Alidade. A movable frame carrying the microscopes‘or verniers of a grad- 
 uated circle. Not generally used in instruments of recent construction. 
 
 Altitude. The apparent angular elevation of a body above the horizon, 
 usually expressed in degrees and minutes. At the horizon the altitude 
 is zero, at the zenith it is 90°. 
 
 Annular (ring-shaped). Having the appearance or form of a ring. 
 
 Anomaly. The angular distance of a planet from that point of its orbit 
 in which it is nearest to the sun, or, in the ancient astronomy, to the 
 earth. Draw two straight lines from the sun, one to the nearest point 
 of the orbit, or the perihelion, and the other to the planet, and the an- 
 gle between these lines will be the anomaly of the planet. 
 
 Anomalistic. Pertaining to the anomaly. The anomalistic year is the 
 period between two consecutive returns of the earth to its perihelion. 
 It is about 4’ 15” longer than the sidereal year. 
 
GLOSSARY OF TECHNICAL TERMS. 563 
 
 Anse (handles). The apparent ends of the rings of Saturn, which look 
 like handles projecting from the planet. 
 
 Aperture of a Telescope. The diameter of the glass or mirror which 
 admits the rays of light, clear of all obstacles. 
 
 Aphelion. The part of the orbit of a planet in which it is farthest from 
 the sun. 
 
 Apogee. The point of an orbit in which the planet is farthest from the 
 earth. In the ancient astronomy the planets were said to be in apogee 
 when beyond the sun, and therefore at their greatest distance from the 
 earth; but the term is now applied only to the most distant point pt 
 the moon’s orbit. 
 
 Apsis (pl. Apsides). The two points of an orbit which are nearest to, and 
 farthest from, the centre of motion, called, respectively, the lower and 
 higher apsis. The line of apsides is that which joins these two points, 
 and so forms the major axis of an elliptic orbit. The term is now near- 
 ly superseded by the more special terms aphelion, perihelion, perigee, etc. 
 See Llements. 
 
 Armillary Sphere. A combination of circles used before the invention of 
 the telescope for determining the relative directions or apparent posi- 
 tions of the heavenly bodies on the celestial sphere. It is now entirely 
 out of use. See p. 105. 
 
 Astrolabe. A simple form of armillary sphere used by the ancient as- 
 tronomers. 
 
 Azimuth. The angular distance of a point of the horizon from the north 
 or south. The azimuth of a horizontal line is its deviation from the 
 true north and south direction. The azimuth of the east and west 
 points is 90°. 
 
 Binary System. A double eats in which the two components are found 
 to revolve round each other. 
 
 Binocular (two-eyed). Applied to a telescope or microscope in wkteu both 
 eyes can be used at once, as an opera-glass. ' 
 
 Black Drop. A distortion of Mercury or Venus at the time of internal 
 contact with the limb of the sun. See p. 179. 
 
 Centesimal. Reckoning by hundreds. Applied to those denominational 
 systems in which each unit is one hundred times that next below it. 
 The centesimal division of the angle is one in which the quadrant is 
 divided into 100 degrees or grades, the grade into 100 minutes, and the 
 minute into 100 seconds. 
 
 Chronograph (time-mark). An instrument for measuring time by mark- 
 ing on a moving paper (see p. 155). Time is then represented by 
 space passed over. 
 
 Circle, Great. A circle which divides the sphere into two equal hemi- 
 spheres, as the equator and the ecliptic. 
 
564 APPENDIX. 
 
 Colures. The four principal meridians of the celestial sphere, all of which 
 -pass from the pole, and one of which passes through each equinox, and 
 one through each solstice. They mark the circles of 04, 64, 12, and 18 
 of right ascension, respectively. 
 
 Conjunction (a joining). The nearest apparent approach of two heavenly 
 bodies which seem to pass each other in their course. They are com- 
 monly considered as in conjunction when they have the same longitude. 
 The term is applied especially in the case of a planet and the sun. The 
 nearest approach is called superior conjunction when the planet is be- 
 yond the sun, inferior when it is this side of it. Mercury and Venus 
 are, of course, the only planets which can be in inferior conjunction. 
 
 Cosmical. Relating to creation at large, in contradistinction to terres- 
 trial, which relates to the earth. By a cosmical phenomenon is meant 
 one which has its origin outside the earth and its atmosphere. 
 
 Culmination. The passage of a heavenly body over the meridian of a 
 place. This passage may be considered as occurring twice in a day, 
 once above the pole, and again below it, twelve hours later. The for- 
 mer is called the upper, the latter the lower, culmination. The upper 
 culmination of the sun occurs at noon, the lower at midnight. 
 
 Cusps (points). The pointed ends of the seeming horns of the moon or 
 of a planet when it presents the appearance of a crescent. 
 
 Cycle (circle). A period of time at the end of which any aspect or rela- 
 tion of the heavenly bodies recurs, as the Metonic cycle. 
 
 Declination. The angular distance of a heavenly body from the equator. 
 When north of the equator, it is said to be in north declination; other- 
 wise, in south declination. 
 
 Deferent. In the ancient astronomy the mean orbit of a planet which 
 was supposed to carry the epicycle. It is represented by the dotted 
 circles in Figs. 10 and 11, pp. 38 and 39. 
 
 Dichotomy (a cutting in two). The aspect of a planet when half illumi- 
 nated, as the moon at first and last quarter. 
 
 Digit. The twelfth part of the diameter of the sun or moon, formerly 
 used to express the magnitude of eclipses. See p. 28. 
 
 Dip of the Horizon. At sea, the depression of the apparent horizon be- 
 low the true level, owing to the height of the observer’s eye above the 
 water. 
 
 Direct Motion. A motion from west to east among the stars, like that 
 of the planets in general. 
 
 Eccentric. In the ancient astronomy, a circle of which the centre was 
 displaced from the centre of motion. See p. 42, Fig. 13. 
 
 Eccentricity. See Elements. 
 
 Ecliptic. The apparent path of the sun among the stars, described in 
 Part I., Chap. I.,§ 3. See p.13. 
 
GLOSSARY OF TECHNICAL TERMS. 565 
 
 Egress (a going forth). The end of the apparent transit of one body over 
 another, when the former seems to leave the latter. 
 
 Elements. In general, the data for predicting an astronomical phenome- 
 non. Especially, the quantities which determine the motion of a plan- 
 etary body. The independent elements of a planet are six in number, 
 namely : 
 
 1. The mean distance, or half the longer axis, AP, of the ellipse in which 
 the planet moves round the sun, the latter being in the focus at S. 
 
 2. The eccentricity, the ratio of the distance CS between the centre 
 and focus of the ellipse to the mean distance. 
 
 These two elements determine the size and form of the elliptic orbit 
 of the planet. 
 
