I04 



anomaly correfted by the firfl operation, be ufed, the error m the fe- 

 cond correfted excentric anomaly will be of the fame order as the 3 + 

 3 + I = 7th power of the excentricity. The enor of the next will be 

 of the 15 th, &c. 



Hence fuppofing the error of c of the order of the firft power of excentricity 



the error of c+c will be of the order of 3d. power. 



of c+c+c of 7th. 

 \ \\ 



of c+c+c-\-c of 15th. 



\ \\ \\\ 



f 



\ \\ \\\ WW 



of c-\-c+c+c+c of 3 I (t. 



Hence this method is general for any elliptic orbit, however e.'scen- 

 tric, as Keil juftjy obferves.* 



On Newton's fecond Method. 



This method confifts in finding the quantity to be applied to the 

 mean anomaly, to find the angle at the higher focus, which being known, 

 the angle at the fun is had by the common proportion. The two correc- 

 tions given by Newton, are of the orders of the fecond and third powers 

 of the excentricity, and the higher powers are neglefted ; confequently 

 this method will not be fufEcient for the orbit of Mercury, and to cor- 

 reft it farther, by extending the terms, would require the fame trou- 

 ble as computing direftly by the feries, the true from the mean ano- 

 maly ; fo that this method offers nothing to be particularly remarked. 



However, 



* -Kewton's Anomaly is reckoned from Perihelion, 



