5io The Orbit and Motion of 



much larger portion of the arch had been obferved ; and, 

 which was of immenfe conlequence, three opoofitions had 

 been obferved, which gave us three positions of the Planet, 

 independent of all hypothefes. The arches defcribed be- 

 tween thefe oppofitions being thus determined, free from all 

 uncertainty, the acceleration of the Planet's motion became 

 known ; and a method now offered of determining, by inter- 

 polation, its heliocentric place, at any intermediate moment, 

 with very great accuracy. And now, by chufing fuch obfer- 

 vations of the Star as mould give a great difference between 

 the heliocentric arid geocentric place, the radius of the earth's 

 orbit became a bafe, by which we could meafure, with confi- 

 derable accuracy, its diftance from the Sun. Thus, having 

 both its pofition and diftance from the Sun, we could aflign its 

 abfolute place in the heavens, and confequently the form of its 

 path. 



IN the beginning of 1785, another oppofition was obferved, 

 and thus a method obtained of deducing the elements direttly. 

 But this required a procefs fo extremely complicated, in order 

 to obtain tolerable accuracy in the refult, that I had not the 

 courage to attempt it. I waited patiently till a fifth oppofition 

 mould be obferved with four intercepted arches. This, I faw, 

 would afford a method extremely fimple and eafy, and, at the 

 fame time, fufceptible of confiderable accuracy. It is this me- 

 thod which I have now the honour to lay before this Society ; 

 and I hope that the Gentlemen who hear me will not think it 

 altogether unworthy of their attention : For it is furely defirable 

 not to reft our knowledge of the motions of this Planet on mere 

 conjecture, whatever probability there may be of its truth from 

 the coincidence of obfervatioris. I nruft, at the fajne time, 

 acknowledge beforehand, that the refult of my inveftigation 

 has not enabled me to determine the elements of its motion 

 with perfect certainty. It has, on the contrary, convinced me, 

 that, if we do not admit that the new Planet is the fame with 



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