K E P 



Of fVieTe notions, which are wholly unfounded in nature, he 

 was fo fond, that hearing of the difcovery of the four fatel- 

 lites of Jupiter by GaUleo, he owns that his lirft refleftions 

 were from a concern liow he could fave his favourite fcheine, 

 which was threatened by this addition to the number of the 

 planets. The fame attachment led him into a wrong iudg- 

 ment concerning the fphere of the fixed ftars : for being 

 obhged, by his doftrinc, to allow a vaft fuperiority to the 

 fun in tlic univerfe, he retrains the fixed tlars within very 

 narrow hmits ; nor did he confider them as funs placed in 

 the centres of tlieir feveral fyllcms, having planets revolving 

 round them. Kepler's great f.igacily, and continued medi- 

 tations on the planetary mrttions, fiiggefted to him fome 

 views of tlie true principles from which thefe motions flow. 

 He fpealis of gravity a.s of a power that was mutual between 

 bodies; and fays, that the earth and moon tend towards 

 each other, and would meet in a point, fo many times nearer 

 to the earth than to the moon, as the earth is greater than 

 the niooii, if their motions did not hinder it. He adds alfo, 

 that the tides arifo from the gravity of the waters towards 

 the moon. But not liaving notions fufRciently ju.'t of the 

 laws of motion, he was unable to make the bell ufe of thefe 

 ideas ; nor did lie fteadily adhere to them, for in his " Epi- 

 tome of Atlronomy," pubhfhed many years after, he pro- 

 pofes a phyfical account of the planetary motions derived 

 from different principles. Kepler was author of feveral 

 pieces bcfidcs thofe already mentioned, of which the follow- 

 ing may be noticed : " Prodromus Didertationiim Cofmo- 

 graphicarum ;' " De Stella nova in Pede Scrpcntarii ; ' 

 " Aftronomia nova, feu Pliyfica Cceleftis, Tradita Com- 

 mentariis dc Motibus Stellas Martis ex Obfervationibus 

 Tychonis Braliei ;" " De Conietis libri tres." 



This great geumerrician and aftronomer, in his " Har- 

 monices Mundi," publiflied at Lintz, in Aullria, in 1619, 

 and dedicated to our James I., fpeaks on the fubject of 

 niufic iike a man who had not only thought of it as a fcience 

 fiibfervient to the laws of calculation, but in the language of 

 one who had ftudied it pratlica!ly as an elegant art, and been 

 truly fenlible of its powers. And though the eloquent 

 aftronomical hi'.lorian Bailly fays, in a fweeping decifion, 

 that " Kepler, from his veneration for Pythagoras and 

 Plato, has plunged into mufical ratios, and blended them 

 with the movement.';, diftanccs, and eccentricities, of the 

 planets, in his vifionary analogies ; they contain not one 

 iingle true ratio or refemblancc : in a crowd of ideas there 

 is not one fiiigle trutli." Tiiis fevere cenfure of M. Bailly 

 ir.uft be confined to the proportions and analogies between 

 mu'ical intervals and tlie diftances of the heavenly bodies : 

 as the ratios of Kepler are accurate, as far as concerns 

 inulic. 



Neither Maclaurin nor Dr. Hutton have expreffed them- 

 felves fo harfhly on his fancied fimihtudes to the divifions of 

 the octave in nuific ; which they indeed cail the dreams of 

 this ingenious man, as t!ie harmony of the fpheres had been 

 of Pythagoras and Plato long before. 



This great mathematician and precurfor of fir Ifaac 

 Newton was fo far from allowing to the ancients, much as 

 he refpecied them, fiich harmony as is prattifed by the mo- 

 derns, tliat he fays, though Plato, in his " Republic," 

 fpeaks a.' if fomttliing like it were in ufe, he fuppofes if 

 tiiey ever had any accoaipaiiiment to their melodies by way 

 of bafe, it mull have been fiich a one as is produced by the 

 drone of a bagpipe This is perhaps being as unjull to the 

 ancients, as thofe are to tlie moderns, who will not allow 

 them to have made any progrefs in mufic, becaufe they are 

 unaljle, by their con-iiofitions and performance, to cure 

 difeafes, tame vviU bcalls, or build to\Vns. 



