244 Mr Glaisher, On the developments of [Mar. 16, 



The left-hand member may evidently be written also in the 

 form 



1.3'. .5'. 7', ,. 



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



Writing the adjuncts at full length, the equation is therefore 



1 . 3 2 . 5 2 . T (1 2 2_2 2_2 2_2 

 2 2 . 4 2 . 6 2 . 8 2 (j 2 + 3 4 + 5 6 + 7 8 



I s . 3 s . 5 s . 7 /2 2222212 



2 2 . 4 2 . 6 s . 8 8 U 2 ' 3 4 ' 5 6 7 



L IV? _ 



; 2 x 2 2 V3 



l 2 . 3 2 . 5 I"/? _ 2 1_2 



+ 2 2_ 4 ^ 6 2 X 2 2 ( g 4 + g g 



i 2 . 3 r. 3 2 / i 



+ <n2 i2 X 



2 2 .4 2 2 2 .4 2 V 3 

 1 r.3 2 ,5 2 / 1 2 2_2 2 

 + 2" 2>< 2 2 .4 2 .6 2 V 1 3 + 4 5 + 6 



§ 44. Similarly from the second relation, viz. JT^ — K 2 I X = 1, 

 we find 



r.3 2 .5 2 .7 2 ^ r.3 2 .5 2 .7 

 2 2 .4 2 .6 2 .8 2 ~2 2 .4 2 .6 2 .8 ( ' 



l 2 3 2 5 l 2 



+ 2 2 74V6 X 2 2(adq) 



i 2 .3 i 2 .3 2 , N 



1 I 2 . 3 2 . 5 2 



+ 2 x 2 a 4 2 6 2 q '' 



that is, writing the adjuncts at full length, 



G- 



l 2 . 3 2 . 5 2 . 7 2 _ r.3 2 .5 2 .7 /2 _ 2 2 _ 2 2 _ 2 1 _ 1 

 2 2 .4 2 .6 2 .8 2- 2 2 .4 2 .6 2 .8 U 2 + 3 4 + 5 6 + 7 8 



1 2 .3 2 .5 l 2 /2 2 

 + ^2 ,. „ x 35 -i + 



5 6/ 



2 2 . 4 2 . 6 2 2 V3 4 



i 2 .3 r.3 2 / i i 



+ 2 2 T4 X 2 2 .4 4 ^ 3 + 4 

 1 l 2 . 3 2 . 5 2 / 1 1 2 2 2 



+ 2 X 2 2 . 4 2 . 6 2 V 1 + 2 3 + 4 5 + 



