264 



d*a 

 dt* 



I. 



■ for JO = 8 - 0.00000000000000000000000112 6.04922n 



JO = 16 - 80 5.90309n 



It will be advantageous to divide the computation of the terras U^i ... V^ i" 

 into two parts. 



Kepresenting the sum of the first five terms of the series by Y*, we have 



« = «„ 4- uu + u^f + zr^f + i^^t' = r,, 



in which the terms IP, f7", C"^, U^^, are those marked with an asterisk on 

 pp. 260, 261. Yi will now remain unchanged, whatever the results for the higher 

 powers of the time. 



We shall have, therefore, 



«= F, + u^f + xr^e + c^'"«',&c. 



The computation of the terms U^t, JJ^f, U^" f, U^t\ may be advantageously 

 performed by the summation of the series of differences derived from the differ- 

 ential coefficients. 



For the instant 4 we have 



da 



A,-'' 



d^a 



A, = 2.3 



d^a 

 df ' 



-.=-"!?• "- 



