390 Mr. J. R. Wilton on 



we shall find the following sequence equation for C r :— 



(r-l)Cr-r[0 r - 1 + C,_ 2 +|0 / ._ 3 +|a-4+ • • •] 



= (r + l)B r+1 + ^-j (r + 2)^ + r [b s B,_ 3 + B 3 B r _ 3 + . 



-BlJov B^B^V 



— 2rB r - 



11 7 



r-1 



2 (r-1) ! 



The corresponding sequence equations for the higher 

 approximations become exceedingly complicated in form. 



I find to the eighth order the f olio win & values of tl 



10 



coefficients :- 



A [ = —a, 



1 9 9 11 23 



A --(^3« 5 +S4 



_8 4 . 313 



19 ,1183 

 + 144 

 103727 



72 ' 4320 ' 

 16603 



A (125 -16603 A 



" 5 a + lb00 





c 



<W2 



,1 , 11 4 167 6 29893 s \ 



229 e 7427 



and to the tenth order — 



A 2 = a 2 + -5a 4 + 2-417a 6 +15-597a 8 --f64-08a 10 , 

 -A 3 = l-5a 3 +l-583a 5 + 8-215a 7 + 55-01a 9 , 



A 4 = 2-667a 4 + 4'347a 6 + 24-01a 8 + 166-2a 10 , 

 - A 5 = 5-208« 5 + ll'53a 7 + 67-40a 9 , 



A 6 =10-8a 6 + 30*26a 8 +-186-5a 10 , 



