,note3 ,images of the original pages are available through ,internet ,archive4 ,see http3_/_/archive4org_/details_/asteroids orminor#jjkirkrich ,transcriber's note3 ,text enclosed by underscores is in italics 7italics74 ,every effort has been made to replicate this text as faithfully as possible1 including non-standard spelling and punctuation4 ,some apparent typographical errors in the indices and names of asteroids in ,tables ,i and ,,ii have been corrected4 ,,the ,,asteroids1 ,or ,minor ,planets ,between ,mars and ,jupiter4 by ,,daniel ,,kirkwood1 ,,ll4,d41 ,professor ,emeritus in the ,university of ,indiana2 ,author of ,comets and ,meteors1 ,meteoric ,astronomy1 etc4 ,philadelphia3 ,j4 ,b4 ,lippincott ,company4 #ahhh4 ,copyright1 #ahhg1 by ,daniel ,kirkwood4 ,illustration ,,preface4 ,the rapid progress of discovery in the zone of minor planets1 the anomalous forms and positions of their orbits1 the small size as well as the great number of these telescopic bodies1 and their peculiar relations to ,jupiter1 the massive planet next exterior1--all entitle this part of the system to more particular consideration than it has hitherto received4 ,the following essay is designed1 therefore1 to supply an obvious want4 ,its results are given in some detail up to the date of publication4 ,part ,i4 presents in a popular form the leading historical facts as to the discovery of ,ceres1 ,pallas1 ,juno1 ,vesta1 and ,astra2 a tabular statement of the dates and places of discovery for the entire group2 a list of the names of discoverers1 with the number of minor planets detected by each2 and a table of the principal elements so far as computed4 ,in ,part ,,ii4 this descriptive summary is followed by questions relating to the origin of the cluster2 the elimination of members from particular parts2 the eccentricities and inclinations of the orbits2 and the relation of the zone to comets of short period4 ,the elements are those given in the ,paris ,annuaire for #ahhg1 or in recent numbers of the ,circular zum ,berliner ,astronomischen ,jahrbuch4 ,,daniel ,,kirkwood4 ,,bloomington1 ,,indiana1 ,november1 #ahhg4 ,,contents4 ,,part ,i4 ,,page ,,planetary ,,discoveries ,,before ,,the ,,asteroids ,,were ,,known #i ,,discovery ,,of ,,the ,,first ,,asteroids #aa ,,table ,i4--,,asteroids ,,in ,,the ,,order ,,of ,,their ,,discovery #ag ,,numbers ,,found ,,by ,,the ,,respective ,,discoverers #bc ,,numbers ,,discovered ,,in ,,the ,,different ,,months #be ,,mode ,,of ,,discovery #be ,,names ,,and ,,symbols #be ,,magnitudes ,,of ,,the ,,asteroids #bf ,,orbits ,,of ,,the ,,asteroids #bh ,,table ,,ii4--,,elements ,,of ,,the ,,asteroids #bi ,,part ,,ii4 ,,extent ,,of ,,the ,,zone #cg ,,theory ,,of ,,olbers #ch ,,small ,,mass ,,of ,,the ,,asteroids #ch ,,limits ,,of ,,perihelion ,,distance #ci ,,distribution ,,of ,,the ,,asteroids ,,in ,,space #dj ,,law ,,of ,,gap ,,formation #db ,,commensurability ,,of ,,periods ,,with ,,that ,,of ,,jupiter #dc ,,orders ,,of ,,commensurability #dd ,,elimination ,,of ,,very ,,eccentric ,,orbits #df ,,relations ,,between ,,certain ,,adjacent ,,orbits #dg ,,the ,,eccentricities #dh ,,the ,,inclinations #di ,,longitudes ,,of ,,the ,,perihelia ,,and ,,of ,,the ,,ascending ,,nodes #ej ,,the ,,periods #ea ,,origin ,,of ,,the ,,asteroids #eb ,,variability ,,of ,,certain ,,asteroids #ec ,,the ,,average ,,asteroid ,,orbit #ed ,,the ,,relation ,,of ,,short-,,period ,,comets ,,to ,,the ,,zone ,,of ,,asteroids #ee ,,appendix #ei ,,part ,i4 ,,the ,,asteroids1 ,,or ,,minor ,,planets ,,between ,,mars ,,and ,,jupiter4 #a4 ,introductory4 ,,planetary ,,discoveries ,,before ,,the ,,asteroids ,,were ,,known4 ,the first observer who watched the skies with any degree of care could not fail to notice that while the greater number of stars maintained the same relative places1 a few from night to night were ever changing their positions4 ,the planetary character of ,mercury1 ,venus1 ,mars1 ,jupiter1 and ,saturn was thus known before the dawn of history4 ,the names1 however1 of those who first distinguished them as wanderers are hopelessly lost4 ,venus1 the morning and evening star1 was long regarded as two distinct bodies4 ,the discovery that the change of aspect was due to a single planet's change of position is ascribed to ,pythagoras4 ,at the beginning of the seventeenth century but six primary planets and one satellite were known as members of the solar system4 ,very few1 even of the learned1 had then accepted the theory of ,copernicus2 in fact1 before the invention of the telescope the evidence in its favor was not absolutely conclusive4 ,on the #gth of ,january1 #afaj1 ,galileo first saw the satellites of ,jupiter4 ,the bearing of this discovery on the theory of the universe was sufficiently obvious4 ,such was the prejudice1 however1 against the ,copernican system that some of its opponents denied even the reality of ,galileo's discovery4 ,those satellites1 said a ,tuscan astronomer1 are invisible to the naked eye1 and therefore can exercise no influence on the earth1 and therefore would be useless1 and therefore do not exist4 ,besides1 the ,jews and other ancient nations1 as well as modern ,europeans1 have adopted the division of the week into seven days1 and have named them from the seven planets2 now1 if we increase the number of planets this whole system falls to the ground4 ,no other secondary planet was discovered till ,march #be1 #afee1 when ,titan1 the largest satellite of ,saturn1 was detected by ,huyghens4 ,about two years later 7,december #g1 #afeg7 the same astronomer discovered the true form of ,saturn's ring2 and before the close of the century 7#afga-afhd7 four more satellites1 ,japetus1 ,rhea1 ,tethys1 and ,dione1 were added to the ,saturnian system by the elder ,cassini4 ,our planetary system1 therefore1 as known at the close of the seventeenth century1 consisted of six primary and ten secondary planets4 ,nearly a century had elapsed from the date of ,cassini's discovery of ,dione1 when1 on the #acth of ,march1 #agha1 ,sir ,william ,herschel enlarged the dimensions of our system by the detection of a planet--,uranus--exterior to ,saturn4 ,a few years later 7#aghg-agid7 the same distinguished observer discovered the first and second satellites of ,saturn1 and also the four ,uranian satellites4 ,he was the only planet discoverer of the eighteenth century4 #b4 ,discovery of the ,first ,asteroids4 ,as long ago as the commencement of the seventeenth century the celebrated ,kepler observed that the respective distances of the planets from the sun formed nearly a regular progression4 ,the series1 however1 by which those distances were expressed required the interpolation of a term between ,mars and ,jupiter1--a fact which led the illustrious ,german to predict the discovery of a planet in that interval4 ,this conjecture attracted but little attention till after the discovery of ,uranus1 whose distance was found to harmonize in a remarkable manner with ,kepler's order of progression4 ,such a coincidence was of course regarded with considerable interest4 ,towards the close of the last century ,professor ,bode1 who had given the subject much attention1 published the law of distances which bears his name1 but which1 as he acknowledged1 is due to ,professor ,titius4 ,according to this formula the distances of the planets from ,mercury's orbit form a geometrical series of which the ratio is two4 ,in other words1 if we reckon the distances of ,venus1 the earth1 etc41 from the orbit of ,mercury1 instead of from the sun1 we find that--interpolating a term between ,mars and ,jupiter--the distance of any member of the system is very nearly half that of the next exterior4 ,baron ,de ,zach1 an enthusiastic astronomer1 was greatly interested in ,bode's empirical scheme1 and undertook to determine the elements of the hypothetical planet4 ,in #ahjj a number of astronomers met at ,lilienthal1 organized an astronomical society1 and assigned one twenty-fourth part of the zodiac to each of twenty-four observers1 in order to detect1 if possible1 the unseen planet4 ,when it is remembered that at this time no primary planet had been discovered within the ancient limits of the solar system1 that the object to be looked for was comparatively near us1 and that the so-called law of distances was purely empirical1 the prospect of success1 it is evident1 was extremely uncertain4 ,how long the watch1 if unsuccessful1 might have been continued is doubtful4 ,the object of research1 however1 was fortunately brought to light before the members of the astronomical association had fairly commenced their labors4#a ,on the #ast of ,january1 #ahja1 ,professor ,giuseppe ,piazzi1 of ,palermo1 noticed a star of the eighth magnitude1 not indicated in ,wollaston's catalogue4 ,subsequent observations soon revealed its planetary character1 its mean distance corresponding very nearly with the calculations of ,de ,zach4 ,the discoverer called it ,ceres ,ferdinandea1 in honor of his sovereign1 the ,king of ,naples4 ,in this1 however1 he was not followed by astronomers1 and the planet is now known by the name of ,ceres alone4 ,the discovery of this body was hailed by astronomers with the liveliest gratification as completing the harmony of the system4 ,what1 then1 was their surprise when in the course of a few months this remarkable order was again interrupted6 ,on the #bhth of ,march1 #ahjb1 ,dr4 ,william ,olbers1 of ,bremen1 while examining the relative positions of the small stars along the path of ,ceres1 in order to find that planet with the greater facility1 noticed a star of the seventh or eighth