 Fre. 112.—Diagram illustrating elliptic elements of a planet. 
 
 3. The longitude of the ascending node, which gives the direction of 
 the line in which the plane.of the orbit intersects that of the ecliptic, or 
 the angle which this line makes with the vernal equinox. 
 
 4, The inclination of the plane of the orbit to that of the ecliptic. 
 
 5. The longitude of the perihelion, P, for which is taken the-tongitude 
 of the node, plus the angular distance from the node to the perihelion, 
 as seen from the sun. 
 
 These three quantities determine the position of the orbit in space. 
 
 6. The mean longitude of the planet at some given epoch, or the time 
 at which it passed the perihelion, P. 
 
 To these six the time of revolution, or mean angular motion in a day 
 or year, is usually added; but as this can always be determined from 
 the mean distance, and vice versa, by Kepler’s third law, the two are not 
 regarded as independent elements. 
 
 The quantities we have described are usually represented by algebraic . 
 symbols, as follows: 
 
 a, the mean distance. ® or m, the longitude of the perihelion. 
 e, the eccentricity. e, the mean longitude at some epoch, 
 9 or Q, the longitude of the node. n, the mean motion. 
 
 t or ¢, the inclination. », the distance from node to perihelion, 
 
566 APPENDIX. 
 
 Ellipticity. Deviation from a truly circular or spherical form, so as to 
 become an ellipse or spheroid. An orbit is Said to be more ellip itp the 
 more it deviates from a circle. 
 
 Blongation. The apparent angular distance of a body from its centre of 
 motion, as of Mercury or Venus from the sun, or of a satellite from its 
 primary. 
 
 Emersion (a coming out). The reappearance of an object after being 
 eclipsed or otherwise hidden from view. 
 
 Ephemeris. A table giving the position of a heavenly body from day to 
 day, in order that observers may know where to look for it. Applied 
 also to an astronomical almanac giving a collection of such tables. 
 
 Epicycle. In the ancient astronomy, a small circle the centre of which 
 moves round on the circumference of a larger one, especially the circle 
 in which the three outer planets seemed to perform an annual revolu- 
 tion-in consequence of the revolution of the earth around the sun. 
 
 Equation of the Centre. The angular distance by which a planet mov- 
 ing in an ellipse is ahead of or behind the mean position which it 
 would occupy if it moved uniformly. It arises from the eccentricity of 
 the ellipse, vanishes at perihelion and aphelion, and attains its greatest 
 value nearly half-way between those points. 
 
 Equation of Time. See p. 164. 
 
 Equator. The great circle half-way between the two poles in the earth 
 or heavens. The celestial equator is the line EF in Fig.3,p.12. See 
 also pp. 62, and 146, 147. 
 
 Equatoreal. <A telescope mounted so as to follow a star in its apparent 
 diurnal course, as described on p. 119. 
 
 Equinox. Hither of the two points in which the sun, in its apparent an- 
 nual course among the stars, crosses the equator. So called because the 
 days and nights are, when the sun is at those points, equal. 
 
 Evection. An inequality in virtue of which the moon oscillates about 
 14° on each side of her mean position in a period of 31 days 19 hours. 
 Eye-piece, of a telescope. The small glasses nearest to the eye, which 
 
 magnify the image. See pp. 110 and 118. 
 
 Facule (small torches). Groups of small shining spots on the surface of 
 the sun which are brighter than other parts of the photosphere. They 
 are generally seen in the neighborhood of the dark spots, and are sup- 
 posed to be elevated portions of the photosphere. 
 
 Filar (made of thread). Applied to micrometers made of spider lines. 
 
 Focus (a fireplace). A point in which converging rays all meet. The 
 focus of a telescope is the point at which the image is formed. See p.109. 
 
 Geocentric. Referred to the centre of the earth. The geocentric posi- 
 tion of a heavenly body is its position as seen or measured from the 
 earth’s centre. 
 
GLOSSARY OF TECHNICAL TERMS. 567 
 
 Geodesy. The art or science of measuring the earth without reference 
 to the heavenly bodies. . 
 
 Gnomon. In the old astronomy, the style of a sundial or any object the 
 shadow of which is measured in order to learn the position of the sun. 
 Golden Number. The number of the year in the Metonic cycle, counted 
 
 from 1 to 19. See p. 48. 
 
 Heliacal (relating to the sun). Applied in the ancient astronomy to those 
 risings or settings of bright stars which took place as near to sunrise 
 or sunset as they could be observed. 
 
 Heliocentric. Referred to the sun as a centre. Applied to the positions 
 of the heavenly bodies as seen from the sun’s centre. 
 
 Heliometer. An instrument in which the object-glass is sawed into two 
 equal parts, each of the parts forming an independent image of a heav- 
 enly body in the focus. When the two parts are together in their origi- 
 nal position, these images coincide, but by sliding one part on the other 
 they may be separated as far as is desired for the purposes of measure- 
 ment. It is much used in Germany for measuring distances too great 
 for the application of a filar micrometer. 
 
 Heliostat. An instrument in which a mirror is moved by clock-work in 
 such a way as to reflect the rays of the sun in a fixed direction, notwith- 
 standing the diurnal motion. 
 
 Heliotrope. An instrument invented by Gauss for throwing a ray of sun- 
 light in the direction of a distant station. It is much used in geodetic 
 measurements. 
 
 Hour Angle. The distance of a heavenly body from the meridian, meas- 
 ured by the angle at the pole. It is commonly expressed in time by the 
 number of hours, minutes, etc., since the body crossed the meridian. 
 
 Immersion (a plunging in). The disappearance of a body in the shadow 
 of another, or behind it. 
 
 Inclination, of an orbit. See Elements. a 
 
 Ingress (a going in). The commencement of the transit of one body over 
 the face of another. . 
 
 Latitude. The angular distance of a heavenly body from the ecliptic, as 
 declination is distance from the equator. 
 
 Libration (a slow swinging, as of a balance). The seeming slight oscillations 
 of the moon around her axis, by which we sometimes see a little on one 
 side of her, and sometimes on the other. 
 
 Longitude. Ifa perpendicular be dropped from a body to the ecliptic, its 
 celestial longitude is the distance of the foot of the perpendicular from 
 the vernal equinox counted towards the east. 
 
 Lunation. The period from one change of the moon to the next. Its 
 duration is 294 days, or, more exactly, 29.5305879 days. 
 
 Mass, of a body. The quantity of matter contained in it, as measured 
 
568 APPENDIX. 
 
 by its weight at a given place. Mass differs from weight in that the 
 
 - latter is different in different places even for the same body, depending 
 on the intensity of gravity, whereas the mass of a body is necessarily the 
 same everywhere. 
 
