1876.] Verification in the Partition of Numbers. 255 



(TIL) 3 ^+ i ^+ I ^+te" 1 _ u J :W ; < , 



2* 3 , 3* 6 . * 



+ 1 — r~7i — ^w^ — ^2 — — &c. 



11 i 2 



(Yin.) izr t = i- t .i-t\i^t 3 . . ~(i-tf .i~f.i-f 



-&c. 



(1„^(1_0 2 1-* 3 ... 



1 1 t 2 t 4 - 



( IX -) i-*.i-* 2 .i-* 3 ... = I^ + (I^ 2+ (i-o 2 .i--* 3 



t 



l * * 4 



( X -) TITT^O 1+ n_n 2 + 



i-*.i-*M-* 3 ... ' (i-o (i-0 2 (i-O* 



+ (l_^(l_f^(l_0 2+&C * 



(XL) T 



■t.l-f.l-t 3 ... l-f.i-t\l-f... 



(l-f)M-fM-i 6 ... ' (l-OXl-O 2 - 1 -^ 





+ (i-f).i-^.i-^ 3 ... + (i-0(i-0 .1-*... ' 



(XIII.) 1 



1-*.1-*M-* 5 ... (l-O-l-^.l-^ 3 ... 



+ (l_^ ) (l_0.1-^...~ &C • 



(xiv.) i+t+?+t*+t«+& G .= 1 _ t ^_* ^ _ 



+ 7i ^\Fi IK— i : &c -'> 



(l-f).i-t.i-t 3 ... ■ (l-^xi-O- 1 -^-.. 



all of which can be deduced without difficulty from the identities, 



in / 3 <?/ 2 



L-fw.l-rtt.l-n*. . . ' 1-* ' 1 — ^.1 — ^ 