K E P 



Kepler's Laivs, is a term ufed by ardronomcrs to denote 

 certain analogies between the diftances of the planetary bo- 

 dies from the fun, and their times of periodic revolution ; as 

 alfo between the rate of motion in any revolving body, 

 whether primary or fecondary, and its diftance from the 

 central body about which it revolves. The latter of thefe, 

 which is generally called Kepler's firft law, being that 

 which he iirfl difcovered, is commonly exprefled as follows, 

 viz. 



r. Equal areas are defcribcd in equal times ; that is, if a 

 line be fuppofed to join the central and revolving body, this 

 line always palTes over, or defcribes equal areas in equal 

 times, whether the planet be in its aphelion, perilielion, or 

 in any other part of its orbit. 



2. The fquares of the times of revolution of the planetary 

 bodies are as the cubes of their refpeftive diftances from the 

 fun. 



Thefe laws were firft difcotered by Kepler, the cele- 

 brated aftronomer, whofe name they bear ; — a name which 

 will be perpetuated as long as the fcience of aftronomy itfelf 

 is known, and the fublimity of its law.s l-.ave charms to cap- 

 tivate the minds of philofophers. The difcovery of thefe 

 analoijies forms a moil important epoch in the hillory ot af- 

 tronomy, as tiicy may be confidered as having paved the 

 way to that fubhme and univerfal fyftem of attraftion, the 

 difcovery of which has immortalized the name of Newton : 

 for Kepler having deduced them from the comparilnn of 

 aftual obfervations, and therefore independent of any theory, 

 they formed a very ufeful criterion for the corroboration of 

 any particular hypothefis, as well as an important datum in 

 the inveftigation of new theories. 



In order to form a proper e.ftimate of the value of thefe 

 improvements, and the difficulty their author had to en- 

 counter in eilablifliing them, we muft look to the ftate of 

 aftronomy at that period". Copernicus had jull revived the 

 Pythagorean fyftem, and Kepler was one of its afeleft ad- 

 vocates : but ftill it was held as a facred principle, that the 

 motions of all the planetary bodies were performed in uni- 

 form circular orbits ; to reconcile which to aftual appear- 

 ances, many ingenious contrivances were made ufe of, and 

 which, it muft be allowed, reprefented the planetary motion 

 with confiderable exaftnefs. 



The angular motion of each of the planets confifts of two 

 parts : one part increa.lng uniformly with the time ; and an- 

 otlier which is periodical, and acquires all degrees of mag- 

 nitude within a certain limit, in the feveral parts of the or- 

 bit. Now every fuch motion was accounted for with a tole- 

 rable degree of accuracy, by the ancient contrivances of epi- 

 cycles and deferents. Accordingly the ancient fyftems re- 

 prefented, with confiderable exaitnefs, rhofe obierved places 

 of the planets that defended only on the real angular mo- 

 tions ; as at the oppofitions. But they failed when ap- 

 plied to the other pofitions of the planets, and to the lati- 

 tudes, where the apparent places depend not only on the 

 angular motions, but likewife on the relative dilhinces. It 

 was here that all the ancient fyftems were alike defetlive ; 

 and it was by a ftrift comparifon of obfervation with theory, 

 that Kepler at laft found himfelf obliged to depart from 

 that principle of uniform circular motion, which had been fo 

 fcrupuloully adhered to by a 1 his predecefTor.' . 



The fituation of the heavenly bodies, in refpeft to one 

 another, depends upon their real angular motions, and their 

 relative diftances. But when a planet is in oppofition, the 

 apparent places, as feen from the earth and fun, arc coinci- 

 dent, and its pofition is effefted only by the angular mo- 

 tions; and, therefore, obfervations in oppofition, being the 

 fimpleft and the leaft hable to inaccuracy, are of great ufe 

 3 ' in 



