7-rABTITTONS OF X. 145 



Putting 6^+6^2+6,^ for 2 X9 and e^+e^+e*. for 2^i, 



and l=6 x +6 x . 1 +6 4r . 8 4-6„3+6^+6^5, 

 we readily obtain 



c=- * | — 409860*6,+255840-*6_ 1 — 275460*6^, 



— 12960-*6,^— 141060'*6^+121440-*6._J 

 Therefore 



(7P * ),= 42^ | "~ 135 ° ^-< 37947 - 28350 #2 -i)* 3 



— *6„-409860:r+*6_ 1 -255840*— *6_ 4 -275460* 

 — ♦6^-12960j>— *6^_ 4 141060j;+*6^-121440z | +<*.. 



The value of the constant d<y is given by equation (C), 

 thus: 



(iP7y=tPrJ'+c^r-j'+ • • +[.*w. (co 



if yZ42 ; for in that case tV^-m has no terms at all on the 

 right side of equation (A), x being z.Q> That of d A2 is ob- 

 tained immediately by putting x=0 in (C) which requires 

 /=0, 7=42 ; so that (C) becomes , by (c) , 

 ( 7 P )'=0+^=0, or 



The remaining 41 values of */<y, or all the 42 values, are 

 obtained by putting for y its successive values, 1, 2, 3 ... 42, 

 in the equation (C), which is, (c) and (P), 



- rf7= 42^20* i - l350 7 3 -(37947-28350-2 7 ^) 7 * 



— 6y 409860 7 -_6 y _ 4 - 14 IO6O7— 6 y _ a -275460 7 

 +6^-2558407+6^1214407— 6^129607! 



+J_( .350 ( (r~i) 8 -27-.+(y-i5) 8 Vie-f-(7~29) 8 -2 7 ^ 



720»| 10 ° H(7-8) 8 -2 7 ^+(7-22)».2 7 _ 23 +(7-^6)»-2 r .^ 



+5400f (Y- 1 )27-»+(7-15)V"+(7-29)2 7 ^ 

 ^+(7-8)2^+(7-22)2 7 _„+(7-36)2 7 V 