magnitude1 forming with two others an equilateral triangle where he was certain no such configuration existed a few months before4 ,in the course of a few hours its motion was perceptible1 and on the following night it had very sensibly changed its position with respect to the neighboring stars4 ,another planet was therefore detected1 and ,dr4 ,olbers immediately communicated his discovery to ,professor ,bode and ,baron ,de ,zach4 ,in his letter to the former he suggested ,pallas as the name of the new member of the system1--a name which was at once adopted4 ,its orbit1 which was soon computed by ,gauss1 was found to present several striking anomalies4 ,the inclination of its plane to that of the ecliptic was nearly thirty-five degrees1--an amount of deviation altogether extraordinary4 ,the eccentricity also was greater than in the case of any of the old planets4 ,these peculiarities1 together with the fact that the mean distances of ,ceres and ,pallas were nearly the same1 and that their orbits approached very near each other at the intersection of their planes1 suggested the hypothesis that they are fragments of a single original planet1 which1 at a very remote epoch1 was disrupted by some mysterious convulsion4 ,this theory will be considered when we come to discuss the tabulated elements of the minor planets now known4 ,for the convenience of astronomers1 ,professor ,harding1 of ,lilienthal1 undertook the construction of charts of all the small stars near the orbits of ,ceres and ,pallas4 ,on the evening of ,september #a1 #ahjd1 while engaged in observations for this purpose1 he noticed a star of the eighth magnitude not mentioned in the great catalogue of ,lalande4 ,this proved to be a third member of the group of asteroids4 ,the discovery was first announced to ,dr4 ,olbers1 who observed the planet at ,bremen on the evening of ,september #g4 ,before ,ceres had been generally adopted by astronomers as the name of the first asteroid1 ,laplace had expressed a preference for ,juno4 ,this1 however1 the discoverer was unwilling to accept4 ,mr4 ,harding1 like ,laplace1 deeming it appropriate to place ,juno near ,jupiter1 selected the name for the third minor planet1 which is accordingly known by this designation4 ,juno is distinguished among the first asteroids by the great eccentricity of its orbit1 amounting to more than #j4be4 ,its least and its greatest distances from the sun are therefore to each other very nearly in the ratio of three to five4 ,the planet consequently receives nearly three times as much light and heat in perihelion as in aphelion4 ,it follows1 also1 that the half of the orbit nearest the sun is described in about eighteen months1 while the remainder1 or more distant half1 is not passed over in much less than three years4 ,schroeter noticed a variation in the light of ,juno1 which he supposed to be produced by an axial rotation in about twenty-seven hours4 ,the fact that ,juno was discovered not far from the point at which the orbit of ,pallas approaches very near that of ,ceres1 was considered a strong confirmation of the hypothesis that the asteroids were produced by the explosion of a large planet2 for in case this hypothesis be founded in truth1 it is evident that whatever may have been the forms of the various orbits assumed by the fragments1 they must all return to the point of separation4 ,in order1 therefore1 to detect other members of the group1 ,dr4 ,olbers undertook a systematic examination of the two opposite regions of the heavens through which they must pass4 ,this search was prosecuted with great industry and perseverance till ultimately crowned with success4 ,on the #bith of ,march1 #ahjg1 while sweeping over one of those regions through which the orbits of the known asteroids passed1 a star of the sixth magnitude was observed where none had been seen at previous examinations4 ,its planetary character1 which was immediately suspected1 was confirmed by observation1 its motion being detected on the very evening of its discovery4 ,this fortunate result afforded the first instance of the discovery of two primary planets by the same observer4 ,the astronomer ,gauss having been requested to name the new planet1 fixed upon ,vesta1 a name universally accepted4 ,though the brightest of the asteroids1 its apparent diameter is too small to be accurately determined1 and hence its real magnitude is not well ascertained4 ,professor ,harrington1 of ,ann ,arbor1 has estimated the diameter at five hundred and twenty miles4 ,according to others1 however1 it does not exceed three hundred4 ,if the latter be correct1 the volume is about #a_/bjjjj that of the earth4 ,it is remarkable that notwithstanding its diminutive size it may be seen under favorable circumstances by the naked eye4 ,encouraged by the discovery of ,vesta 7which he regarded as almost a demonstration of his favorite theory71 ,dr4 ,olbers continued his systematic search for other planetary fragments4 ,not meeting1 however1 with further success1 he relinquished his observations in #ahaf4 ,his failure1 it may here be remarked1 was doubtless owing to the fact that his examination was limited to stars of the seventh and eighth magnitudes4 ,the search for new planets was next resumed about #ahca1 by ,herr ,hencke1 of ,driessen4 ,with a zeal and perseverance worthy of all praise1 this amateur astronomer employed himself in a strict examination of the heavens represented by the ,maps of the ,berlin ,academy4 ,these maps extend fifteen degrees on each side of the equator1 and contain all stars down to the ninth magnitude and many of the tenth4 ,dr4 ,hencke rendered some of these charts still more complete by the insertion of smaller stars2 or rather1 made for himself special charts of particular districts4 ,on the evening of ,december #h1 #ahde1 he observed a star of the ninth magnitude where none had been previously seen1 as he knew from the fact that it was neither found on his own chart nor given on that of the ,academy4 ,on the next morning he wrote to ,professors ,encke and ,schumacher informing them of his supposed discovery4 ,it is very improbable1 he remarked in his letter to the latter1 that this should prove to be merely a variable star1 since in my former observations of this region1 which have been continued for many years1 ,i have never detected the slightest trace of it4 ,the new star was soon seen at the principal observatories of ,europe1 and its planetary character satisfactorily established4 ,the selection of a name was left by the discoverer to ,professor ,encke1 who chose that of ,astra4 ,the facts in regard to the very numerous subsequent discoveries may best be presented in a tabular form4 ,,table ,i4 ,the ,asteroids in the ,order of their ,discovery4 ---------------------------------------- -------------------- ,asteroids4 ,date of ,name of ,place of ,discovery4 ,discoverer4 ,discovery4 ---------------------------------------- -------------------- #a4 ,ceres #ahja1 ,jan4 #a ,piazzi ,palermo #b4 ,pallas #ahjb1 ,mar4 #bh ,olbers ,bremen #c4 ,juno #ahjd1 ,sept4 #a ,harding ,lilienthal #d4 ,vesta #ahjg1 ,mar4 #bi ,olbers ,bremen #e4 ,astra #ahde1 ,dec4 #h ,hencke ,driessen #f4 ,hebe #ahdg1 ,july #a ,hencke ,driessen #g4 ,iris #ahdg1 ,aug4 #ad ,hind ,london #h4 ,flora #ahdg1 ,oct4 #ah ,hind ,london #i4 ,metis #ahdh1 ,apr4 #bf ,graham ,markree #aj4 ,hygeia #ahdi1 ,apr4 #ab ,de ,gasparis ,naples #aa4 ,parthenope #ahej1 ,may #aa ,de ,gasparis ,naples #ab4 ,victoria #ahej1 ,sept4 #ac ,hind ,london #ac4 ,egeria #ahej1 ,nov4 #b ,de ,gasparis ,naples #ad4 ,irene #ahea1 ,may #ai ,hind ,london #ae4 ,eunomia #ahea1 ,july #bi ,de ,gasparis ,naples #af4 ,psyche #aheb1 ,mar4 #ag ,de ,gasparis ,naples #ag4 ,thetis #aheb1 ,apr4 #ag ,luther ,bilk #ah4 ,melpomene #aheb1 ,june #bd ,hind ,london #ai4 ,fortuna #aheb1 ,aug4 #bb ,hind ,london #bj4 ,massalia #aheb1 ,sept4 #ai ,de ,gasparis ,naples #ba4 ,lutetia #aheb1 ,nov4 #ae ,goldschmidt ,paris #bb4 ,calliope #aheb1 ,nov4 #af ,hind ,london #bc4 ,thalia #aheb1 ,dec4 #ae ,hind ,london #bd4 ,themis #ahec1 ,apr4 #e ,de ,gasparis ,naples #be4 ,phocea #ahec1 ,apr4 #f ,chacornac ,marseilles #bf4 ,proserpine #ahec1 ,may #e ,luther ,bilk #bg4 ,euterpe #ahec1 ,nov4 #h ,hind ,london #bh4 ,bellona #ahed1 ,mar4 #a ,luther ,bilk #bi4 ,amphitrite #ahed1 ,mar4 #a ,marth ,london #cj4 ,urania #ahed1 ,july #bb ,hind ,london #ca4 ,euphrosyne #ahed1 ,sept4 #a ,ferguson ,washington #cb4 ,pomona #ahed1 ,oct4 #bf ,goldschmidt ,paris #cc4 ,polyhymnia #ahed1 ,oct4 #bh ,chacornac ,paris #cd4 ,circe #ahee1 ,apr4 #f ,chacornac ,paris #ce4 ,leucothea #ahee1 ,apr4 #ai ,luther ,bilk #cf4 ,atalanta #ahee1 ,oct4 #e ,goldschmidt ,paris #cg4 ,fides #ahee1 ,oct4 #e ,luther ,bilk #ch4 ,leda #ahef1 ,jan4 #ab ,chacornac ,paris #ci4 ,ltitia #ahef1 ,feb4 #h ,chacornac ,paris #dj4 ,harmonia #ahef1 ,mar4 #ca ,goldschmidt ,paris #da4 ,daphne #ahef1 ,may #bb ,goldschmidt ,paris #db4 ,isis #ahef1 ,may #bc ,pogson ,oxford #dc4 ,ariadne #aheg1 ,apr4 #ae ,pogson ,oxford #dd4 ,nysa #aheg1 ,may #bg ,goldschmidt ,paris #de4 ,eugenia #aheg1 ,june #bg ,goldschmidt ,paris #df4 ,hestia #aheg1 ,aug4 #af ,pogson ,oxford #dg4 ,aglaia #aheg1 ,sept4 #ae ,luther ,bilk #dh4 ,doris #aheg1 ,sept4 #ai ,goldschmidt ,paris #di4 ,pales #aheg1 ,sept4 #ai ,goldschmidt ,paris #ej4 ,virginia #aheg1 ,oct4 #d ,ferguson ,washington #ea4 ,nemausa #aheh1 ,jan4 #bb ,laurent ,nismes #eb4 ,europa #aheh1 ,feb4 #d ,goldschmidt ,paris #ec4 ,calypso #aheh1 ,apr4 #d ,luther ,bilk #ed4 ,alexandra #aheh1 ,sept4 #aj ,goldschmidt ,paris #ee4 ,pandora #aheh1 ,sept4 #aj ,searle ,albany #ef4 ,melete #aheg1 ,sept4 #i ,goldschmidt ,paris #eg4 ,mnemosyne #ahei1 ,sept4 #bb ,luther ,bilk #eh4 ,concordia #ahfj1 ,mar4 #bd ,luther ,bilk #ei4 ,olympia #ahfj1 ,sept4 #ab ,chacornac ,paris #fj4 ,echo #ahfj1 ,sept4 #af ,ferguson ,washington #fa4 ,dana #ahfj1 ,sept4 #i ,goldschmidt ,paris #fb4 ,erato #ahfj1 ,sept4 #ad ,foerster and ,berlin ,lesser #fc4 ,ausonia #ahfa1 ,feb4 #aj ,de ,gasparis ,naples #fd4 ,angelina #ahfa1 ,mar4 #d ,tempel ,marseilles #fe4 ,maximiliana #ahfa1 ,mar4 #h ,tempel ,marseilles #ff4 ,maia #ahfa1 ,apr4 #i ,tuttle ,cambridge1 ,u4,s4 #fg4 ,asia #ahfa1 ,apr4 #ag ,pogson ,madras #fh4 ,leto #ahfa1 ,apr4 #bi ,luther ,bilk #fi4 ,hesperia #ahfa1 ,apr4 #bi ,schiaparelli ,milan #gj4 ,panopea #ahfa1 ,may #e ,goldschmidt ,paris #ga4 ,niobe #ahfa1 ,aug4 #ac ,luther ,bilk #gb4 ,feronia #ahfb1 ,may #bi ,peters and ,clinton ,safford #gc4 ,clytie #ahfb1 ,apr4 #g ,tuttle ,cambridge #gd4 ,galatea #ahfb1 ,aug4 #bi ,tempel ,marseilles #ge4 ,eurydice #ahfb1 ,sept4 #bb ,peters ,clinton #gf4 ,freia #ahfb1 ,oct4 #ba ,d',arrest ,copenhagen #gg4 ,frigga #ahfb1 ,nov4 #ab ,peters ,clinton #gh4 ,diana #ahfc1 ,mar4 #ae ,luther ,bilk #gi4 ,eurynome #ahfc1 ,sept4 #ad ,watson ,ann ,arbor #hj4 ,sappho #ahfd1 ,may #b ,pogson ,madras #ha4 ,terpsichore #ahfd1 ,sept4 #cj ,tempel ,marseilles #hb4 ,alcmene #ahfd1 ,nov4 #bg ,luther ,bilk #hc4 ,beatrix #ahfe1 ,apr4 #bf ,de ,gasparis ,naples #hd4 ,clio #ahfe1 ,aug4 #be ,luther ,bilk #he4 ,io #ahfe1 ,sept4 #ai ,peters ,clinton #hf4 ,semele #ahff1 ,jan4 #ad ,tietjen ,berlin #hg4 ,sylvia #ahff1 ,may #af ,pogson ,madras #hh4 ,thisbe #ahff1 ,june #ae ,peters ,clinton #hi4 ,julia #ahff1 ,aug4 #f ,stephan ,marseilles #ij4 ,antiope #ahff1 ,oct4 #a ,luther ,bilk #ia4 gina #ahff1 ,nov4 #d ,borelly ,marseilles #ib4 ,undina #ahfg1 ,july #g ,peters ,clinton #ic4 ,minerva #ahfg1 ,aug4 #bd ,watson ,ann ,arbor #id4 ,aurora #ahfg1 ,sept4 #f ,watson ,ann ,arbor #ie4 ,arethusa #ahfg1 ,nov4 #bd ,luther ,bilk #if4 gle #ahfh1 ,feb4 #ag ,coggia ,marseilles #ig4 ,clotho #ahfh1 ,feb4 #ag ,coggia ,marseilles #ih4 ,ianthe #ahfh1 ,apr4 #ah ,peters ,clinton #ii4 ,dike #ahfh1 ,may #bh ,borelly ,marseilles #ajj4 ,hecate #ahfh1 ,july #aa ,watson ,ann ,arbor #aja4 ,helena #ahfh1 ,aug4 #ae ,watson ,ann ,arbor #ajb4 ,miriam #ahfh1 ,aug4 #bb ,peters ,clinton #ajc4 ,hera #ahfh1 ,sept4 #g ,watson ,ann ,arbor #ajd4 ,clymene #ahfh1 ,sept4 #ac ,watson ,ann ,arbor #aje4 ,artemis #ahfh1 ,sept4 #af ,watson ,ann ,arbor #ajf4 ,dione #ahfh1 ,oct4 #aj ,watson ,ann ,arbor #ajg4 ,camilla #ahfh1 ,nov4 #ag ,pogson ,madras #ajh4 ,hecuba #ahfi1 ,apr4 #b ,luther ,bilk #aji4 ,felicitas #ahfi1 ,oct4 #i ,peters ,clinton #aaj4 ,lydia #ahgj1 ,apr4 #ai ,borelly ,marseilles #aaa4 ,ate #ahgj1 ,aug4 #ad ,peters ,clinton #aab4 ,iphigenia #ahgj1 ,sept4 #ai ,peters ,clinton #aac4 ,amalthea #ahga1 ,mar4 #ab ,luther ,bilk #aad4 ,cassandra #ahga1 ,july #bc ,peters ,clinton #aae4 ,thyra #ahga1 ,aug4 #f ,watson ,ann ,arbor #aaf4 ,sirona #ahga1 ,sept4 #h ,peters ,clinton #aag4 ,lomia #ahga1 ,sept4 #ab ,borelly ,marseilles #aah4 ,peitho #ahgb1 ,mar4 #ae ,luther ,bilk #aai4 ,althea #ahgb1 ,apr4 #c ,watson ,ann ,arbor #abj4 ,lachesis #ahgb1 ,apr4 #aj ,borelly ,marseilles #aba4 ,hermione #ahgb1 ,may #ab ,watson ,ann ,arbor #abb4 ,gerda #ahgb1 ,july #ca ,peters ,clinton #abc4 ,brunhilda #ahgb1 ,july #ca ,peters ,clinton #abd4 ,alceste #ahgb1 ,aug4 #bc ,peters ,clinton #abe4 ,liberatrix #ahgb1 ,sept4 #aa ,prosper ,henry ,paris #abf4 ,velleda #ahgb1 ,nov4 #e ,paul ,henry ,paris #abg4 ,johanna #ahgb1 ,nov4 #e ,prosper ,henry ,paris #abh4 ,nemesis #ahgb1 ,nov4 #be ,watson ,ann ,arbor #abi4 ,antigone #ahgc1 ,feb4 #e ,peters ,clinton #acj4 ,electra #ahgc1 ,feb4 #ag ,peters ,clinton #aca4 ,vala #ahgc1 ,may #bd ,peters ,clinton #acb4 thra #ahgc1 ,june #ac ,watson ,ann ,arbor #acc4 ,cyrene #ahgc1 ,aug4 #af ,watson ,ann ,arbor #acd4 ,sophrosyne #ahgc1 ,sept4 #bg ,luther ,bilk #ace4 ,hertha #ahgd1 ,feb4 #ah ,peters ,clinton #acf4 ,austria #ahgd1 ,mar4 #ah ,palisa ,pola #acg4 ,meliba #ahgd1 ,apr4 #ba ,palisa ,pola #ach4 ,tolosa #ahgd1 ,may #ai ,perrotin ,toulouse #aci4 ,juewa #ahgd1 ,oct4 #aj ,watson ,pekin #adj4 ,siwa #ahgd1 ,oct4 #ac ,palisa ,pola #ada4 ,lumen #ahge1 ,jan4 #ac ,paul ,henry ,paris #adb4 ,polana #ahge1 ,jan4 #bh ,palisa ,pola #adc4 ,adria #ahge1 ,feb4 #bc ,palisa ,pola #add4 ,vibilia #ahge1 ,june #c ,peters ,clinton #ade4 ,adeona #ahge1 ,june #c ,peters ,clinton #adf4 ,lucina #ahge1 ,june #h ,borelly ,marseilles #adg4 ,protogenea #ahge1 ,july #aj ,schulhof ,vienna #adh4 ,gallia #ahge1 ,aug4 #g ,prosper ,henry ,paris #adi4 ,medusa #ahge1 ,sept4 #ba ,perrotin ,toulouse #aej4 ,nuwa #ahge1 ,oct4 #ah ,watson ,ann ,arbor #aea4 ,abundantia #ahge1 ,nov4 #a ,palisa ,pola #aeb4 ,atala #ahge1 ,nov4 #b ,paul ,henry ,paris #aec4 ,hilda #ahge1 ,nov4 #b ,palisa ,pola #aed4 ,bertha #ahge1 ,nov4 #d ,prosper ,henry ,paris #aee4 ,scylla #ahge1 ,nov4 #h ,palisa ,pola #aef4 ,xantippe #ahge1 ,nov4 #bb ,palisa ,pola #aeg4 ,dejanira #ahge1 ,dec4 #a ,borelly ,marseilles #aeh4 ,coronis #ahgf1 ,jan4 #d ,knorre ,berlin #aei4 milia #ahgf1 ,jan4 #bf ,paul ,henry ,paris #afj4 ,una #ahgf1 ,feb4 #bj ,peters ,clinton #afa4 ,athor #ahgf1 ,apr4 #ai ,watson ,ann ,arbor #afb4 ,laurentia #ahgf1 ,apr4 #ba ,prosper ,henry ,paris #afc4 ,erigone #ahgf1 ,apr4 #bf ,perrotin ,toulouse #afd4 ,eva #ahgf1 ,july #ab ,paul ,henry ,paris #afe4 ,loreley #ahgf1 ,aug4 #i ,peters ,clinton #aff4 ,rhodope #ahgf1 ,aug4 #ae ,peters ,clinton #afg4 ,urda #ahgf1 ,aug4 #bh ,peters ,clinton #afh4 ,sibylla #ahgf1 ,sept4 #bg ,watson ,ann ,arbor #afi4 ,zelia #ahgf1 ,sept4 #bh ,prosper ,henry ,paris #agj4 ,maria #ahgg1 ,jan4 #aj ,perrotin ,toulouse #aga4 ,ophelia #ahgg1 ,jan4 #ac ,borelly ,marseilles #agb4 ,baucis #ahgg1 ,feb4 #e ,borelly ,marseilles #agc4 ,ino #ahgg1 ,aug4 #a ,borelly ,marseilles #agd4 ,phdra #ahgg1 ,sept4 #b ,watson ,ann ,arbor #age4 ,andromache #ahgg1 ,oct4 #a ,watson ,ann ,arbor #agf4 ,idunna #ahgg1 ,oct4 #ad ,peters ,clinton #agg4 ,irma #ahgg1 ,nov4 #e ,paul ,henry ,paris #agh4 ,belisana #ahgg1 ,nov4 #f ,palisa ,pola #agi4 ,clytemnestra #ahgg1 ,nov4 #aa ,watson ,ann ,arbor #ahj4 ,garumna #ahgh1 ,jan4 #bi ,perrotin ,toulouse #aha4 ,eucharis #ahgh1 ,feb4 #b ,cottenot ,marseilles #ahb4 ,elsa #ahgh1 ,feb4 #g ,palisa ,pola #ahc4 ,istria #ahgh1 ,feb4 #h ,palisa ,pola #ahd4 ,deiopea #ahgh1 ,feb4 #bh ,palisa ,pola #ahe4 ,eunice #ahgh1 ,mar4 #a ,peters ,clinton #ahf4 ,celuta #ahgh1 ,apr4 #f ,prosper ,henry ,paris #ahg4 ,lamberta #ahgh1 ,apr4 #aa ,coggia ,marseilles #ahh4 ,menippe #ahgh1 ,june #ah ,peters ,clinton #ahi4 ,phthia #ahgh1 ,sept4 #i ,peters ,clinton #aij4 ,ismene #ahgh1 ,sept4 #bb ,peters ,clinton #aia4 ,kolga #ahgh1 ,sept4 #cj ,peters ,clinton #aib4 ,nausicaa #ahgi1 ,feb4 #ag ,palisa ,pola #aic4 ,ambrosia #ahgi1 ,feb4 #bh ,coggia ,marseilles #aid4 ,procne #ahgi1 ,mar4 #ba ,peters ,clinton #aie4 ,euryclea #ahgi1 ,apr4 #bb ,palisa ,pola #aif4 ,philomela #ahgi1 ,may #ad ,peters ,clinton #aig4 ,arete #ahgi1 ,may #ba ,palisa ,pola #aih4 ,ampella #ahgi1 ,june #ac ,borelly ,marseilles #aii4 ,byblis #ahgi1 ,july #i ,peters ,clinton #bjj4 ,dynamene #ahgi1 ,july #bg ,peters ,clinton #bja4 ,penelope #ahgi1 ,aug4 #g ,palisa ,pola #bjb4 ,chryseis #ahgi1 ,sept4 #aa ,peters ,clinton #bjc4 ,pompeia #ahgi1 ,sept4 #be ,peters ,clinton #bjd4 ,callisto #ahgi1 ,oct4 #h ,palisa ,pola #bje4 ,martha #ahgi1 ,oct4 #ac ,palisa ,pola #bjf4 ,hersilia #ahgi1 ,oct4 #ac ,peters ,clinton #bjg4 ,hedda #ahgi1 ,oct4 #ag ,palisa ,pola #bjh4 ,lachrymosa #ahgi1 ,oct4 #ba ,palisa ,pola #bji4 ,dido #ahgi1 ,oct4 #bb ,peters ,clinton #baj4 ,isabella #ahgi1 ,nov4 #ab ,palisa ,pola #baa4 ,isolda #ahgi1 ,dec4 #aj ,palisa ,pola #bab4 ,medea #ahhj1 ,feb4 #f ,palisa ,pola #bac4 ,lila #ahhj1 ,feb4 #af ,peters ,clinton #bad4 ,aschera #ahhj1 ,feb4 #bf ,palisa ,pola #bae4 none #ahhj1 ,apr4 #g ,knorre ,berlin #baf4 ,cleopatra #ahhj1 ,apr4 #aj ,palisa ,pola #bag4 ,eudora #ahhj1 ,aug4 #cj ,coggia ,marseilles #bah4 ,bianca #ahhj1 ,sept4 #d ,palisa ,pola #bai4 ,thusnelda #ahhj1 ,sept4 #bj ,palisa ,pola #bbj4 ,stephania #ahha1 ,may #ai ,palisa ,vienna #bba4 ,eos #ahhb1 ,jan4 #ah ,palisa ,vienna #bbb4 ,lucia #ahhb1 ,feb4 #i ,palisa ,vienna #bbc4 ,rosa #ahhb1 ,mar4 #i ,palisa ,vienna #bbd4 ,oceana #ahhb1 ,mar4 #cj ,palisa ,vienna #bbe4 ,henrietta #ahhb1 ,apr4 #ai ,palisa ,vienna #bbf4 ,weringia #ahhb1 ,july #ai ,palisa ,vienna #bbg4 ,philosophia #ahhb1 ,aug4 #ab ,paul ,henry ,paris #bbh4 ,agathe #ahhb1 ,aug4 #ai ,palisa ,vienna #bbi4 ,adelinda #ahhb1 ,aug4 #bb ,palisa ,vienna #bcj4 ,athamantis #ahhb1 ,sept4 #c ,de ,ball ,bothcamp #bca4 ,vindobona #ahhb1 ,sept4 #aj ,palisa ,vienna #bcb4 ,russia #ahhc1 ,jan4 #ca ,palisa ,vienna #bcc4 ,asterope #ahhc1 ,may #aa ,borelly ,marseilles #bcd4 ,barbara #ahhc1 ,aug4 #ac ,peters ,clinton #bce4 ,caroline #ahhc1 ,nov4 #bi ,palisa ,vienna #bcf4 ,honoria #ahhd1 ,apr4 #bf ,palisa ,vienna #bcg4 ,clestina #ahhd1 ,june #bg ,palisa ,vienna #bch4 ,hypatia #ahhd1 ,july #a ,knorre ,berlin #bci4 ,adrastea #ahhd1 ,aug4 #ah ,palisa ,vienna #bdj4 ,vanadis #ahhd1 ,aug4 #bg ,borelly ,marseilles #bda4 ,germania #ahhd1 ,sept4 #ab ,luther ,dusseldorf #bdb4 ,kriemhild #ahhd1 ,sept4 #bb ,palisa ,vienna #bdc4 ,ida #ahhd1 ,sept4 #bi ,palisa ,vienna #bdd4 ,sita #ahhd1 ,oct4 #ad ,palisa ,vienna #bde4 ,vera #ahhe1 ,feb4 #f ,pogson ,madras #bdf4 ,asporina #ahhe1 ,mar4 #f ,borelly ,marseilles #bdg4 ,eukrate #ahhe1 ,mar4 #ad ,luther ,dusseldorf #bdh4 ,lameia #ahhe1 ,june #e ,palisa ,vienna #bdi4 ,ilse #ahhe1 ,aug4 #ag ,peters ,clinton #bej4 ,bettina #ahhe1 ,sept4 #c ,palisa ,vienna #bea4 ,sophia #ahhe1 ,oct4 #d ,palisa ,vienna #beb4 ,clementina #ahhe1 ,oct4 #bg ,perrotin ,nice #bec4 ,mathilde #ahhe1 ,nov4 #ab ,palisa ,vienna #bed4 ,augusta #ahhf1 ,mar4 #ca ,palisa ,vienna #bee4 ,oppavia #ahhf1 ,mar4 #ca ,palisa ,vienna #bef4 ,walpurga #ahhf1 ,apr4 #c ,palisa ,vienna #beg4 ,silesia #ahhf1 ,apr4 #e ,palisa ,vienna #beh4 ,tyche #ahhf1 ,may #d ,luther ,dusseldorf #bei4 ,aletheia #ahhf1 ,june #bh ,peters ,clinton #bfj4 ,huberta #ahhf1 ,oct4 #c ,palisa ,vienna #bfa4 ,prymno #ahhf1 ,oct4 #ca ,peters ,clinton #bfb4 ,valda #ahhf1 ,nov4 #c ,palisa ,vienna #bfc4 ,dresda #ahhf1 ,nov4 #c ,palisa ,vienna #bfd4 ,libussa #ahhf1 ,dec4 #ag ,peters ,clinton #bfe4 ,anna #ahhg1 ,feb4 #be ,palisa ,vienna #bff4 ,aline #ahhg1 ,may #ag ,palisa ,vienna #bfg4 ,tirza #ahhg1 ,may #bg ,charlois ,nice #bfh4 #ahhg1 ,june #i ,borelly ,marseilles #bfi4 #ahhg1 ,sept4 #ba ,palisa ,vienna #bgj4 #ahhg1 ,oct4 #h ,peters ,clinton #bga4 #ahhg1 ,oct4 #af ,knorre ,berlin ---------------------------------------- -------------------- #c4 ,remarks on ,table ,i4 ,the numbers discovered by the thirty-five observers are respectively as follows3 ,palisa #fj ,peters #dg ,luther #bc ,watson #bb ,borelly #ae ,goldschmidt #ad ,hind #aj ,de ,gasparis #i ,pogson #h ,paul ,henry #g ,prosper ,henry #g ,chacornac #f ,perrotin #f ,coggia #e ,knorre #d ,tempel #d ,ferguson #c ,olbers #b ,hencke #b ,tuttle #b ,foerster 7with ,lesser7 #a ,safford 7with ,peters7 #a and ,messrs4 ,charlois1 ,cottenot1 ,d',arrest1 ,de ,ball1 ,graham1 ,harding1 ,laurent1 ,piazzi1 ,schiaparelli1 ,schulhof1 ,stephan1 ,searle1 and ,tietjen1 each #a ,before arrangements had been made for the telegraphic transmission of discoveries between ,europe and ,america1 or even between the observatories of ,europe1 the same planet was sometimes independently discovered by different observers4 ,for example1 ,virginia was found by ,ferguson1 at ,washington1 on ,october #d1 #aheg1 and by ,luther1 at ,bilk1 fifteen days later4 ,in all cases1 however1 credit has been given to the first observer4 ,hersilia1 the two hundred and sixth of the group1 was lost before sufficient observations were obtained for determining its elements4 ,it was not rediscovered till ,december #ad1 #ahhd4 ,menippe1 the one hundred and eighty-eighth1 was also lost soon after its discovery in #ahgh4 ,it has not been seen for more than nine years1 and considerable uncertainty attaches to its estimated elements4 ,of the two hundred and seventy-one members now known 7#ahhg71 one hundred and ninety-one have been discovered in ,europe1 seventy-four in ,america1 and six in ,asia4 ,the years of most successful search1 together with the number discovered in each1 were3 ,asteroids4 #ahgi #bj #ahge #ag #ahfh #ab #ahgh #ab ,and six has been the average yearly number since the commencement of renewed effort in #ahde4 ,all the larger members of the group have1 doubtless1 been discovered4 ,it seems not improbable1 however1 that an indefinite number of very small bodies belonging to the zone remain to be found4 ,the process of discovery is becoming more difficult as the known number increases4 ,the astronomer1 for instance1 who may discover number two hundred and seventy-two must know the simultaneous positions of the two hundred and seventy-one previously detected before he can decide whether he has picked up a new planet or merely rediscovered an old one4 ,the numbers discovered in the several months are as follows3 ,january #ac ,february #bc ,march #ai ,april #ce ,may #ba ,june #ac ,july #ad ,august #bh ,september #df ,october #bh ,november #bf ,december #e ,this obvious disparity is readily explained4 ,the weather is favorable for night watching in ,april and ,september2 the winter months are too cold for continuous observations2 and the small numbers in ,june and ,july may be referred to the shortness of the nights4 #d4 ,mode of ,discovery4 ,the astronomer who would undertake the search for new asteroids must supply himself with star-charts extending some considerable distance on each side of the ecliptic1 and containing all telescopic stars down to the thirteenth or fourteenth magnitude4 ,the detection of a star not found in the chart of a particular section will indicate its motion1 and hence its planetary character4 ,the construction of such charts has been a principal object in the labors of ,dr4 ,peters1 at ,clinton1 ,new ,york4 ,in fact1 his discovery of minor planets has in most instances been merely an incidental result of his larger and more important work4 ,,names ,,and ,,symbols4 ,the fact that the names of female deities in the ,greek and ,roman mythologies had been given to the first asteroids suggested a similar course in the selection of names after the new epoch of discovery in #ahde4 ,while conformity to this rule has been the general aim of discoverers1 the departures from it have been increasingly numerous4 ,the twelfth asteroid1 discovered in ,london1 was named ,victoria1 in honor of the reigning sovereign2 the twentieth and twenty-fifth1 detected at ,marseilles1#b received names indicative of the place of their discovery2 ,lutetia1 the first found at ,paris1 received its name for a similar purpose2 the fifty-fourth was named ,alexandra1 for ,alexander von ,humboldt2 the sixty-seventh1 found by ,pogson at ,madras1 was named ,asia1 to commemorate the fact that it was the first discovered on that continent4 ,we find1 also1 ,julia1 ,bertha1 ,xantippe1 ,zelia1 ,maria1 ,isabella1 ,martha1 ,dido1 ,cleopatra1 ,barbara1 ,ida1 ,augusta1 and ,anna4 ,why these were selected we will not stop to inquire4 ,as the number of asteroids increased it was found inconvenient to designate them individually by particular signs1 as in the case of the old planets4 ,in #ahdi1 ,dr4 ,b4 ,a4 ,gould proposed to represent them by the numbers expressing their order of discovery enclosed in a small circle4 ,this method was at once very generally adopted4 #e4 ,magnitudes of the ,asteroids4 ,the apparent diameter of the largest is less than one-second of arc4 ,they are all too small1 therefore1 to be accurately measured by astronomical instruments4 ,from photometric observations1 however1 ,argelander1#c ,stone1#d and ,pickering#e have formed estimates of the diameters1 the results giving probably close approximations to the true magnitudes4 ,according to these estimates the diameter of the largest1 ,vesta1 is about three hundred miles1 that of ,ceres about two hundred1 and those of ,pallas and ,juno between one and two hundred4 ,the diameters of about thirty are between fifty and one hundred miles1 and those of all others less than fifty2 the estimates for ,menippe and ,eva giving twelve and thirteen miles respectively4 ,the diameter of the former is to that of the earth as one to six hundred and sixty-four2 and since spheres are to each other as the cubes of their diameters1 it would require two hundred and ninety millions of such asteroids to form a planet as large as our globe4 ,in other words1 if the earth be represented by a sphere one foot in diameter1 the magnitude of ,menippe on the same scale would be that of a sand particle whose diameter is one fifty-fifth of an inch4 ,its surface contains about four hundred and forty square miles1--an area equal to a county twenty-one miles square4 ,the surface attractions of two planets having the same density are to each other as their diameters4 ,a body1 therefore1 weighing two hundred pounds at the earth's surface would on the surface of the asteroid weigh less than five ounces4 ,at the earth's surface a weight falls sixteen feet the first second1 at the surface of ,menippe it would fall about one-fourth of an inch4 ,a person might leap from its surface to a height of several hundred feet1 in which case he could not return in much less than an hour4 ,but of such speculations1 ,sir ,john ,herschel remarks1 there is no end4 ,the number of these planetules between the orbits of ,mars and ,jupiter in all probability can never be known4 ,it was estimated by ,leverrier that the quantity of matter contained in the group could not be greater than one-fourth of the earth's mass4 ,but this would be equal to five thousand planets1 each as large as ,vesta1 to seventy-two millions as large as ,menippe1 or to four thousand millions of five miles in diameter4 ,in short1 the existence of an indefinite number too small for detection by the most powerful glasses is by no means improbable4 ,the more we study this wonderful section of the solar system1 the more mystery seems to envelop its origin and constitution4 #f4 ,the ,orbits of the ,asteroids4 ,the form1 magnitude1 and position of a planet's orbit are determined by the following elements3 #a4 ,the semi-axis major1 or mean distance1 denoted by the symbol a4 #b4 ,the eccentricity1 e4 #c4 ,the longitude of the perihelion1 4 #d4 ,the longitude of the ascending node1 4 #e4 ,the inclination1 or the angle contained between the plane of the orbit and that of the ecliptic1 i4 ,and in order to compute a planet's place in its orbit for any given time we must also know #f4 ,its period1 ,p1 and #g4 ,its mean longitude1 l1 at a given epoch4 ,these elements1 except the last1 are given for all the asteroids1 so far as known1 in ,table ,,ii4 ,in column first the number denoting the order of discovery is attached to each name4 ,,table ,,ii4 ,elements of the ,asteroids4 ---------------------------------------- ------------------------------ ,name a ,p e i ---------------------------------------- ------------------------------ #adi4 ,medusa #b4acbg #aacg4g;d #j4aaid #bdf #cg #cdb #ac #a #f #bdd4 ,sita #b4agfe #aagb4h #j4acgj #ac #h #bjh #cg #b #ej #bbh4 ,agathe #b4bjji #aaib4f #j4bdje #cbi #bc #cac #ah #b #cc #h4 ,flora #b4bjad #aaic4c #j4aefg #cb #ed #aaj #ah #e #ec #dc4 ,ariadne #b4bjcc #aaid4e #j4afga #bgg #eh #bfd #ce #c #bh #bed4 ,augusta #b4bjfj #aaif4h #j4abbg #bfj #dg #bh #i #d #cf #gb4 ,feronia #b4bffa #abdf4j #j4aaih #cjg #eh #bjg #di #e #bd #dj4 ,harmonia #b4bfgc #abdg4j #j4jdff #j #ed #ic #ce #d #af #bjg4 ,hedda #b4bhci #abfj4g #j4jcja #bag #b #bh #ea #c #di #acf4 ,austria #b4bhfc #abfb4g #j4jhdi #caf #f #ahf #g #i #cc #ah4 ,melpomene #b4bief #abgj4d #j4bagg #ae #f #aej #d #aj #i #hj4 ,sappho #b4bifb #abgj4i #j4bjja #cee #ah #bah #dd #h #cg #bfa4 ,prymno #b4cjfb #abgh4d #j4jgid #agi #ce #if #cc #c #ch #ab4 ,victoria #b4ccdb #acjb4g #j4bahi #cja #ci #bce #ce #h #bc #bg4 ,euterpe #b4cdgb #acac4e #j4agci #hg #ei #ic #ea #a #cf #bai4 ,thusnelda #b4cedb #acai4d #j4bbdg #cdj #cd #bjj #dd #aj #dg #afc4 ,erigone #b4cefj #acbj4i #j4aefg #ic #df #aei #b #d #db #afi4 ,zelia #b4cegg #acbb4c #j4acac #cbf #bj #ced #ch #e #ca #d4 ,vesta #b4cfaf #acbe4f #j4jhhd #bej #eg #ajc #bi #g #h #ahf4 ,celuta #b4cfbc #acbf4b #j4aeab #cbg #bd #ad #cd #ac #f #hd4 ,clio #b4cfbi #acbf4g #j4bcfj #cci #bj #cbg #bh #i #bb #ea4 ,nemausa #b4cfeb #acbh4f #j4jfgb #agd #dc #age #eb #i #eg #bbj4 ,stephania #b4cfff #acbi4h #j4bfec #ccb #ec #beh #bd #g #ce #cj4 ,urania #b4cffg #acbi4i #j4abff #ca #df #cjh #ab #b #f #aje4 ,artemis #b4cgdd #accf4d #j4agdi #bdb #ch #ahh #c #ba #ca #aac4 ,amalthea #b4cgfa #accg4h #j4jhgd #aih #dd #abc #aa #e #b #aae4 ,thyra #b4cgia #acdj4c #j4aici #dc #b #cji #e #aa #ce #afa4 ,athor #b4cgib #acdj4e #j4achi #caj #dj #ah #bg #i #c #agb4 ,baucis #b4cgid #acdj4f #j4aaci #cbi #bc #cca #ej #aj #b #bdi4 ,ilse #b4cgie #acdj4f #j4baie #ad #ag #ccd #di #i #dj #bcj4 ,athamantis #b4chdb #acdd4f #j4jfae #ag #ca #bci #cc #i #bf #g4 ,iris #b4chfb #acdf4d #j4bcjh #da #bc #bei #dh #e #bh #i4 ,metis #b4chff #acdf4g #j4abcc #ga #d #fh #cb #e #cf #bcd4 ,barbara #b4chgc #acdg4c #j4bddj #ccc #bf #add #i #ae #bb #fj4 ,echo #b4cicd #aceb4d #j4ahch #ih #cf #aib #e #c #ce #fc4 ,ausonia #b4cigi #acef4c #j4abci #bgj #be #ccg #eh #e #dh #be4 ,phocea #b4djje #aceh4e #j4beec #cjb #dh #bjh #bg #ba #ce #aib4 ,nausicaa #b4djad #acei4c #j4bdac #cdc #ai #afj #df #f #ej #bj4 ,massalia #b4djbd #acfe4h #j4adbi #ii #g #bjf #cf #j #da #bfe4 ,anna #b4djif #acff4b #j4bfbh #bbf #ah #cce #bf #be #bd #ahb4 ,elsa #b4daeg #acga4d #j4aheb #ea #eb #ajf #cj #b #j #adb4 ,polana #b4daid #acgd4e #j4acbb #bai #ed #cag #cd #b #ad #fg4 ,asia 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#bcg #b #bhe #ch #c #di #bei4 ,aletheia #c4acfi #bjbi4c #j4aagf #bda #de #hh #cb #aj #dj #bbg4 ,philosophia #c4acic #bjca4f #j4baca #bbf #bc #ccj #eb #i #af #adg4 ,protogenea #c4acic #bjca4f #j4jbdg #be #ch #bea #af #a #ed #aga4 ,ophelia #c4adcb #bjce4d #j4aafh #adc #ei #aja #aj #b #cd #bji4 ,dido #c4adcf #bjce4i #j4jfcg #beg #cc #b #j #g #ae #ca4 ,euphrosyne #c4adfh #bjci4j #j4bbbh #ic #bf #ca #ca #bf #bg #ij4 ,antiope #c4adge #bjci4g #j4afde #cja #ae #ga #bi #b #ag #ajd4 ,clymene #c4aejg #bjdb4g #j4aegi #ei #cb #dc #cb #b #ed #eg4 ,mnemosyne #c4aeaj #bjdc4j #j4aade #ec #be #bjj #b #ae #ab #bej4 ,bettina #c4aebd #bjdd4c #j4acjb #hg #bh #bf #ab #ab #ed #beb4 ,clementina #c4aeeb #bjdg4a #j4jhcg #cee #h #bjh #ai #aj #b #id4 ,aurora #c4afjb #bjeb4j #j4jhbg #dh #df #d #i #h #d #ajf4 ,dione #c4afgj #bjeh4f #j4aghh #be #eg #fc #ad #d #ch #aii4 ,byblis #c4aggg #bjfi4j #j4afhg #bfa #bj #hi #eb #ae #bb #ib4 ,undina #c4ahea #bjgf4c #j4ajbd #cca #bg #ajb #eb #i #eg #ahd4 ,deiopea #c4ahhc #bjgi4d #j4jgbe #afi #bb #ccf #ah #a #ab #agf4 ,idunna #c4aijf #bjha4f #j4afda #bj #cd #bja #ac #bb #ca #aed4 ,bertha #c4aigf #bjhh4e #j4jghh #aij #dg #cg #ce #bj #ei #ajh4 ,hecuba #c4baac #baja4j #j4ajje #agc #di #ceb #ag #d #bd #abb4 ,gerda #c4bagg #bajh4b #j4jdae #bjc #de #agh #dc #a #cf #afh4 ,sibylla #c4cgfe #bbff4b #j4jgjg #aa #bf #bji #dg #d #cc #bbe4 ,henrietta #c4djjg #bbgg4h #j4bffa #bii #ac #bjj #de #bj #de #bbi4 ,adelinda #c4dabi #bcjb4i #j4aefb #ccb #g #cj #di #b #aa #gf4 ,freia #c4dadj #bcjd4a #j4agjj #ij #di #bab #e #b #c #bfj4 ,huberta #c4dbab #bcaa4e #j4aaac #cac #bb #afh #dh #f #ah #fe4 ,maximiliana #c4dbgj #bcag4b #j4ajig #bfj #cf #aeh #ej #c #bi #aba4 ,hermione #c4dece #bcdd4b #j4abee #ceg #ej #gf #df #g #cf #hg4 ,sylvia #c4dhcc #bcgd4e #j4jibb #ccc #dh #ge #di #aj #ee #ajg4 ,camilla #c4dhdg #bcgf4j #j4jgef #aae #ec #agf #ah #i #ed #age4 ,andromache #c4ejga #bcii4j #j4cdgf #bic #j #bc #ce #c #df #aij4 ,ismene #c4idga #bhfd4c #j4afcd #aje #ci #agg #j #f #g #aec4 ,hilda #c4iebc #bhfi4i #j4agba #bhe #dg #bbh #bj #g #ee ---------------------------------------- ------------------------------ ,,part ,,ii4 ,,discussion ,,of ,,the ,,facts ,,in ,,table ,,ii4 #a4 ,extent of the ,zone4 ,in ,table ,,ii4 the unit of column a is the earth's mean distance from the sun1 or ninety-three million miles4 ,on this scale the breadth of the zone is #a4haif4 ,or1 if we estimate the breadth from the perihelion of thra 7#a4fab7 to the aphelion of ,andromache 7#d4gbf71 it is #c4aad1--more than three times the radius of the earth's orbit4 ,a very remarkable characteristic of the group is the interlacing or intertwining of orbits4 ,one fact1 says ,d',arrest1 seems above all to confirm the idea of an intimate relation between all the minor planets2 it is1 that if their orbits are figured under the form of material rings1 these rings will be found so entangled that it would be possible1 by means of one among them taken at hazard1 to lift up all the rest4#f ,our present knowledge of this wide and complicated cluster is the result of a vast amount1 not only of observations1 but also of mathematical labor4 ,in view1 however1 of the perturbations of these bodies by the larger planets1 and especially by ,jupiter1 it is easy to see that the discussion of their motions must present a field of investigation practically boundless4 ,while the known minor planets were but few in number the theory of ,olbers in regard to their origin seemed highly probable2 it has1 however1 been completely disproved by more recent discoveries4 ,the breadth of the zone being now greater than the distance of ,mars from the sun1 it is no more probable that the asteroids were produced by the disruption of a single planet than that ,mercury1 ,venus1 the earth1 and ,mars originated in a similar manner4 #b4 ,the ,small ,mass of the ,asteroids4 ,in taking a general view of the solar system we cannot fail to be struck by the remarkable fact that ,jupiter1 whose mass is much greater than that of all other planets united1 should be immediately succeeded by a region so nearly destitute of matter as the zone of asteroids4 ,leverrier inferred from the motion of ,mars's perihelion that the mass of ,jupiter is at least twelve hundred times greater than that of all the planets in the asteroid ring4 ,the fact is suggestive of ,jupiter's dominating energy in the evolution of the asteroid system4 ,we find also something analogous among the satellites of ,jupiter1 ,saturn1 and ,uranus4 ,jupiter's third satellite1 the largest of the number1 is nearly four times greater than the second4 ,immediately within the orbit of ,titan1 the largest satellite of ,saturn1 occurs a wide hiatus1 and the volume of the next interior satellite is to that of ,titan in the ratio of one to twenty-one4 ,in the ,uranian system the widest interval between adjacent orbits is just within the orbit of the bright satellite1 ,titania4 ,the foregoing facts suggest the inquiry1 ,what effect would be produced by a large planet on interior masses abandoned by a central spheroid8 ,as the phenomena in all instances would be of the same nature1 we will consider a single case1--that of ,jupiter and the asteroids4 ,the powerful mass of the exterior body would produce great perturbations of the neighboring small planets abandoned at the solar equator4 ,the disturbed orbits1 in some cases1 would thus attain considerable eccentricity1 so that the matter moving in them would1 in perihelion1 be brought in contact with the equatorial parts of the central body1 and thus become reunited with it4#g ,the extreme rarity of the zone between ,mars and ,jupiter1 regarded as a single ring1 is thus accounted for in accordance with known dynamical laws4 #c4 ,the ,limits of ,perihelion ,distance4 ,it is sufficiently obvious that whenever the perihelion distance of a planet or comet is less than the sun's radius1 a collision must occur as the moving body approaches the focus of its path4 ,the great comet of #ahdc passed so near the sun as almost to graze its surface4 ,with a perihelion distance but very slightly less1 it would have been precipitated into the sun and incorporated with its mass4 ,in former epochs1 when the dimensions of the sun were much greater than at present1 this falling of comets into the central orb of the system must have been a comparatively frequent occurrence4 ,again1 if ,mercury's orbit had its present eccentricity when the radius of the solar spheroid was twenty-nine million miles1 the planet at its nearest approach to the centre of its motion must have passed through the outer strata of the central body4 ,in such case a lessening of the planet's mean distance would be a necessary consequence4 ,we thus see that in the formation of the solar system the eccentricity of an asteroidal orbit could not increase beyond a moderate limit without the planet's return to the solar mass4 ,the bearing of these views on the arrangement of the minor planets will appear in what follows4 #d4 ,was the ,asteroid ,zone originally ,stable8--,distribution of the ,members in ,space4 ,one of the most interesting discoveries of the eighteenth century was ,lagrange's law securing