SYSTEMS OF ASTRONOMY. gll 



mean annual motion required ; but if M x n, ex- 

 ceeded the real mean place by the quantity d, then 



M ~, would be the motion required. Hence, 



it must be evident, that the mean annual motions 

 deduced on these principles, must be always affect- 

 ed by the differences between the real mean places 

 of the planets, and that assumed at the epoch. 



The motions requisite to give the real mean 

 places of the planets being ascertained, the astro- 

 nomer in the next place assumes, at pleasure, any . 

 convenient cycle of years, and assigns the number 

 of revolutions of each planet in that cycle. 



In computing the number of revolutions of each 

 planet, in order to avoid fractions, he rejects such 

 as are less than six signs, as of no consequence ; 

 and, for the rest, he takes the next greater entire 

 number. Unless he may deem it necessary, in 

 some instances, to encrease or diminish a little the 

 motions; in which case, though the fraction may 

 be under six signs, he may take the next higher 

 number to encrease the motion, or if above six 

 signs, he may reject it, to diminish the motion. 



From the revolutions thus obtained, the mean 

 places of the planets in the heavens are determined 

 by the following proportion : — ■ 



As the immher of years m the cycle, assumed, 

 Is to the revolutions of any planet in that cycle ; 

 So is the time expired from the epoch assumed^ 

 To the planets mean longitude. 



These are the principles on which tiie system. 

 given in the Surya Siddhanta, as far as relates to 

 the planets, is founded, and which I shall now urg- 

 ceed to demonstrate* 



P2 



