140 



REV. T. P. KIRKMAN ON THE 



the terms in x of 6 P*, would easily give us 7 P X ; for they give 

 us, as we shall see, very readily all the terms in x of 7 Pa.. 

 But as this does not appear certainly true, it becomes neces- 

 sary to write out in full the constant term of qP x9 that we 

 have it in our power accurately to express the constant of 

 7 P X , which, unlike this of 6 P.r, we may find essential to the 

 value. 



This constant is, writing the numerators^, Jq, &c, 



These numbers can all be obtained from 

 /eo=0, /«,=— 16889, /«=— 9328, /„==— 4617, /«,=— 6656, and 

 fu=— 31225, by the formula 



.£+^="664(12^+12.^+12,^+12^+12^,0+12^ 



X(l— 20_ r -20^„) 



-53136(12,+ 12 x _,+ 12^+12^+12^+12._ 8 ) 



X(l— 20_,— 20_, 6 ) 

 + 115344.(20_«+20_„)+50544.(20_ 1 +20_ 16 ). 

 And it is remarkable, that 



/*W;=±180 2 . 



