192 Mr Glaisher, On the developments of [Nov. 24, 



then, by § 2, 



12 -I 2 o2 1 2 o2 r 2 12 98 K! W 



K = 1 4- — P 4- Z" 4 I F 4- ' • ' ' P 4. &p 



Ji -i - 1 ^ 2 2 2 2 4 2 2 2 4 2 6 2 2 4 2 6 2 8 



-I 12 Q 12 q2 e 12 02 R2 hr 



tf = 1 - — F - A- 4 - £ 6 - ' ' F - &o 



1 2 2 ^.4 2 2 2 .4 2 .6 2 2 2 .4 2 .6 2 .8 2 ' 



1 12 q 12 q2 k -12 02 R2 17 



1 2 2 2 .4 2 2 .4 2 .6 2 2 .4 2 .6 2 .8 ' 



1 12 1 2 q2 1 2 q2 K2 



G * = 2^ + 2T4^ 4 + 2^4 2 T6 A;6 + 2 2 .4 2 ',6 2 .8 F + &C - 



-12 12 02 12 02 p-2 



2 U = - — — A* - ' F - * P - &r 



1 2.4^ 2 2 .4.6 A; 2».4\6".8- C " 



10 12 12 q2 18 02 R2 



2^=i+gy+^-,y+ 2 , ', 6 , y+ 2 , 4 , •, 8> *"+&&, 



Let iT 2 , j£ 8 , 7 2 , £ 2 , 2Z7 2 , 2F 2 , 2Tf 2 be seven quantities defined 

 by the following series, in which the coefficients of the terms are 

 connected with the coefficients in the above series for K , E v I , 

 G lt 2U lt 2V 1 , 2W t by the law explained in § 4. 



12 1 2 02 



K= ^(!-|)^ 2 +2^4-2(f-f + f-|)A ; 4 +&c., 



^=i-^(i-|)^ 2 -^(f-| + J-!)^-&c. J 

 J.-i-g (*-«*■ -^(f-f + i-i)^ 4 -^., 



G.= l +£(*-*)*■ +2^ ¥ (f-|-i) ^ 4 -&c, 



2F 2 =2+^(f-f)F 4-^(1-1-1)^- &c, 



I O 12 q (? 



2W =2 — —— (1 — 2 4- l|jp X - 00 /2_2 1 1 _2 1 1\W_ & P 



^ rr 2 ^ 2' x 2^3^ 2 2 4 2 T ¥ F ¥ ^ ' <KC ' 



In all the seven series, the law noticed in § 4 is followed 

 in the formation of the coefficients of ¥ and higher powers of 

 k\ It is followed also by the coefficients of & 2 , except in the 

 case of 2J7 2 , and, with reference to this case of exception, it is to 

 be observed that the series for 2U 1} from which that for 2?7 2 is 

 derived, begins with the term in h\ and that the law of the 



