138 REV. T. P. KIRKMAN ON THE 



of the Manchester Memoirs will be found most easily appli- 

 cable. 



It will at least be interesting, for a comparison of methods, 

 to show how very easily the 7-partitions of X can be obtained 

 by my method, which requires no expansions, transformations, 

 or summations of any kind, nor anything more than very 

 simple eliminations. Nor has the formula for the 7-partitions, 

 so far as I know, been explicitly found by any one. 



That for the 6-partitions was first given by me at p. 143 of 

 the twelfth volume of the Manchester Memoirs, as follows : 



JP-at( 



2^22 ( 6^+1 35#M- 760# 3 — 5046* 



W.12 

 (P) — (1350:z 2 +5400:z;)*2 x _ 



+ 7926**6*— 8424*(*6 x _ 1 +*6,_ 5 ) 

 + 1 1 76*-*6,_a— 1674* (*6 x _ 2 +*6^) 

 +*6, (—47556^ +I80(e? 5 +tf n + rf 17 + . . to k terms)) 



+*6*_ 1 (+50544£— 31225+ 1 80(d +«Ze +d 12 + . . to k terms)) 

 +*6,_ 2 ( + 10044&— 6656+180(^+^+4,+ . . to k terms)) 

 +*6 X _3(— 7056£— 4617+180(c^+^+* 4 + . . to k terms)) 

 +*6*_ 4 ( + 10044£— 9328+ 180(rf 3 + J 9 +rf 15 + . . to k terms)) 

 +*6,_ 5 ( + 50544£— 16889+180(^+rf 10 +d 16 + . . to k terms)) j; 

 where #— 60A+6(£— l)+c; (670, Z7); 



=60*+/»+l; (*70, Z10); 



and ogftT) 1S ^he co-efficient of the circulator *60 av _ p in gP^. 



In the expression given at p. 143 above quoted, the con- 

 stant *2, r _ 1 C'+F is by inadvertence omitted, which stands at 

 the top of p. 142; and at line 13, p. 143, there is a mis- 

 print of — 3598 for — 3528. The omission of the constant 

 *2, r _ 1 C'+F makes no difference in the value of 6P#, because 

 that value is always the integer nearest, whether over or 

 under, to the sum of the terms in x. 



The 60 numbers d pi are given at p. 139 of the Memoirs 

 quoted above. It is not necessary for our purpose here to 