the stability of the solar system4 ,this celebrated theorem1 however1 is not to be understood in an absolute or unlimited sense4 ,it makes no provision against the effect of a resisting medium1 or against the entrance of cosmic matter from without4 ,it does not secure the stability of all periodic comets nor of the meteor streams revolving about the sun4 ,in the early stages of the system's development the matter moving in unstable orbits may have been1 and probably was1 much more abundant than at present4 ,but even now1 are we justified in concluding that all known asteroids have stable orbits8 ,for the major planets the secular variations of eccentricity have been calculated1 but for the orbits between ,mars and ,jupiter these limits are unknown4 ,with an eccentricity of #j4beb 7less than that of many asteroids71 the distance of ,hilda's aphelion would be greater than that of ,jupiter's perihelion4 ,it seems possible1 therefore1 that certain minor planets may have their orbits much changed by ,jupiter's disturbing influence4#h ,whoever looks at a table of asteroids arranged in their order of discovery will find only a perplexing mass of figures4 ,whether we regard their distances1 their inclinations1 or the forms of their orbits1 the elements of the members are without any obvious connection4 ,nor is the confusion lessened when the orbits are drawn and presented to the eye4 ,in fact1 the crossing and recrossing of so many ellipses of various forms merely increase the entanglement4 ,but can no order be traced in all this complexity8 ,are there no breaks or vacant spaces within the zone's extreme limits8 ,has ,jupiter's influence been effective in fixing the position and arrangement of the cluster8 ,such are some of the questions demanding our attention4 ,if the universe is a book written for man's reading1 patient study may resolve the problem contained in these mysterious leaves4 ,simultaneously with the discovery of new members in the cluster of minor planets1 near the middle of the century1 occurred the resolution of the great nebula in ,orion4 ,this startling achievement by ,lord ,rosse's telescope was the signal for the abandonment of the nebular hypothesis by many of its former advocates4 ,to the present writer1 however1 the partial resolution of a single nebula seemed hardly a sufficient reason for its summary rejection4 ,the question then arose whether any probable test of ,laplace's theory could be found in the solar system itself4 ,the train of thought was somewhat as follows3 ,several new members have been found in the zone of asteroids2 its dimensions have been greatly extended1 so that we can now assign no definite limits either to the ring itself or to the number of its planets2 if the nebular hypothesis be true1 the sun1 after ,jupiter's separation1 extended successively to the various decreasing distances of the several asteroids2 the eccentricities of these bodies are generally greater than those of the old planets2 this difference is probably due to the disturbing force of ,jupiter2 the zone includes several distances at which the periods of asteroids would be commensurable with that of ,jupiter2 in such case the conjunctions of the minor with the major planet would occur in the same parts of its path1 the disturbing effects would accumulate1 and the eccentricity would become very marked2 such bodies in perihelion would return to the sun1 and hence blanks or chasms would be formed in particular parts of the zone4 ,on the other hand1 if the nebular hypothesis was not true1 the occurrence of these gaps was not to be expected4 ,having thus pointed out a prospective test of the theory1 it was announced with some hesitation that those parts of the asteroid zone in which a simple relation of commensurability would obtain between the period of a minor planet and that of ,jupiter are distinguished as gaps or chasms similar to the interval in ,saturn's ring4 ,the existence of these blanks was thus predicted in theory before it was established as a fact of observation4 ,when the law was first publicly stated in #ahff1 but ten asteroids had been found with distances greater than three times that of the earth4 ,the number of such now known is sixty-five4 ,for more than a score of years the progress of discovery has been watched with lively interest1 and the one hundred and eighty new members of the group have been found moving in harmony with this law of distribution4#i ,,commensurability ,,of ,,periods4 ,when we say that an asteroid's period is commensurable with that of ,jupiter1 we mean that a certain whole number of the former is equal to another whole number of the latter4 ,for instance1 if a minor planet completes two revolutions to ,jupiter's one1 or five to ,jupiter's two1 the periods are commensurable4 ,it must be remarked1 however1 that ,jupiter's effectiveness in disturbing the motion of a minor planet depends on the order of commensurability4 ,thus1 if the ratio of the less to the greater period is expressed by the fraction #a_/b1 where the difference between the numerator and the denominator is one1 the commensurability is of the first order2 #a_/c is of the second2 #b_/e1 of the third1 etc4 ,the difference between the terms of the ratio indicates the frequency of conjunctions while ,jupiter is completing the number of revolutions expressed by the numerator4 ,the distance #c4bgg1 corresponding to the ratio #a_/b1 is the only case of the first order in the entire ring2 those of the second order1 answering to #a_/c and #c_/e1 are #b4ej and #c4gj4 ,these orders of commensurability may be thus arranged in a tabular form1 the radius of the earth's orbit being the unit of distance3 ----------------------------------- ,order4 ,ratio4 ,distance4 ----------------------------------- ,first #a_/b #c4bgg ,second #a_/c1 #c_/e #b4ej #c4gj #b4hb ,third #b_/e1 #d_/g1 #e_/h #c4eh #c4hj #b4ie ,fourth #c_/g1 #e_/i1 #g_/aa #c4ea #c4he ----------------------------------- ,do these parts of the ring present discontinuities8 and1 if so1 can they be ascribed to a chance distribution8 ,let us consider them in order4 ,i4--,the ,distance #c4bgg4 ,at this distance an asteroid's conjunctions with ,jupiter would all occur at the same place1 and its perturbations would be there repeated at intervals equal to ,jupiter's period 7#aa4hf y474 ,now1 when the asteroids are arranged in the order of their mean distances 7as in ,table ,,ii47 this part of the zone presents a wide chasm4 ,the space between #c4bah and #c4cgf remains1 hitherto a perfect blank1 while the adjacent portions of equal breadth1 interior and exterior1 contain fifty-four minor planets4 ,the probability that this distribution is not the result of chance is more than three hundred billions to one4 ,the breadth of this chasm is one-twentieth part of its distance from the sun1 or one-eleventh part of the breadth of the entire zone4 ,,ii4--,the ,second ,order of ,commensurability4--,the ,distances #b4ej and #c4gj4 ,at the former of these distances an asteroid's period would be one-third of ,jupiter's1 and at the latter1 three-fifths4 ,that part of the zone included between the distances #b4cj and #b4gj contains one hundred and ten intervals1 exclusive of the maximum at the critical distance #b4ej4 ,this gap--between ,thetis and ,hestia--is not only much greater than any other of this number1 but is more than sixteen times greater than their average4 ,the distance #c4gj falls in the wide hiatus interior to the orbit of ,ismene4 ,,iii4--,chasms corresponding to the ,third ,order4--,the ,distances #b4hb1 #c4eh1 and #c4hj4 ,as the order of commensurability becomes less simple1 the corresponding breaks in the zone are less distinctly marked4 ,in the present case conjunctions with ,jupiter would occur at angular intervals of #abj4 ,the gaps1 however1 are still easily perceptible4 ,between the distances #b4gfe and #b4hjh we find twenty minor planets4 ,in the next exterior space of equal breadth1 containing the distance #b4hb1 there is but one4 ,this is ,no4 #ahh1 ,menippe1 whose elements are still somewhat uncertain4 ,the space between #b4hea and #b4hid--that is1 the part of equal extent immediately beyond the gap--contains thirteen asteroids4 ,the distances #c4eh and #c4hj are in the chasm between ,andromache and ,ismene4 ,,iv4--,the ,distances #b4ie1 #c4ea1aj and #c4he1 corresponding to the ,fourth ,order of ,commensurability4 ,the first of these distances is in the interval between ,psyche and ,clytemnestra2 the second and third1 in that exterior to ,andromache4 ,the nine cases considered are the only ones in which the conjunctions with ,jupiter would occur at less than five points of an asteroid's orbit4 ,higher orders of commensurability may perhaps be neglected4 ,it will be seen1 however1 that the distances #b4be1 #b4gj1 #c4jc1 and #c4bc1 corresponding to the ratios of the fifth order1 #b_/g1 #c_/h1 #d_/i1 and #f_/aa1 still afford traces of ,jupiter's influence4 ,the first is in the interval between ,augusta and ,feronia2 the last falls in the same gap with #c4bgg2 and the second and third are in breaks less distinctly marked4 ,it may also be worthy of notice that the rather wide interval between ,prymno and ,victoria is where ten periods of a minor planet would be equal to three of ,jupiter4 ,the distance of ,medusa is somewhat uncertain4 ,the ,,fact of the existence of well-defined gaps in the designated parts of the ring has been clearly established4 ,but the theory of probability applied in a single instance gives1 as we have seen1 but one chance in #cjj1jjj1jjj1jjj that the distribution is