WHICH SATISFY GIVEN CONDITIONS. 
141 
[] is =5 ; and I form a kind of tree as follows: 
the formation of which is obvious ; and I derive from it in the manner about to be 
explained the expressions for the coefficients [14], [23] See. in terms of the corresponding 
coefficients in ( ) ; viz. we have 
[14]=- 
(14), 
[23]=- 
(23), 
[H3]= 
2 
(14)(13) 
+ 
(28)(11) 
- 
(113), 
[122] — 
(14)(22) 
+ 
2 
(23)(12) 
- 
(H2), 
[H12]=- 
6 
(14)(13)(12) 
- 
3 
(14)(22)(11) 
+ 
3 
(14)(112) 
- 
6 
(23)(12)(11) 
+ 
3 
(113X12) 
+ 
1 
(23)(111) 
+ 
3 
(122)(11) 
- 
1 
(1112), 
[11111]= + 6o 
(14)(13)(12)(11) 
— 20 
(14X13XU1) 
+ 15 
(14)(22)(11)(11) 
-3° 
(14X112)(11) 
+ 
5 
(14X1111) 
