THEORY OF THE PARTITIONS OF NUMBERS. 



Remarking that 



(l-P 1 P 8 )(l-P 1 P 4 )(l-P 3 P a )(l-P 2 P 4 ) 

 1 



(i-p 1 p 4 )(i-p s p 8 )(i-p s p 4 ) 



We eliminate A and find 



ft 



^1-4 X.X.X.o ) (1 -BDX 4 X S ) ( 1 -CD?X 4 X,) ( 1 - ^ 7 X 2 X U 



\jLs(f/t 



-Br///X s )(l- 



1 



i \ / / 



1 "VVY lit ,/VVV \ / l TJTiV V \ / i l V V 



1 TTT AiAsAjo I ""TOT AjAoAn, (1 .DlJA.,A 8 ) l ~ 7TST~r -^-a-^-io 

 C/i B nrk^j, 



- - X 3 X 1U (1 -B^X 6 ) (1 -CX H ) (1 -DAX 7 ) 



Eliminating B from the first fraction and C from the second, we have 



n l 





-CD<7X 4 X 9 ) (1 - 



~~rm~7 XjXj 



(1-CXe) (1-/X 1 X B X 9 X 10 ) ( l - - 



tS 



1- 



k 



VOL. CCV. A. 



/ 1 T^Ti Y \ i 1 "V V AT Y i 



1 1 ~~ J-'/i-A.j ) II A.J AgJi.gA.jQ I 



G 



41 