 Mean Distance. See Elements. 
 
 Meridian. The terrestrial meridian of a place is the north and south 
 vertical plane passing through that place, or, the great circle in which 
 this plane intersects the celestial sphere. It passes through the pole, 
 the zenith, and the north and south points of the horizon. Celestial 
 meridians are great circles passing from one pole of the heavens to 
 the other in all directions, as shown in Fig. 45, p. 147. Every celes- 
 tial meridian coincides with the terrestrial meridian of some point on 
 the earth. 
 
 Metonic Cycle. See p. 48. 
 
 Micrometer (small measurer). Any instrument for the accurate measure- 
 ment of very small distances or angles. 
 
 Nadir. The point of the celestial sphere directly beneath our feet, or the 
 direction exactly downwards. 
 
 Node. The point in which an orbit intersects the ecliptic, or other plane 
 of reference. See Hlements, and p. 23. 
 
 Nutation. A very small oscillation of the direction of the earth’s axis. 
 It arises from the fact that the forces which produce the precession of 
 the equinoxes do not act uniformly, and may therefore be considered as 
 the inequality of precession arising from the inequality of the force 
 which produces it. 
 
 Oblate. Applied to a round body which differs from a sphere in being 
 flattened at the poles, as in the case of the earth. 
 
 Obliquity of the Ecliptic. The inclination of the plane of the equator 
 to that of the ecliptic, which is equal to half the difference between the 
 greatest meridian altitude of the sun, which occurs about June 21st, and 
 the least, which occurs about December 21st. At the beginning of 1850 
 its value was about 23° 274’, and it is diminishing at the rate of about 
 .47’’ per century. 
 
 Occultation (a hiding). The disappearance of a distant body through the 
 interposition of a nearer one of greater angular magnitude. Applied 
 especially to the case of the moon passing over a star or planet, and to 
 that of Jupiter hiding one of his satellites. 2 
 
 Opposition. The relation of two bodies in opposite directions. The 
 planets are said to be in opposition when their longitude differs 180° 
 from that of the sun, so that they rise at sunset, and set at sunrise. 
 
 Orbit. The path described by a planet around the sun, or by a satellite 
 around its primary planet. 
 
 Parallax. The difference of direction of a heavenly body as seen from 
 
GLOSSARY OF TECHNICAL TERMS. 569 
 
 two points, as the centre of the earth and some point on its surface. 
 See Part II., Chap. IIL, § 1. 
 
 Parallels. Imaginary circles on the earth or in the heavens parallel to 
 the equator, and having the pole as their centre. The parallel of 40° N. 
 is one which is everywhere 40° from the equator and 50° from the north 
 pole. See Fig. 45, p. 147. 
 
 Penumbra. A partial shadowing. Applied generally in cases where 
 light is partially, but not entirely, cut off. 
 
 Peri- (near). A general prefix to denote the point at which a body revolv- 
 ing in orbit comes nearest its centre of motion; as, perihelion, the point 
 nearest the sun; perigee, that nearest the earth; peri-Saturnium, that 
 nearest the planet Saturn, etc. 
 
 Perturbation. A disturbance in the regular elliptic or other motion of a 
 heavenly body, produced by some force additional to that which causes 
 its regular motion. The perturbations of the planets are caused by 
 their attraction on each other. 
 
 Photometer (light-measurer). An instrument for estimating the intensity 
 of light. The number of kinds of photometers is very great. 
 
 Precession of the Equinoxes. <A motion of the pole of the equator 
 around that of the ecliptic in about 26,000 years. See pp. 19, 62, 88. 
 
 Prime Vertical. The vertical circle passing due east and west through 
 the zenith, and therefore intersecting the horizon in its east and west 
 points. 
 
 Quadrature. The positions of the moon when she is 90° from the sun, 
 and therefore in her first or last quarter. 
 
 Radiant Point. That point of the heavens from which the meteors all 
 seem to diverge during a meteoric shower. See p. 390. 
 
 Refraction (a breaking). The bending of a ray of light by passing through 
 amedium. Astronomical refraction means the refraction of the light of a 
 heavenly body caused by the atmosphere, as described on p. 306. 
 
 Retrograde (backward). Applied to the motion of a planet from east to 
 west among the stars. 
 
 Saros. A period or cycle of 18 years 11 days, in which eclipses recur. 
 See p. 30. 
 
 Scintillation (a twinkling). The twinkling of the stars. 
 
 Secular (relating to the ages). Applied to those changes in the planetary 
 orbits which require immense periods for their completion. See p. 95. 
 Selenography. A description of the surface of the moon, as geography is 
 a description of the earth’s surface. We might call it lunar geography 
 
 but for the etymological absurdity. 
 
 Sexigesimal. Counting by sixties. Applied to those denominate sys- 
 tems in which one unit is sixty times the next inferior one, as the usual 
 subdivision of time and arc. 
 
570 APPENDIX. 
 
 Sextant. The sixth part of a circumference. Also an instrument much 
 used in practical astronomy and navigation, for the ready measurement of 
 the angular distance of two points, or of the altitude of a heavenly body. 
 
 Sidereal. Relating to the stars. Sidereal time is time measured by the 
 diurnal revolution of the stars. Each unit of sidereal time is about 
 325th part shorter than the usual one. See p. 150. 
 
 Signs of the Zodiac. The twelve equal parts into which the ecliptic or 
 zodiac was divided by the ancient astronomers. These signs, begin- 
 ning at the vernal equinox, are: 
 
 Aries, the Ram. Libra, the Balance. 
 
 Taurus, the Bull. Scorpius, the Scorpion. 
 Gemini, the Twins. Sagittarius, the Archer. 
 Cancer, the Crab. Capricornus, the Goat. 
 
 Leo, the Lion. Aquarius, the Water-bearer. 
 Virgo, the Virgin. Pisces, the Fishes. 
 
 Solstices (standing-points of the sun). Those points of the ecliptic which 
 are most distant from the equator, and through which the sun passes 
 about June 21st and December 21st. So called because the sun, having 
 then attained its greatest declination, stops its motion in declination, 
 and begins to return towards the equator. The two solstices are desig- 
 nated as those of summer and winter respectively, the first being in 6 
 hours and the second in 18 hours of right ascension. 
 
 Sothic Period. That in which the Egyptian year of 365 days correspond- 
 ed in succession to all the seasons. The equinoctial year being supposed 
 to be 3654 days, this persod would be 1461 years, but it is really longer. 
 See p. 47. 
 
 Speculum (a mirror). The concave mirror of a reflecting telescope. 
 
 Stationary. Applied to those aspects of the planets occurring between 
 the periods of direct and retrograde motion when they appear for a short 
 time not to move relatively to the stars. 
 
