236 A NEW and UNIVERSAL SOLUTION 



trouble. I flisU give an example in the orbit of the famous co- 

 met of 16S2. 



The comet of 1682, which re-appeared in 1759, according 

 to the predii!^ion of Dr Halley, is the only one of which the 

 period is known with any tolerable degree of certainty. M. de 

 la Lande has fixed the period of this comet at aSoyodays: 

 computing from this the mean diftance from the fun, by the 

 law of Kepler, that the cubes of the mean diftances are as the 

 fquares of the periodic times, we fhall find, that half the great- 

 er axis of the ellipfe defcribed by the comet, is iS. 07575, the 

 mean diftance of the earth from the fun being unity. Accord- 

 ing to the determination of the fame aftronomer, the perihe- 

 lion diftance, eftimated in parts of the fame \mit, is 0.5835 ; 

 confequently, the diftance of the focus of the ellipfe from the 

 centre, is 17.49225. Therefore, in the orbit of this comet, the 



17.4922 c _ f- 

 eccentricity, or the quantity s, is equal to ^g q^^-- — ^-S^ll^ 



nearly : and we can now affign the true place of the comet in 

 the orbit, as well as its trvie diftance from the fun, at any given 

 diftance of time, from the paffiige over the perihelion or aphe- 

 lion. 



Example. Let it be required to find the anomaly of the ec- 

 centric of the comet 1759. (from which the true place and true 

 diftance from the fun are derived by eafy and known rules), 

 1 6 days, 4 hours, 44' before or after the paiTage over the peri- 

 .helion. 



The mean anomaly, correfponding to the given time, is 

 o" 12' 27".83, reckoned from the pei-ihelion ; but as our me- 

 thod requires the mean anoinaly to be reckoned from the aphe- 

 lion, we have m =179° 47' 32". 17. 



1 . 1 o compute the firft approximation to the eccentric ano- 

 maly fought, we have e ■= i — 0,96772 ; hence — =^ 1.0678 ; 



I ^ n fin ;« „ , 



- — I =.0678 = a ; —^ - .0038715 = b. 



Then, 



