236 A NEW and UNIVERSAL SOLUTION 



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

 met of 1682. 



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

 to the prediction 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 28070 days: 

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

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

 Squares of the periodic times, we mail find, that half the great- 

 er axis of the ellipfe defcribed by the comet, is 18.07575, the 

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

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

 lion diftance, eflimated in parts of the fame unit, 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 



. . , 17.4922c- _ g. 

 eccentricity, or the quantity s, is equal to ~ — 0.90772 



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

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

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

 lion. 



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

 centric of the comet 17595 (from which the true place and true 

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

 16 days, 4 hours, 44' before or after the paflage over the peri- 

 .helion. 



The mean anomaly, correfponding to the given time, is 

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

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

 lion, we have m — iyg° 47' 32", 17. 



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

 maly fought, we have e = & '= 0.96772 ; hence — = 1.0678 5 



C 



J — I =.0678 = a ; — 0038715 = b. 



Then, 