 Synodic. Applied to movements or periods relative to the sun. The 
 synodic movement of a planet is the amount by which its motion ex- 
 ceeds or falls short of that of the earth round the sun, while its synodic 
 period is the time which elapses between two consecutive returns to 
 inferior or superior conjunction, or to opposition. 
 
 Syzygy. The points of the moon’s orbit in which it is either new moon or 
 
 -full moon. The line of the syzygies is that which passes through these 
 points, crossing the orbit of the moon. 
 
 Terminator. The bounding line between light and darkness on the moon 
 
 or a planet. 
 Transit (a passing across). The passage of an object across some fixed line, 
 
 as the meridian, for example, or between the eye of an observer and an 
 apparently larger object beyond, so that the nearer object appears on 
 the face of the more distant one. Applied especially to passages of Mer- 
 
. GLOSSARY OF TECHNICAL TERMS. wen 
 
 cury and Venus over the disk of the sun, and of the satellites of Jupiter 
 over the disk of the planet. 
 
 Trepidation. A slow oscillation of the ecliptic, having a period of 7000 
 years, imagined by the Arabian astronomers to account for the discord- 
 ance in the determinations of the precession of the equinoxes. In con- 
 sequence of this motion the equinox was supposed to oscillate backward 
 and forward through a space of about twenty degrees. The trepidation 
 continued to figure in astronomical tables until the end of the sixteenth 
 century, but it is now known to have no foundation in fact. 
 
 Umbra (a shadow). That darkest part of the shadow of an object where 
 no part of the luminous object can be seen. Also, the interior and dark- 
 est part of a sun-spot. 
 
 Vertical, Angle of. The small angle by which the real direction of the 
 earth’s centre from any point on its surface differs from that which is 
 directly downward, as indicated by the plumb-line. It arises from the 
 elipticity of the earth, vanishes at the equator and poles, and attains its 
 greatest value of about 12’ at the latitude of 45°. 
 
 Vortex (a whirlpool); pl. Vortices. The theory of vortices is that which 
 assumed the heavenly bodies to be carried round in a whirling fluid. 
 See p. 72. 
 
 Zenith. The point of the celestial sphere which is directly overhead, and 
 from which a plumb-line falls. The geocentric zenith is the point*in which 
 a straight line rising from the centre of the earth intersects the celestial 
 sphere. It is a little nearer the celestial equator than the apparent or 
 astronomical zenith, owing to the ellipticity of the earth. See Vertical, 
 Angle of. 
 
 Zodiac. A belt encircling the heavens on each side of the ecliptic, within 
 which the larger planets always remain. Its breadth is generally con- 
 sidered to be about sixteen degrees—eight degrees on each side the 
 ecliptic. In the older astronomy it was divided up into twelve parts, 
 called signs of the zodiac. 
 
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 brmits, nrg 
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 eT ie he 
 
 sank ta he! 
 
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 Aca 
 
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 PAGE 
 
 Abbe, distribution of the nebule......... 464 
 parallax Of SIviussm ss sreitsse ys ce oes 549 
 Aberration of light described........... 213 
 Acceleration of moon’s motion.......... 96 
 Adams determines moon’s acceleration. 96 
 investigates motions of Uranus..... 368 
 Aérolites, description of............ 397, 399 
 Airy, his water telescope 22. ses<-5>- a6 216 
 density: of the earths. ssc sssi0c cs os 46 
 
 A LGOU a VATIA DIG Sisitein yo cresleletele sleet sicietats 438 
 Apparition, circle of perpetual.......... 11 
 Argelander catalogues the stars........ 426 
 AT GUSY hy A VATA DIE Stat sete tcleteltte == 2 oe 440 
 
 Aristarchus attempts to measure the dis- 
 fancer ok thersumieas acne artistes circle 
 
 Asten, motion of Encke’s comet........ 390 
 
 Asteroids:(see also Planets, small).. 329, 542 
 Astrolabe described Wie 4.. 4-48 2.06 ee 107, 558 
 Astronomer Royal, duties of............ 162 
 Attraction of a. mountain’..2.... ssn. 85 
 of. small: massess7 isi venience acts 81 
 AUrOrG, GESCription Ofsi. sees xs 'e alles 309 
 heronty natuney eters steer elerlaacen 310 
 Periodicity: OF. ss ./isede ost Peete dais 255 
 SVCCENITMN OL ses 2 acta reste eters settee 211 
 
 Auwers, motion of Sirius and Procyon.. 451 
 
 Baily determines density of earth ...... 84 
 Baily’s beads explained ................ 314 
 Barker, spectrum of Aurora............ 311 
 Bayer system of naming stars.......... 427 
 Bernoulli (J.) sustains theory of vortices. 80 
 Bessel, parallax of 61 Cygni............. 208 
 Black drop in transits of Venus......... 181 
 
 ItB CAUBGi cormareeere do dcaes Sees 183 
 Blanchini, his great telescope........... 114 
 
 rotationiof Venus desecsses-ceeates 297 
 Bode’s law of planetary distances....... 237 
 Bond discovers satellite of Saturn....... 358 
 
 intensity of moonlight.............. 323 
 
 investigates rings of Saturn......... 358 
 Books, list of, for reference..... ia ass ores 555 
 
 PAGE 
 
 Bradley attacks stellar parallax......... 206 
 detects aberration of light.......... 213 
 Brahe (Tycho), his obs. and system..... 66 
 
 Briimnouw, researches, in stellar parallax. 210 
 
 Calendar; Nistory, €tCrcmcccidene dese ess ne 44 
 Julian and Gregorian............... 49 
 Cassegrainian telescope ................ 126 
 Cassini discovers satellites of Saturn... 360 
 theory of Saturn’swines 4s... eas. 358 
 Cavendish, density of the earth......... 82 
 Cayley determines moon’s acceleration. 98 
 Challis searches for Neptuhe........... 368 
 Chromosphere of the sun.............:. 262 
 its violent movements, etc.......... 268 
 Chronograph described... 0.3.5.3. .6..06 157 
 Circles of the celestial sphere........... 148 
 Clark (Alvan), his telescopes............ 139 
 discovers companion of Sirius...... 140 
 Glustersyof starsi. gs 20. sels sasiea soles 453 
 Comet, event, Of 1680s. ean =... aisle ttace citer 382 
 of 1682 (Halley’s).......... 383 
 
