THEORY OF THE PARTITIONS OF NTMI'.KRS. 

 and in general 



(l-p l X)(l-p a X)...(l-p.X)L(l; tt,,a fc ...,a.) = x*L(l-l ; a,, a,, ...,.); 

 wherein /> is the symbol of Art. 3, and symbolically 



X" = 

 Art. 22. Also, from the relation 



L(/; a,, a,, .... a m ) 



n _ 1)(n _ 1) ... (aa+n _ 2 ) ..... .(l).. 



for the orders 2 and 3 we have 



L(Z ; a-1, 6-1) = 

 (I+a+2) (l+b+l)(l+c) IL(1 ; a, 6, c) 



(I) (1+1) (1+2) IL (I- 1 ; a, b, c). 

 While in general, if r, be a symbol such that 



^ IL (/ ; a,, ...,.-!, ...,.), 



S i n 8 / 



r I )...(l--.)lL(/;a I , ..., a.) 



Art. 23. I propose to obtain solutions of these functional equations. In order to 

 ascertain the form of the required solutions it was necessary to examine several 

 particular cases appertaining to the order 2 ; the result was the conjecture that 



- i M----i 

 (2)(3)...(a+l).(l)(2)...(b) 



VOL. CCXI. A. 3 A 



