222 



DR THOMAS MUIR ON THE 



In the first four cases the expansions therefore stand thus : — 



+ * 2 ; 



a 



h — V 



h + v j = 

 b 



a h 

 h b 





a h + v y — fj. 



= 



a h g 





h-v b f+X 





h b f 





9+fjL f-\ c 





9 f c 



a h + v g — p. r+r 



= 



a h g 



h — v b /+X <[ — <* 





h b f 



9 + fA f-\ c p + p 





9 f c 



r — r 



q+v p — p d 





r q p 



+ 



V 



X 



M 



V 



a 



h 



9 



h 



b 



f 



9 



f 



c 



X' 



v 



+ B + C, 



where 



B = 



and 



a h 

 h b 



' 



a g 



a h 1 





9 fy' 





C = I X 



fX V 



p or 



T 



a h + v g — fji r+ 



h — v b f+X q — a- m + x 



g + f* f-\ c p + p 



r — r q + a p — p d 



n + yfs m—% l + (j> k — 



*l — \p- 





a 



h 



9 



r 



n 



i + X 





h 



b 



f 



q 



m 



1 — <P 



= 



9 



f 



c 



p 



I 



h+e 





r 



q 



p 



d 



h 



e 





n 



m 



I 



h 



e 



X 



T 

 ft 



+ D + E, 



where 



D = 







+ 



!* 



123 

 123 



124 

 123 





123 

 124 



124 

 124 





123 

 125 





123 



134 





123 

 135 





123 

 145 





123 

 234 



123 

 235 





123 



245 





123 

 345 



125 

 123 



P 



X 