 E1643 B22 8.35 Basics 387 
 
 its near approach to sun.. 265 
 
 of 1858 (Donati’s).......'... 387 
 
 VICWSUOL 2casnnee> 376, 388 
 
 Of Bielaiccaceaccw teadee Bane tees 386, 407 
 
 Of Hnckeiiscs.2 as aaitaieaets Seesl cate las 389 
 Comets, aspects’ of, Cl@zadesiesg es a4 euie- 373 
 developments. . 2 ssudels sis oe secie ase 374 
 relations to meteors...........6.... 402 
 THOUIONS' <6 ses datisaddaciet sete teas 377 
 NUMDEMS «5 cai sis sida pala ole of hoo aad s 381 
 orbits! of; their form... 2.0 i. sees 3TT 
 physical constitution of............. 409 
 remarkable, description of.......... 382 
 tails of, repelled by the sun.. ..... 411 
 Constellations, antiquity of names...... 426 
 Cescriptionrofsea des ads ccesss sels ate 429 
 Copernicus founds modern astronomy.. 51 
 publishes’ his systems 25.42. 0n. ee 53 
 
 his system explained............... 54 
 
574 INDEX. 
 
 PAGE PAGE 
 Copernicus rep. eccentricity of orbits.... 60} Galaxy, or Milky Way, its aspect....... 428 
 his distances of the planets......... 60 | Galileo reinvents the telescope.......... 108 
 estimate of his work. ....--.. 56-2. se’ 61 discovers phases of Venus.......... 296 
 work condemned by Inquisition.... 72 satellites of Jupiter...... 344 
 Cornu measures velocity of light.... 220, 222 resolves the Milky Way............ 420 
 Corona of the sun described ............ 258 | Galle, parallax of asteroids ............. 202 
 its probable nature. os eo... cece 264 optical discoverer of Neptune...... 369 
 its SpeChrum?. oui, ck.. ice teenie 263 | Gentil, his unfortunate voyage.......... 182 
 Cosmogony, the system of............... 503 | Giliiss, expedition to Chili.............. 176 
 Gycte, the MetOniCsc > eniceeicmwiste einem cits 48 | Glacial epoch, its possible cause........ 247 
 Glasenapp, velocity of light............. 216 
 Dean determ. transatlantic longitude.... 161 | Gnomon, its use by the ancients........ 106 
 Delaunay, secular accelerution of moon. 97 | Golden number.....-........-. Soe Dit sisis § 48 
 Density ot the earth sene.-eecee eee. 84 | Gould determ. transatlantic longitude .. 161 
 Descartes’ theory of vortices ............ 72 | Gravitation not newly discovered....... 48 
 Donati’s comet, description of .......... 387 how generalized by Newton........ 76 
 Wid WA8-OL.Acr din AMOS nee teas 376, 388 universal law (of... 02. sees 81 
 Draper, his great telescope.............. 137 exerted by small masses............ 81 
 photograph of the moon............ 319 explains motion of the planets ...98, 102 
 theory of the solar spectrum........ 232 | Grubb constructs Melbourne telescope.. 134 
 Harth; Geusity: Of. senses ve! bs Hacles atate 84 | Hall observes spot on Saturn........... 349 
 elements:of Orbits: Vases. | ve siclectel sores 540 discovers satellites of Mars ..... 329, 331 
 figure of, view of Ptolemy .......... 32 | Halley discovers secular accel. of moon. 96 
 on Newton’s theory....... 86 total eclipseiini171b 2 Feet ee cee 258 
 the French investigations. 87 periodicity of his:comets...2...6...%, 383 
 theory offitsifiniditiy. > 2.6... ce eee 305 proposes obs. of transit of Venus.... 178 
 difficulties of this theory ........... 306 | Hansen, moon’s secular acceleration.... 97 
 temperature of interior.......... 304, 523 solar parallaxss. oss huGes tes eae 184 
 secular cooling Of.t.nc. ta s.beieeaes 523 | Harkness, spectrum of the corona ...... 263 
 Easter, how determined ................ 48 observes meteoric shower.......... 400 
 Eastman, view of total eclipse in 1869 .. 259 | Herschel, his telescopes............ Be ey 128 
 Eccentric in ancient astronomy......... 41 discovery of Uranus {2-- ns. eeeuieee 362 
 Eclipses, geometrical explanation....... 24 of two satellites of Uranus.......... 363 
 CIASSIMICALION: 2/1005 -14 socio tame sete ote 25 his Star: PAUSES howe Meee eaee eeee 418 
 Curation Of... <ciec astaest Jets ie see 28 structure of the universe............ 480 
 ancient observations of............. 257 nebular hypothesis.:2.-- 50.3%... 507 
 seasons and periodic recurrence.... 29 Song of the Telescopes tn sitesi. oe 129 
 totaly phenomenaohee: Aes .ce) 2 >. 258 | Hilgard determ. transatlantic longitude. 161 
 of 1869, general view of....... 259 | Hipparchus observes motions of planets 40 
 observations of....... 263 catalogues the stars. ...2...6ss.cnes 425 
 Heliptic, Gescription Of .....0.c0tse-eeee 15 | Holden investigates satellites of Uranus. 365 
 obliquity explained. ....a4<teelerwert 61 | Hooke, problem of stellar parallax ...... 205 
 Elements of the planetary orbits....540, 565 | Horroz first observes transit of Venus .. 177 
 Encke determines solar parallax........ 183 | Huggins, appearance of suu’s surface... 243 
 investigates resisting medium...... 387 motion of stars in line of sight ..... 468 
 Epicycles, ancient system of ............ 37 spectrum of nebule................. 459 
 explained by Copernicus............ 54 of new star.:-: S-ueeeeee see 447 
 EQuator, COlCStIAl Jens ee ee's- os cee 12, 149 | Huyghens prep. the way for gravitation. 738 
 Evection discovered by Ptolemy......... 43 discovers rings of Saturn........... 350 
 
 Eye-piece of telescope.........c.sseeeee 120 
 
 Inquisition condemns work of Coper- 
 
 Haculce OF TG SUN. ok: rele detesiercsa see BGG) FP MACHS 00.0051. a's is wae ge 72 
 Faye, constitution of the sun........... 279 | Intra-Mercurial planets, supposed. ..102, 287 
 his.comet, motions Ofsin.a-. J.s¥<. 391 pretended observations of...... 2067 293 
 
 Fizeau measures velocity of light....... 219 
 Foucault measures velocity of light..... 220 | Jansen, supposed inventor of telescope.. 109 
 
