KEPLER'S LAWS. 



in adronomy. But in obfcrving oppofitions, a praftice had 

 been introduced, ■ tliat in part defeated the pnrpofe for 

 which fuch obfervation3 had been preferred to all others. A 

 planet was reckoned to be in oppofition, \\h^n its place in 

 the heavens was removed iSo" in longitude, not from the 

 real place of the fun, but from his mean place. It is evi- 

 dent, therefore, that by this pracliee the obferver was VjOt 

 fituatcd in the fame line with the fun and the planet, at the 

 computed time of oppolition ; and, therefore, the apparent 

 place of the planet was not entirely divefted of the fecond 

 inequality, excepting in the rare cafe when the true 

 place of the fun coincided with liis mean place. To this 

 pradice Kepler objefted, and conceived the dtfip^n of de- 

 termining the orbit of M.irs from real, in Head of apparent 

 oppofitions ; and he entertained the moll fantruine expecta- 

 tions of completely reforming the theory of the planets, by 

 his projected innovation. Kepler's intended fubilitution of 

 real for mean oppofitions led him to examine the practice of 

 allronomers in another important point. It very feldom 

 l»appens that a planet is found in the plane of the ecliptic, 

 in which the motion of the fun is performed ; and in order 

 to afcertain the place of the planet in its orbit at the time cf 

 obfervation, a reduftion from the ecliptic to the plane of the 

 orbit becomes necelTary : and in examining the ancient me- 

 thods of reduction, Kepler found them to be erroneous and 

 inconfillent ; and his invefligation ultimately eftablidicd tins 

 important conclufion, " that the orbits of the planets are 

 invariable planes, interfedting each other in lines paiTing 

 through the fun's centre." This was a moll important im- 

 provement, and of greater conlequence in fimplifying the 

 fcience of aftronomy than any that had been introduced in 

 all the preceding ages ; and his fuccefsful and decifive ella- 

 bliihment of its truth may be julliy ranked among his 

 gieateft difcoveries 



Kepler having overcome all the difEcukics that oppofed 

 his projecled mnovation, at length completed a theory of 

 Mars, derived folely from apparent oppofitions ; and its ac- 

 curacy was unqueftionabie in reprefenting the oppofitions ; 

 but it totally failed when applied to the latitudes, and to the 

 longitudes out of oppofition. Uiiappointed in the high ex- 

 petlation he had formed of his new theory, he yet drew 

 from its failure an important inference, the firil ilcp to 

 emancipation from the ancient prejudice of uniform circular 

 -motion. For as the theory involved only two fiippofitions, 

 •y.'z. that the orbit of Mars was a circle, and that tiie mo- 

 tion of the planet was uniform about a fixed point in the 

 line of apfides, he juiliy concluded that one at Icall of thefe 

 two fuppofitions was falfe. He now prepared for further 

 refearches ; but, firft of all, judged it necelfary to examine 

 the circumftance that affeAed tlie theory of the earth's an- 

 nual motion : for as the latitudes of the planets, and the 

 longitudes out of oppofition, (the phenomena which had 

 hitherto rendered his attempts abortive,) depended on the 

 ditlances of the earth from the fun, it vva^ requifite to be 

 affured that no eiTors crept in from tliis quarter. 



Nor was Kepler wit'nout fufpicions of inaccuracy in 

 the terrellrial orbit. He had early remarked it as an 

 anomaly, that an equant was afligned to all the planets, 

 the Earth or Sun excepted ; and although the autlioiity 

 of all aftonomers was againil him, he even then pre- 

 fumed to doubt of the jiiilnefs of the exception. Ke- 

 fumiiig the examination of this point on the prefent occafion, 

 he ellablifhed, by multiplied and undeniable proof, that the 

 eceeiitricitv was bifefted in the orbit of tiic Earth or Sun, 

 as well as in the orbits of the other planets. Kepler, in 

 turning his attention to the folar theory, had alfo a farther 

 improvement in view, viz. a method for dcfivhig the cqv.a.- 



VoL. XIX. 