accidental4 ,this improbability is increased many millions of times when we include all the gaps corresponding to simple cases of commensurability4 ,we conclude1 therefore1 that those discontinuities cannot be referred to a chance arrangement4 ,what1 then1 was their physical cause8 and what has become of the eliminated asteroids8 ,what was said in regard to the limits of perihelion distance may suggest a possible answer to these interesting questions4 ,the doctrine of the sun's gradual contraction is now accepted by a majority of astronomers4 ,according to this theory the solar radius at an epoch not relatively remote was twice what it is at present4 ,at anterior stages it was #j4d1 #a4j1 #b4j1aa etc4 ,at the first mentioned the comets of #ahdc and #affh1 as well as several others1 could not have been moving in their present orbits1 since in perihelion they must have plunged into the sun4 ,at the second1 ,encke's comet and all others with perihelia within ,mercury's orbit would have shared a similar fate4 ,at the last named all asteroids with perihelion distances less than two would have been re-incorporated with the central mass4 ,as the least distance of thra is but #a4ehg1 its orbit could not have had its present form and dimensions when the radius of the solar nebula was equal to the aphelion distance of ,mars 7#a4ffe74 ,it is easy to see1 therefore1 that in those parts of the ring where ,jupiter would produce extraordinary disturbance the formation of chasms would be very highly probable4 #e4 ,relations between certain ,adjacent ,orbits4 ,the distances1 periods1 inclinations1 and eccentricities of ,hilda and ,ismene1 the outermost pair of the group1 are very nearly identical4 ,it is a remarkable fact1 however1 that the longitudes of their perihelia differ by almost exactly #ahj4 ,did they separate at nearly the same time from opposite sides of the solar nebula8 ,other adjacent pairs having a striking similarity between their orbital elements are ,sirona and ,ceres1 ,fides and ,maia1 ,fortuna and ,eurynome1 and perhaps a few others4 ,such coincidences can hardly be accidental4 ,original asteroids1 soon after their detachment from the central body1 may have been separated by the sun's unequal attraction on their parts4 ,such divisions have occurred in the world of comets1 why not also in the cluster of minor planets8 #f4 ,the ,eccentricities4 ,the least eccentric orbit in the group is that of ,philomela 7#aif72 the most eccentric that of thra 7#acb74 ,comparing these with the orbit of the second comet of #ahfg we have ,the eccentricity of ,philomela #j4ja thra #j4ch ,comet ,,ii4 #ahfg 7ret4 in #ahhe7 #j4da ,the orbit of thra1 it is seen1 more nearly resembles the last than the first4 ,it might perhaps be called the connecting-link between planetary and cometary orbits4 ,the average eccentricity of the two hundred and sixty-eight asteroids whose orbits have been calculated is #j4aefi4 ,as with the orbits of the old planets1 the eccentricities vary within moderate limits1 some increasing1 others diminishing4 ,the average1 however1 will probably remain very nearly the same4 ,an inspection of the table shows that while but one orbit is less eccentric than the earth's1 sixty-nine depart more from the circular form than the orbit of ,mercury4 ,these eccentricities seem to indicate that the forms of the asteroidal orbits were influenced by special causes4 ,it may be worthy of remark that the eccentricity does not appear to vary with the distance from the sun1 being nearly the same for the interior members of the zone as for the exterior4 #g4 ,the ,inclinations4 ,the inclinations in ,table ,,ii4 are thus distributed3 ,from #j to #d #gj #d to #h #hc #h to #ab #ei #ab to #af #cb #af to #bj #h #bj to #bd #h #bd to #bh #g #bh to #cb #j above #cb #a ,one hundred and fifty-four1 considerably more than half1 have inclinations between #c and #aa1 and the mean of the whole number is about #h1--slightly greater than the inclination of ,mercury1 or that of the plane of the sun's equator4 ,the smallest inclination1 that of ,massalia1 is #j #da1 and the largest1 that of ,pallas1 is about #ce4 ,sixteen minor planets1 or six per cent4 of the whole number1 have inclinations exceeding #bj4 ,does any relation obtain between high inclinations and great eccentricities8 ,these elements in the cases named above are as follows3 ---------------------------------------- ,asteroid4 ,inclination4 ,eccentricity4 ---------------------------------------- ,pallas #cd #db #j4bch ,istria #bf #cj #j4cec ,euphrosyne #bf #bi #j4bbh ,anna #be #bd #j4bfc ,gallia #be #ba #j4ahe thra #be #j #j4chj ,eukrate #bd #eg #j4bcf ,eva #bd #be #j4cdg ,niobe #bc #ai #j4agc ,eunice #bc #ag #j4abi ,electra #bb #ee #j4bjh ,idunna #bb #ca #j4afd ,phocea #ba #ce #j4bee ,artemis #ba #ca #j4age ,bertha #bj #ei #j4jhe ,henrietta #bj #dg #j4bfj ---------------------------------------- ,this comparison shows the most inclined orbits to be also very eccentric2 ,bertha and ,eunice being the only exceptions in the foregoing list4 ,on the other hand1 however1 we find over fifty asteroids with eccentricities exceeding #j4bj whose inclinations are not extraordinary4 ,the dependence of the phenomena on a common cause can1 therefore1 hardly be admitted4 ,at least1 the forces which produced the great eccentricity failed in a majority of cases to cause high inclinations4 #h4 ,longitudes of the ,perihelia4 ,the perihelia of the asteroidal orbits are very unequally distributed2 one hundred and thirty-six--a majority of the whole number determined--being within the #abj from longitude #bij #ej to #ei #ej4 ,the maximum occurs between #cj and #fj1 where thirty-five perihelia are found in #cj of longitude4 #i4 ,distribution of the ,ascending ,nodes4 ,an inspection of the column containing the longitudes of the ascending nodes1 in ,table ,,ii41 indicates two well-marked maxima1 each extending about sixty degrees1 in opposite parts of the heavens4 ,i4 ,from #caj to #aj1 containing #fa ascending nodes4 ,,ii4 #abj to #ahj1 #ei --- ,making in #abj #abj ,a uniform distribution would give #hi4 ,an arc of #hd--;from #df to #acj--;contains the ascending nodes of all the old planets4 ,this arc1 it will be noticed1 is not coincident with either of the maxima found for the asteroids4 #aj4 ,the ,periods4 ,since1 according to ,kepler's third law1 the periods of planets depend upon their mean distances1 the clustering tendency found in the latter must obtain also in the former4 ,this marked irregularity in the order of periods is seen below4 ,between #aajj and #abjj days #f periods4 #abjj #acjj #g #acjj #adjj #dc #adjj #aejj #ac #aejj #afjj #df #afjj #agjj #ed #agjj #ahjj #bj #ahjj #aijj #ac #aijj #bjjj #ai #bjjj #bajj #cc #bajj #bbjj #b #bbjj #bcjj #b #bcjj #bdjj #h #bdjj #bhjj #j #bhjj #bijj #b ,the period of ,hilda 7#aec7 is more than two and a half times that of ,medusa 7#adi74 ,this is greater than the ratio of ,saturn's period to that of ,jupiter4 ,the maximum observed between #bjjj and #bajj days corresponds to the space immediately interior to chasm ,i4 on a previous page1 that between #acjj and #adjj to the space interior to the second1 and that between #aejj and #agjj to the part of the zone within the fourth gap4 ,the table presents quite numerous instances of approximate equality2 in forty-three cases the periods differing less than twenty-four hours4 ,it is impossible to say1 however1 whether any two of these periods are exactly equal4 ,in cases of a very close approach two asteroids1 notwithstanding their small mass1 may exert upon each other quite sensible perturbations4 #aa4 ,origin of the ,asteroids4 ,but four minor planets had been discovered when ,laplace issued his last edition of the ,systme du ,monde4 ,the author1 in his celebrated seventh note in the second volume of that work1 explained the origin of these bodies by assuming that the primitive ring from which they were formed1 instead of collecting into a single sphere1 as in the case of the major planets1 broke up into four distinct masses4 ,but the form and extent of the cluster as now known1 as well as the observed facts bearing on the constitution of ,saturn's ring1 seem to require a modification of ,laplace's theory4 ,throughout the greater part of the interval between ,mars and ,jupiter an almost continuous succession of small planetary masses--not nebulous rings--appears to have been abandoned at the solar equator4 ,the entire cluster1 distributed throughout a space whose outer radius exceeds the inner by more than two hundred millions of miles1 could not have originated1 as supposed by ,laplace1 in a single nebulous zone the different parts of which revolved with the same angular velocity4 ,the following considerations may furnish a suggestion in regard to the mode in which these bodies were separated from the equator of the solar nebula4 7a7 ,the perihelion distance of ,jupiter is #d4iej1 while the aphelion distance of ,hilda is #d4fbc4 ,if1 therefore1 the sun once extended to the latter1 the central attraction of its mass on an equatorial particle was but five times greater than ,jupiter's perihelion influence on the same4 ,it is easy to see1 then1 that this giant planet would produce enormous tidal elevations in the solar mass4 7b7 ,the centrifugal force would be greatest at the crest of this tidal wave4 7c7 ,three periods of solar revolution were then about equal to two periods of ,jupiter4 ,the disturbing influence of the planet would therefore be increased at each conjunction with this protuberance4 ,the ultimate separation 7not of a ring but7 of a planetary