INDEX. 575 
 LLNS PAGE 
 Janssen analyzes solar protuberances... 260 | Meteors ana shooting-stars.............. 395 
 photographs of the sun............. 244. HOW Cased... 5 ates aoe be. eae eae 398 
 PU DULCE OS DIANEL. . hey driaisle ea eaeaters e's > 339 combustion of, by motion.......... - 899 
 appearance of surface.............-. 340 OUDIES Ob Whi Fi <5 22 .00Re aroje wie eteeeiae 405 
 elements: Of Otbit en sews oaene sss 540 relations £0, Cometssisés oie oss anides 402 
 light and activity of.......... ate sere 342 | Metonic cycle...... SUpE Ce CrGt AREER sotich: 48 
 POLALIOM Of, ON AXISu eee ase eee ek 343 | Milky Way described..............s00-- 498 
 satellites of..... CR SiS ee 344 | Moller, motion of Faye’s comet.......... 398 
 Month, origin OL Ay sides ieee ves: 45-47 
 Kant, structure of the universe......... 474 | Moon, revolution and DNRSES. ahaade tax ee 21 
 founds nebular hypothesis.......... 505 acceleration of its motion .......... 96 
 Kepler investigates motions of planets, 68 unexplained changes of motion..... 98 
 first two laws of planetary motion.. 69 path among the stars............... 23 
 third law ier evaeeeeeose) Sci weed 70 nodes, motion, of: gai. jese sateen 23 
 structure of the universe.. ..-:...... 473 eclipses of, how caused............+ 24 
 gravitation of, found by Newton.... 76 
 Lambert, structure of the universe...... 417 investigations of the ancients....... 42 
 Langley, appearance of the sun......... 242 AEMOSPHELe ss. Was aesadeteneseccuwe 320 
 Heatorcthesunra. pss eh sieaees eect 243 suriace described yaaa s sees ce aee 317 
 on the sun’s constitution........... 286 distance and magnitude............ 312 
 Laplace, cause of moon’s acceleration... 96 figure, rotation, and libration....... 313 
 nebularshypotnesisizaes ace ccs: eres 507 ERANIZOR OL SULIACE action okies erent 322 
 Lassell, his great telescopes............. 133 light.and, heat, of, soce2ssen ee avon 323 
 discovery of satellites .......... 8364, 372 efect on the earthssese cs emer niches 325 
 Latitude, how determ. astronomically... 150 | Music of the spheres...............-.+-- 4 
 Leverrier investigates motion of Mercury 102 
 discovery of Neptune...... alee siete 367 | Nasmyth, appearance of the sun ........ 242 
 Libration of the moon...... i egie Saikiecie 313 | Webwice; appearance: Of renal om cistteleiste 452 
 Tight; MoOwOn Ofaseen ss iiects eletesitese aes 212 VICWS Ofeiees canicies cose ovics .. 460, 462 
 time of coming from sun............ 215 GIBLLIDULLON |. Setosteiee es eeteet ase eet 462 
 VElOCItyaGL, MCASULed spies tenes 217 great, Of. Orioneiy sac tian satiate 2 457 
 Lipperhey an inventor of the telescope. 109 PASCOUSMUALMVEION. 2). eeislduisias-lsioie <lakes 459 
 Lockyer analyzes sun’s protuberances... 261 | Nebular hypothesis...............-..0++ 505 
 Longitude, terrestrial, how found........ 152 reached by reasoning back- 
 the transatlantic........... eee 161 ward from the present... 511 
 Loomis, periodicity of the aurora, etc.... 255 conclusions respecting ..... 526 
 Lovering, periodicity of the aurora..... 255 | Neptune, history of its discovery........ 306 
 Lyman investigates atmosphere of Venus 300 elements Of OLDIb 5. 2c. acessories 540 
 PHYsical aspect Of-ce cme eae eee = 372 
 Mars ctherplanet.«,.....,<tsa:csiaisteisidn gales eee O26 Batellitesof.. wc seas cieittedomcaiiase 312 
 ASWSCE OL sie .y site anise! bw eeatneeen + 327 | Newall, his great telescope..........5-- . 140 
 ClEMED ts OL ORD ils dace «ire cie'elceisic'elersise 540 | Newton (H. A.), meteoric showers....... 402 
 ITV lier at, + gc 1e wi tiariele siete cle ble ae 328, 329 | Newton (Sir 1.), bis work... ...02.0..--- 74 
 EOTAUEGNLO Leen eects ests ninco os SNE 328 laws ofamotioni 274-8 aah 75 
 SALSINGES Olsen ec maitte ele ste stats 5/0!ee.wleyelats 541 theory Of COMES: s.26 cas wis v3.4 sclene 413 
 Maskelyne, attraction of mountain...... 85 
 Maxwell, theory of Saturn’s rings........ 358 | Olbers, hypothesis of the explosion of a: 
 Mercury. the-pIsnelswessmie. sities ts sep ZOO DANS bette sels gees ctteraste as AB Re, Bey Bae 
 elements of orbit......... A BAe 540 | Orbits of the planets.............. . 540, 542 
 ancient theory of....... Banoo nota: 40 
 aspect and rotation... 26.6. 200 290 | Parallax, definition Of..........++++-++» 167 
 motion of perihelion ........... 102, 292 Pia Kose on oboneUOOL: Nestle herewiess’s 172 
 CIADAIES: OF, i bidtae Shade eco g.ke pth Ph ate, 291 solar, measures of......... low gener’ . 173 
 Meridian circle described.........2.5.06. 154 from transit of Venus........ 177 
 Meteorsie, ADOW CLSs 2614 i e10ie 15 olka itis) suahetenae 393 most probable value......... 202 
 radiant point of ..... . 401 list of papers ON........2.+-+- 550 
 
