THEORY OF THK I'AKTITIONS OF NUMBERS. 



373 



) + a; 11 , 



A dividing line has been placed after each letter that has to be noted. Thence, by 

 the rules given, 



Lo(oo;22;22)= 1, 



L, ( oo ; 22 ; 22) = 2x'+2x 3 +3a; 4 +2:r 5 +2z 9 , 



L,(t ; 22; 22) = 



La( oo ; 22 ; 22) = 



L 1 (oo;22;22) = x w , 



supplying a complete verification of the work in Part II. 

 We have, therefore, 



GF(/; 22; 22) 



- r (L+ll v JL+ 8) L (1). ..(1+7) L (l-l)...(l+8) 

 (1)...(8) (1)...(8) (1)...(8) 



Q-2). .. 



We have evidently, potentially, the complete solution of the problem of three- 

 dimensional partition, and it remains to work it out and bring it to the same 

 completeness as has been secured in this Part for the problem in two dimensions. 



This will form the subject of Part VII. of this Memoir. 



