K E P 



achieved ; but many difficulties wcro yet to be overcome, 

 bcFore the empire of trinh could be firinly cllabliflicd. 



It was proved, that the orbit of Mars was not circular, 

 b«t its real form wr.s yet undifcovered. The hypothefis 

 which tirit prefented itfe'i was, that this orbit is an oval or 

 ellipfis, coinciding with t!ie fuppofed circiitar orbit at trie 

 tv.o apiides, but falli:ig very much within it i:i the middie 

 between them ; and Kepler having affigned the proportions 

 of the longer and (liorter axes of the curve, according to 

 viev.-s that he thougiit found, but which proved to be" ex- 

 tremely fallacious, proceeded to defcribe the elliplis, to 

 obtain its quadrature, to cut its area in any given propor- 

 tion, and to derive from thence the equations of the mean 

 motion ; all which was accompanied with fuch labour as no- 

 thing but his fortitude and perfeverance would have been able 

 to overcome. He com.pared the dillances of Mars, thus 

 •computed for no lefs than forty different arcs of anomaly, 

 with the fame as deduced from obfervntion, and had the 

 mortification to find, that they did by no means agree, but 

 that the real places of the planet fell as far witin ut the new 

 oval, as within the old circular orbit. After frying many 

 <lift'erent means of corrediiig thcfe errors with' incredible 

 labour, and always fv.bjccting eaeh hypothelis to the fevered 

 fell, he found, at'length, that an ellipfe, with the fun in one 

 of Its foci, and its greater axis equal to the mean diflance of 

 Mars, roprefented the whole motion of the planet with 

 wonderful txaftnefs. The phnds, therefore, defcribe ellipfes, 

 having the fun in their common focus ; and this is the fecond 

 great difcovery which delighted the mind, and has immorta- 

 lized the name of Kepler. 



His third difcovery was that of a law of no lefs im- 

 portance than either, the defcription of equal areas, or tlie 

 elliptic orbits of the planets ; but it was made more eafily 

 th'.n them, and without the fame elaborate deductions. 

 His (Irong propenfity to trace out l.iws and difcover ana- 

 logies in nature, fet him eagerly at work to find out what 

 relation fublilh between the d'iilances of the planets from 

 the fun, and the times of their revolutions round him. The 

 data here lay in a much fmaller compafs, and were much 

 Jefs various than in the two former refearches ; and Kepler, 

 after making fome fanciful comiiarifons between the dif- 

 lances of the planets, and tiie regular folids in ^reometry, 

 and alfo between the fame and the divifions of the mono- 

 chord, thought at laft of comparing the different powers 

 ot thcfe quantities with one another, from which compa- 

 rifon, though not without fome abortive attempts, this 

 truth at laft emerged, thiit the flares of the periodic times of 

 thr planets, are ets the cubes of their mean dijtances from the fun. 

 He cxprcifed, in ftrong terms, the dehght and aftoniihment 

 lie felt on the difcovery of this fimple and beautiful ana- 

 logy. He has carefully marked the day on which the dif- 

 covery was made, (.8th May, 1618,) "and few," fays a 

 writer on this fubjeft, " are the days in the hiftory of the 

 world that deferve fo well to be remembered." 



After the happy idea of comparing the powers of the 

 dillances and times, the ftep to the final refuit was ex- 

 tremely fimple and eafy ; though it does not appear that 

 Kepler employed any particular m.ethod for this purpofe, 

 but had rccoui-fc to various trials before the real law was 

 difcoveied. 



Suppofe, for inftance, D, d, and J, to reprefent the dif- 

 tances of any three planets, and T, /, t, the three corre- 

 fjKinding tim.es of periodic revolution ; then, in order to 

 ilfcertain whether any law fublifts between thefe two feries 

 of i.i^uan:itie3, let us affiime the following proportions : v/s. 



D"- : d" :: T" : t- 



D" ! i™ :: T" : t' 



K E P 



which equality muft neceffarily obtain if any lawfubfill, \ 

 it is remarkable that it fliould' be totally independent (-t •: .; 

 law itfclf. Therefore, it was only neceffary to fubmit the 

 above equality to examination, in order to be affurcd of the 

 exiftence or non-exillence of any analogy; and having thus 

 afcertained that fome law muil: have place, the law itfelf is 

 readily difcovered from any of the above equations. Thus 



D T 



the equation m log. — = n log. - gives immediately 



-" ,/ 



log. 



D 



__, which fraction being reduced to the loweS; 



log. 



terms v.'ill fiirnifli the particular values of ;n and'«. As 

 thefe formula: are applicable to any two feries of quantities, , 

 between which any law of this kind is fufpecled to obtain, 

 they are not altogether unworthy of attention. We li.ive 

 thus given a flight Hcetch of the difcoveries of this cele- 

 brated allronomer, which, had the limits of our article ad- 

 mitted of it, might have been extended to a much greater 

 length ; in the prefent inilance, however, we can only refer 

 the reader who wiihes for more complete information on this 

 interefting fubject, to Dr. Small's " Account of the AUro- 

 nomical Difcoveries of Kepler." 



Kepler'.s Pr'jbkm. See Problicm. 



KEPPEL, Augustus, in Biography, a celebrated Eng- 

 lifli admiral, the fecond fon of William, earl of Albemarle, was 

 born April 2d, 1725'. He entered the fea-fervice while he was 

 young, accompanied commodore Anfon round the world, 

 and by the zeal which he manifefted in his profeffion, was 

 railed to the firil honours which it had to beilow. The moll 

 important occurrence in his life took place in 1778, when lie 

 had the command of the channel fleet, to wliich he had been 

 appointed at the perfonal and urgent folicitation of the 

 king, and which he readily accepted, though he could not 

 help obferving, that " his forty years fervices were not 

 marked by any favour from the crown, except that of its 

 confidence in the time of danger." On the 12th of July he 

 fell in with the French licet, under count d'Orvilliers, off 

 Ulhant : an engagement enfued, which, though partial, was 

 very warm while it lafled. It was necelTary to take a ftiort 

 time to repair the damages : which being done, the admiral 

 made proper fignals for the van and rear divilion to take 

 their refpedive ftations. This order was obeyed with great 

 alacrity by fir Robert Harland of the van, but admiral fir 

 Hugh Pallifer of the rear took no notice of the fignal, and 

 i-efufed to join his commander, till night prevented a renewal, 

 of the battle. The French, taking advantage of the darkncfs, 

 elcaped to their owji coall. Adiniral Kcppe), .willing to ex. 



gufe 