 -produced by comet... 407 
 
 stellar, efforts to find.........ssee0. 204 
 
 38 
 
W 
 
 576 INDEX. 
 
 PAGE PAGR 
 Parallax, list of measures.............0 547 | Saturn, elements of orbit............-.- 540 
 PEi'ce, VINES) OL SALT. .c ileal eleteisi< te aoe 358 TOUMION- Of AXIG Thieves et: eoee 348 
 perturbations of Neptune........... 371 remarkable BpOh Ons sees en aces es 349 
 theory of. comets:.n.tans.citevie nates 414 TINGCS..:.c1. cum tee ae eee ae eee. 349, 358 
 Photosphere, its appearance............. 242 old views @f 7Wgn ca etstthcss ts: 351 
 light and probable nature.......... 269 phases ofii203 225. aie Pele ase « 352 
 Pickering, intensity of sunlight......... 245 satellites of....... elie mare ela eie aes 3 359 
 Planets, the seven, of the ancients........ 14] Schiaparelli theory of meteors.......... 404 
 order of distance, ancient........... 40 | Schonfeld catalogue of variable stars... 441 
 modern...... 235, 239 | Schwabe, periodicity of sun-spots....... 254 
 laws of their motion ............. 69, 93 | Seasons, explanation Of: .2:.2-...0.....- 63 
 secular variations of orbits ......... 95 | Secchi, temperature of the sun.......... 247 
 aspects Of. cnincereh west teleseanraeeat 239 on the sun’s constitution........... 271 
 distances and masses..........-0.+. 237 view of lunarcratetyc..¢..5 eee 321 
 of other suns: -ctle.cemesteee 528 spectrum of nebula........ ens . 459 
 supposed intra-Mercurial........... 102 Secondary spectrum in telescope........ 240) 
 small, fill gap between Mars and Ju- | Seidel, photometric researches........... 425 
 PILE Loo ee elo wie elkete ayn tetelern 831 | Sirius, brillianey Of) c,ess se et eee 425 
 earlier discoveries............ 332 companion Of- c.<es eee ek eee 451 
 number and mass............. 336 | Solar system, relation to the stars ...... 103 
 elements of orbits ........... - 542 StructarerOh's. -ce 214 Mente lean 235 
 Pleiades, map of..... Behan ee siete ete ttate-s 454 PlanOf nein: vee ee ee eeele eee 240 
 Pir lity. Of WOLdSiccaws ssieols'ssie sites cea oie 528 | Spectroscope described............+e0.: 995 
 Pole of the heavens...........:..- Mie. 10 | Spectrum analysis explained......... oe. 229 
 Precession of the equinoxes............. 19 | Sphere, celestial, described. ....t........ * 
 explained by Copernicus ........... 62 circles ofan nee 148 
 cause Of .'...2.. aioe tate stout oie aera alate 88 | Spheres, crystalline, of Pythagoras,..... 8 
 Proctor, arrangement of the stars....... 488 | Stars (see also Universe)..........22000: 419 
 Prominences. See Protuberances. arrangement of, in space....... 472, 490 
 Protuberances of the sun................ 258 binary, systems Of.4. ae ene one 450 
 spectroscopic observation of........ 260 catalogues of ..G Site erate ae ees 495 
 Ptolemy, his system of the world........ 32 changes among thems. y...2. seen 471 
 his answers to objectors............ 35 cliisters7ofs 2.405 2 eee eee eee 453 
 his relations to Copernicus ......... 58 constellations, formation of......... 426 
 his catalogue Ofstars Me .. a.2.6' 1.12 425 description of........ 429 
 Pythagoras, crystalline spheres of...... 8 double. .00i5 65 Hoek BAe eee 448 
 his SUpPOsed System ss. del eae -ulele 4, 52 lightefy how, pradedinavaccetee ene 423 
 H magnitudes of, apparent............ 422 
 Radiant point of meteors.............. . 4013 intringic.. jacd ok ve tea 495 
 Refraction, astronomical...........s000- 306 numberol wisi blere cance ere sete oe 422 
 Reich, density of earth... cic. cesces 1s ee S4 motions of, apparent........... 464, 496 
 Resisting medium, indications of....... 391 inline oMsight 2)... 468 
 researches relating t0......-.......+ 392 Tames, Of NOW GIVE Fe cass d see's Jee be 497 
 RIGS OL SAvULD. «iis 5 2/1 wiele sielieltic eis oes 849 NCAVESt aes wees eh bine oes vecud owutioee 209 
 Rittenhouse observes transit of Venus .. 300 new, explanation of......... ase taee 442 
 Roemer searches for stellar parallax.... 205 BYDEILEC, Olivis.c isles c.u's socaree serene 445 
 Rosse, his great telescope............00.- 133 observations of some.......... 444. 
 heat of the moon i esscd.ee vec noe taes 324 parailazer of. 4.0.5. .53.5 eee 204, 548 
 Rutherford, photographic measurements 186 probable orbits of some............. 488 
 , BYStEMSOl.% 4. bree etoee Re teceeset 46 
 
 Saros, or period of eclipses............ 7650 shooting. See Meteors. 
 Satellites of Jupiter...........000. Dati 344 variable ........ Pad Bie Py sVesen wen dae 
 of Saturn....... secccsscovccoesecs.. a0 | Stone corrects solar parallax..........- . 201 
 of Uranus...... steeitere Ao he Aer 363 | Struve (O.), changes in rings of Saturn.. 355 
 of Neptunes. 71,005 ates Orns seen 372 inner satellites of Uranus.......... . 364 
 Saturn, the planet.......... sesesecessee 346 | Struve (W.) investigates stellar parallax. 207 
 
 aspect of .....+.. 
 
 ee 
 
 parallax ofa Lyr@ivWess oayse ee ere 
 
INDEX 577 
 PAGE PAGE 
 Struve (W.), structure of the Universe... 486) Transits of Mercury............eee2e008 . 291 
 SUE CLO lures aaa a aceiaessises sede erases 521 | Tycho Brahe, his work.........00.+--+e 66 
 ANPEALANCE OL vacacie cscs ajc a, ee 
 atmosphere of....... Sohacleres na ete 246 | Ulugh Beigh, catalogue of stars......... 425 
 GONSHICULION Oli. ciciels eecere ste haw sooo 264) Cariverse, structure Ofc. vers .s ores cece 472 
 brightness of, a8 a star, .....:00 ses - 010 491 stability of, not necessary .......... 502 
 contraction of, probable ............ BID | Uranusg; the planet 2.0 8eik ae dees cones 361 
 distance of, most probable value of. 202 elementSrOn OnDiteecs sees es eehinae 540 
 distance of, methods of finding .. 196 old observations of............ SCRE RUL: 
 enseous: theory Of acer aaciel. qacite esti. 970 satellite of..... eae le Seicieis slate cislsancran eteoOU) 
 heat of, quantity radiated........... 247 deviations of its motion........ site a OOU 
 how maintained........ 253, se 
 lawrobradiationten. + oo. 6 513! Venus, ancient theory of motion........ 39 
 motion, apparent annual .......... . 14 ElementsrotOrihee stasis teiecie eae 540 
 probable real ..... BOP ASR Se 466 general description........ eee acts - 295 
 parallax, how measured.......... 173-203 PRASES. cs (ices cane cass saan emanted ah 296 
 most probable value...... 203 results Of late transit. s. ea sate ood= ee 1i7 
 listiof papersOny.. 2/0! « 551 transits Of. 22. aes. .esces Sailaeisieters LT 
 rotation on axis, law of............. 255 | supposed axial rotation............. 297 
 spots, their appearance............. 248 ALMOSPMETEs. an. sie Saar cteiy saelecete tats 299 
 LHEIP PELIOMICICY.. .. 4% eee see's 254 ADOCELUMI Se toca cesc node weceiech fee 301 
 APPEAL ASiICAVILIES aie. « eroi re ies 251 visibility of dark side..... Saeleatters . 302 
 surroundings of........ pre ne ata fetaiivess 257 satellite of, suspected........ oho oresiets 302 
 LEY OVAL UTC er cris tetera clernensel sree saunsrats 247 | Vogel, photogr. measures of sun’s rays, 245 
 rotation of Venus........ Stolehs othatete ele 299 
 Telescope, origin of ..........- ee eae .- 108 SPECHRUMMTOL AULOLA sero ctd sles arts 311 
 Cra MOAeROLIN Ole .is)s sic'eie'e Wels) <eisis'sials « 110 | views of Encke’s comet............. 375 
 principle of construction of......... NAO ZOTELCES LIVC ON Va Ol sgtelerateln'e'e aleyerertateleierolel alae 72 
 magnifying power of........... 112, 141 
 aberration, defect of....... eiareaet hs, 112 | Walker, motions of Neptune............ 370 » 
 AGIIOTO hl Oars fare cata oltvetste as ais, chars aisles AG) Week, days Of the toc. 22 sacle swraien . 46 
 how mounted for use... ......:..... 120 | Wheatstone revolving mirror........... . 220 
 reflecting, how made. ..2...5..-...% 123 | Winnecke, parallax of a star............. 211 
 great ones of modern times......... 127 | Wolf, periodicity of sun-spots........... 254 
 list of the principal........ See Seon 533 | Wright, spectrum of zodiacal light...... 414 
 Thomson, rigidity of the earth.......... 304 i 
 Tides, how produced........-.... seseeee 90] Year, sidereal and tropical.............. 20 
 friction of, retards earth........ ...- 98} Young, constitution of the sun...... Seen y 
 Time, mean and apparent........ soGnagic 164 researches in spectrum analysis.... 263 
 sidereal... ..... a ore urerenitisage scree Lee 
 See also Calendar. Zodiac, definition Of. ..., cesses csceeces 15 
 Titus, law of planetary distances.... ... 269 signs of..... sal sresitemtaays sia resale as dare LG 
 Transits of stars, how observed......... 156 | Zodiacal light..... eee eels bssinees 1290, 416 
 of Venus, law of recurrence..... .oe. 177 | Zoliner, law of sun’s rotation............ 256 
 old observations ......... 180 nature of photosphere.............-. 270 
 hn TEC Ae ereeontoeanane 185, 192 intensity of moonlight............ 0 B28 
 