mass would be the probable result of these combined and accumulating forces4 #ab4 ,variability of ,certain ,asteroids4 ,observations of some minor planets have indicated a variation of their apparent magnitudes4 ,frigga1 discovered by ,dr4 ,peters in #ahfb1 was observed at the next opposition in #ahfd2 but after this it could not be found till #ahfh1 when it was picked up by ,professor ,tietjen4 ,from the latter date its light seems again to have diminished1 as all efforts to re-observe it were unsuccessful till #ahgi4 ,according to ,dr4 ,peters1 the change in brightness during the period of observation in that year was greater than that due to its varying distance4 ,no explanation of such changes has yet been offered4 ,it has been justly remarked1 however1 that the length of the period of the fluctuation does not allow of our connecting it with the rotation of the planet4 #ac4 ,the ,average ,asteroid ,orbit4 ,at the meeting of the ,american ,association for the ,advancement of ,science in #ahhd1 ,professor ,mark ,w4 ,harrington1 of ,ann ,arbor1 ,michigan1 presented a paper in which the elements of the asteroid system were considered on the principle of averages4 ,two hundred and thirty orbits1 all that had then been determined1 were employed in the discussion4 ,professor ,harrington supposes two planes to intersect the ecliptic at right angles2 one passing through the equinoxes and the other through the solstices4 ,these planes will intersect the asteroidal orbits1 each in four points1 and the mean intersection at each solstice and equinox may be considered a point in the average orbit4 ,in #ahhc the ,royal ,academy of ,denmark offered its gold medal for a statistical examination of the orbits of the small planets considered as parts of a ring around the sun4 ,the prize was awarded in #ahhe to ,m4 ,svedstrup1 of ,copenhagen4 ,the results obtained by these astronomers severally are as follows3 ---------------------------------------- -------------- ,harrington4 ,svedstrup4 ---------------------------------------- -------------- ,longitude of perihelion #ad #ci #aja #dh of ascending node #aac #ef #acc #bg ,inclination #a #j #f #f ,eccentricity #j4jddh #j4jbha ,mean distance #b4gjaj #b4fdce ---------------------------------------- -------------- ,these elements1 with the exception of the first1 are in reasonable harmony4 #ad4 ,the ,relation of ,short-,period ,comets to the ,zone of ,asteroids4 ,did comets originate within the solar system1 or do they enter it from without8 ,laplace assigned them an extraneous origin1 and his view is adopted by many eminent astronomers4 ,with all due respect to the authority of great names1 the present writer has not wholly abandoned the theory that some comets of short period are specially related to the minor planets4 ,according to ,m4 ,lehmann-,filhs1 the eccentricity of the third comet of #ahhd1 before its last close approach to ,jupiter1 was only #j4bghg4ab ,this is exceeded by that of twelve known minor planets4 ,its mean distance before this great perturbation was about #d4fa1 and six of its periods were nearly equal to five of ,jupiter's1--a commensurability of the first order4 ,according to ,hind and ,krueger1 the great transformation of its orbit by ,jupiter's influence occurred in ,may1 #ahge4 ,it had previously been an asteroid too remote to be seen even in perihelion4 ,this body was discovered by ,m4 ,wolf1 at ,heidelberg1 ,september #ag1 #ahhd4 ,its present period is about six and one-half years4 ,the perihelion distance of the comet #ahfg ,,ii4 at its return in #ahhe was #b4jgc2 its aphelion is #d4hig2 so that its entire path1 like those of the asteroids1 is included between the orbits of ,mars and ,jupiter4 ,its eccentricity1 as we have seen1 is little greater than that of thra1 and its period1 inclination1 and longitude of the ascending node are approximately the same with those of ,sylvia1 the eighty-seventh minor planet4 ,in short1 this comet may be regarded as an asteroid whose elements have been considerably modified by perturbation4 ,it has been stated that the gap at the distance #c4bgg is the only one corresponding to the first order of commensurability4 ,the distance #c4ifhc1 where an asteroid's period would be two-thirds of ,jupiter's1 is immediately beyond the outer limit of the cluster as at present known2 the mean distance of ,hilda being #c4iebc4 ,the discovery of new members beyond this limit is by no means improbable4 ,should a minor planet at the mean distance #c4ifhc attain an eccentricity of #j4c--;and this is less than that of eleven now known--its aphelion would be more remote than the perihelion of ,jupiter4 ,such an orbit might not be stable4 ,its form and extent might be greatly changed after the manner of ,lexell's comet4 ,two well-known comets1 ,faye's and ,denning's1 have periods approximately equal to two-thirds of ,jupiter's4 ,in like manner the periods of ,d',arrest's and ,biela's comets correspond to the hiatus at #c4ea1 and that of #ahfg ,,ii4 to that at #c4bgg4 ,of the thirteen telescopic comets whose periods correspond to mean distances within the asteroid zone1 all have direct motion2 all have inclinations similar to those of the minor planets2 and their eccentricities are generally less than those of other known comets4 ,have these facts any significance in regard to their origin8 ,,appendix4 ,,note ,a4 ,,the ,,possible ,,existence ,,of ,,asteroids ,,in ,,undiscovered ,,rings4 ,if ,jupiter's influence was a factor in the separation of planetules at the sun's equator1 may not similar clusters exist in other parts of our system8 ,the hypothesis is certainly by no means improbable4 ,for anything we know to the contrary a group may circulate between ,jupiter and ,saturn2 such bodies1 however1 could not be discovered--at least not by ordinary telescopes--on account of their distance4 ,the ,zodiacal ,light1 it has been suggested1 may be produced by a cloud of indefinitely small particles related to the planets between the sun and ,mars4 ,the rings of ,saturn are merely a dense asteroidal cluster2 and1 finally1 the phenomena of luminous meteors indicate the existence of small masses of matter moving with different velocities in interstellar space4 ,,note ,b4 ,,the ,,origin ,,and ,,structure ,,of ,,cosmical ,,rings4 ,the general theory of cosmical rings and of their arrangement in sections or clusters with intervening chasms may be briefly stated in the following propositions3 ,i4 ,whenever the separating force of a primary body on a secondary or satellite is greater than the central attraction of the latter on its superficial stratum1 the satellite1 if either gaseous or liquid1 will be transformed into a ring4 ,,examples4--,saturn's ring1 and the meteoric rings of ,april #bj1 ,august #aj1 ,november #ad1 and ,november #bg4 ,see ,payne's ,sidereal ,messenger1 ,april1 #ahhe4 ,,ii4 ,when a cosmical body is surrounded by a ring of considerable breadth1 and has also exterior satellites at such distances that a simple relation of commensurability would obtain between the periods of these satellites and those of certain particles of the ring1 the disturbing influence of the former will produce gaps or intervals in the ring so disturbed4 ,see ,meteoric ,astronomy1 ,chapter ,,xii42 also the ,proceedings of the ,american ,philosophical ,society1 ,october #f1 #ahga2 and the ,sidereal ,messenger for ,february1 #ahhd2 where the papers referred to assign a physical cause for the gaps in ,saturn's ring4 ,,the ,,end4 ,,footnotes3 #a ,the discoverer1 ,piazzi1 was not1 as has been so often affirmed1 one of the astronomers to whom the search had been especially committed4 #b ,massalia was discovered by ,de ,gasparis1 at ,naples1 ,sept4 #ai1 #aheb1 and independently1 the next night1 by ,chacornac1 at ,marseilles4 ,the name was given by the latter4 #c ,astr4 ,nach41 ,no4 #icb4 #d ,monthly ,notices1 vol4 xxvii4 #e ,annals of the ,obs4 of ,harv4 ,coll41 #ahgi4 #f ,this ingenious idea may be readily extended4 ,the least distance of thra is less than the present aphelion distance of ,mars2 and the maximum aphelion distance of the latter exceeds the perihelion distance of several known asteroids4 ,moreover1 if we represent the orbits of the major planets1 and also those of the comets of known periods1 by material rings1 it is easy to see that the major as well as the minor planets are all linked together in the manner suggested by ,d',arrest4 #g ,the effects of ,jupiter's disturbing influence will again be resumed4 #h ,not only nebul are probably unstable1 but also many of the sidereal systems4 ,the ,milky ,way itself was so regarded by ,sir ,william ,herschel4 #i ,menippe1 ,no4 #ahh1 is placed in one of the gaps by its calculated elements2 but the fact that it has not been seen since the year of its discovery1 #ahgh1 indicates a probable error in its elements4 #aj ,the minor planet ,andromache1 immediately interior to the critical distance #c4ea1 has elements somewhat remarkable4 ,with two exceptions1 thra 7#acb7 and ,istria 7#ahc71 it has the greatest eccentricity 7#j4cega71--nearly equal to that of the comet #ahfg ,,ii4 at its last return4 ,its perihelion distance is #b4bhhj1 its aphelion #d4gbfb2 hence the distance from the perihelion to the aphelion of its orbit is greater than its least distance from the sun1 and it crosses the orbits of all members of the group so far as known2 its least distance from the sun being considerably less than the aphelion of ,medusa1 and its greatest exceeding the aphelion of ,hilda4 #aa ,the unit being the sun's distance from the earth4 #ab ,annuaire1 #ahhf4