THE PARTITION OF NUMBERS. 
97 
into three or fewer parts are enumerated by 
(iii.) Since 
D to+ ,QiQa= (Sm + 2)HA ta 
-^ 67*1 + 2^3 = 9 , 
we, as above, derive, for the partitions of the multipartite number 
the enumerating number 
6m 1 + 2 67710+2 ... 67n s + 2, 
J jy6777! + 4\ /6 tti 2 + 4 
( >»h+ 4 \ +3 (3777 1 + 2)(3 t77 2 +2) 
.. ( 3 774 f + 2 ) j 
(iv.) Since 
T) Q , 3 - / 6 w + 5 \ q 3 
D 6m + 3 Q]Q 2 = (3777+2) Q^, 
1^607 + 3^3 = ^ 3 ) 
we obtain, for the multipartite number 
6777,+ 3 6777 2 +3 ... 6777,+ 3, 
the enumerating number 
+ = (3777+ 3) QiQa, 
1 ^ 67)7 + 4^3 = 9 , 
and we obtain, for the multipartite number 
6777, + 4 6777 2 +4 ... 6t77,+ 4, 
VOL. OCXVII.—A. P 