 in 1882, where visible..... 196 
 
 theory Of COMEES .....seeereececeees 413 
 
EXPLANATION OF THE STAR MAPS. 
 
 THESE maps show all the stars to the fifth magnitude inclusive be- 
 tween the north pole and 40° south declination, the middle of each map 
 extending to 50° declination. They therefore include all the stars which 
 can be readily seen with the naked eye in our latitudes, except the very 
 smallest. They are, for the most part, founded on Heis’s Atlas Ceelestis 
 and the catalogue accompanying it. 
 
 To recognize the constellations on the maps, reference may be had to 
 the descriptions on pp. 418-426, To find what constellations are on the 
 meridian at any hour of any day in the year, it will be necessary to cal- 
 culate the sidereal time by the precepts on p.151: the corresponding hour 
 of right ascension is then to be sought around the margin of Map L., and 
 at the top and bottom of the other maps. Then, if Map I. be held with 
 this hour upwards, it will show the exact position of the northern constel- 
 lations, while on Maps II.-V. it will show the position of the meridian. 
 Each of these four last maps extends about from the zenith to the south 
 horizon. 
 
 The several dates on the ecliptic show the positions of the sun during 
 its apparent annual course as described in part i., chap. i., § 3, and ex- 
 plained on pp. 54,55. The apparent path of the moon in 1877 is marked 
 out, in order to illustrate § 6, p. 21. 
 
 To illustrate precession, the position of the equator 2000 years ago is 
 shown on Map II., where it can be compared with the present position, 
 marked 0° on the sides of Maps IIl—V. For the same object the circle 
 which the celestial pole seems to describe around the pole of the ecliptic 
 in 25,000 years is shown on Map I. 
 
 The small circles marked here and there on the maps show the positions 
 of the more remarkable nebule and star clusters, a list of which is given 
 in No. III. of the Appendix. 
 
nay 
 
 nH Le i 
 
. 5 Mag. © Nebula or Cluster 
 
 ~ Weenie a hie 
 
 Nd eae 
 
 \ BE 
 Ds 
 
 e 4 Mag : 
 
 e3 Mag. 
 
 ee 
 
 = 
 = 
 ° 
 > 
 ss 
 
 *K 
 
 ~ 
 
 Map I.—The Northern Constellations within 50° of the Pole. 
 
 Fares: 
 
 shales? th AR en 9 ee Pe 
 ral j 
 
 LU 
 
 TAU IR 
 
 fi 
 
 Peal erates ar Sta ny ; ‘ RS x eee 
 a mi Th 0) Ww Ry Re aoe Wal ‘ ta ge oa ' , 
 
 a . \ 
 acer See See . a ens LS ee sine open etre EA re > 
 
 = a ne tg ee 
 
 x auc Neyo Vib. 
 
MK IMay. @2 Mag.- #3Mag. ai Mag, | Pa Mag. 6) Nebula or Clister 
 
 XX 
 
 { 
 
 ee fe Stuy or ve Ete, F 
 
 0 
 
 ; TAUR Ug 
 Lore es ee 
 
 2 
 
 a FO RNAX: 
 
 tL 
 
 Map II.—Southern Constellations visible in Autumn and Winter. 
 
“1May. e2Mag. e3Mag. e4Mag. +«5Mag. © Nebula or Cluster 
 
 PONS 
 
 XUN 
 
 / 
 
 / 
 
 . 
 
 ‘ % » 
 “ “ / 
 ; ‘ 
 
 SEIU ERS, gs re asta Uae ia OE ae tote tel: pe Be 
 
 Mil; 0 00 MER a ee aS ap ee Simo. - VI 
 
 VA iaiel 
 
 Map III.—Southern Constellations visible in Winter and Spring. 
 
—#KIMay. e2Mug. e3Mag. o4Mag. +5Mag. © Nebula cr Cluster 
 AVI VI 
 
 H | ea 
 
 = fos 0) N ge 
 
 Sa 
 
 \ 
 
 ee a os ake canes aaah enema eminent abated went 
 
 Map IV.—Southern Constellations visible in Spring and Summer. 
 
nsisimenthuiens ce ieee es 
 
 a 
 Do 
 
 SE SIV ERS | RTE ES er thn Ae pe omen A WD 
 
 nM 
 S3 
 
 ee COD 
 
 ee 
 
 pings StH BpLORT gear 
 
 FO Wve eT LS ne aT 
 
 = 
 
 eer 
 ‘ 
 
 ° 
 
 “CAPRIC 
 
 UBL HS ms 
 
 XXII 
 
 Map V.—Southern Constellations visible in Summer and Autumn. 
 
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