tions of the planetary orbits from a lefs arbitrary and preti- 

 rious priniriple than that cf the equant, or a centre of uni- 

 form angular motion. He had remarked, that it is a gene- 

 ral fad in the folar fydem, that the velocity of a planet 

 diminifhes as it recedes from tlie Sun, and increafes as it ap>- 

 proaches that luminary ; and he concluded, that thefe two 

 quantities, the velocity of a planet, and its diftance from the 

 Sun, mull be related according to fome law, which, if dif- 

 covered, would enable allronomers to calculate the rate of a 

 planet's motion for all points of its orbit, and, of courfe, 

 to determine the equation, or correftion due to the mean 

 motion in every fuch point. This was undoubtedly the 

 conclufion of a man of genius and originality ; for tliough 

 we are now familiar with the notion, that whenever the 

 variations uf one quantity depend on th; fe of another, the 

 one of the quantities may be exprelTed by fome fundlions of 

 the other ; yet, in the days of Kepler, it muli: have required 

 no fmall effort of generalization to perceive this truth, and 

 the important confequences which refult from it. Great 

 difficulties, however, flood in the way of the in- 

 veiligatio;! ; and Kep'er had to ftruggle, not only with his 

 own precioitancy, which frequently led him into error, but 

 witli the imperfeclions of the geometry of that age, which 

 were great in all matters connected with the quadrature of 

 curves. 



His ingenuity and perfeverance, however, atlart prevailed. 

 He found that the times of defcribing fmall arcs of the 

 Earth's orbit, are as the ditlances fro.Ti the Sun ; that there- 

 fore the times of defcribing any arcs whatever, mud be as 

 the fums of thofe alliances ; and having fatisfied himfelf, from 

 geometrical coiifiderations, that the fum of the dillaiices 

 maybe expounded (at lead nearly) by the area contained 

 between the arc and tlie radii drawn from its extremity to 

 the centre, he inferred that the times of defcribing any arcs 

 whatever, arc proportional to thefe areas, or which is the 

 fame, Tkit equal areas are ckfcrihcd in equal times. In coiife- 

 qucnce of this improvement, Kepler began to fpeculate on 

 the nature of the force which produced fo curious an ad- 

 judment ; but the honour of this difcovery was referved for 

 the genius of the iinn.ortal Newton. Wlien he again re- 

 fumed the confidcration of the orbit of Mars, he foon faw 

 rcafon to conclude that this body defcribed its orbit under 

 the guidance of the fame law that he hadjuft found to hold 

 on the Earth ; ws. that the areas defcribed by a line drawn 

 from tiic planet to the Sun, are every where proportional 

 to the time of defcription. 



The attempt, however, of computing the equation of 

 Mars's motion on this principle, was attended with much 

 didiculty, on account of the great eccentricity of the orbit, 

 but dill more from that prejudice in favour of the old doc- 

 trine of circular orbits, which has been already mentioned. 

 In his new method of computing the equations, Kepler 

 fuppofed tlie orbit to be accurate ; but the refuks, from the 

 combination of the two principles, were fuch as could not 

 be reconciled with the places of Mars, obferved by Tycho 

 Brahe. In this dilemma, finding that he m.iid give up one 

 ot the principles which he had adopted in his calculation, he 

 fird propofed to facrifice his own theory to the authority 

 of the old fyllem ; thus giving one of the mod memorable 

 examples which has ever occurred, of the influence of can. 

 dour and prejudice at the fame moment. He foon found, 

 however, that this facrifice would not anfwer his purpofe, 

 and that, in order to make the calculus agree with obfer- 

 vations, it vvas the old liypothefis, and not the new one, that 

 mud be abandoned. 



Thus the idol was overthrown by which Kepler had been 



fo long deceived, and the emancipation of adronomy was 



4 Z acliieved ; 



