932] ON SYMMETRIC FUNCTIONS AND SEMIN VARIANTS. 305 
cannot appear, we must have terms of this form destroying each other. The simplest 
mode of effecting the development is to write 
( a ~ /3) 8 (a _ 7) (/? — 7) = (a — /3) 8 {a/3 — 7 (a + /3) + 7 2 }: 
we may herein put at once 7 = b, 7 s = c, and thus the form is 
(a-/3) 8 {a/3-&(a+/3) + c}; 
I develop thus: 
(a-/3) 8 1, — 8, + 28, - 56, + 70, - 56, + 28, - 8, +1, 
+ 1, - 8, +28, - 56, + 70, -56, +28, -8, +1 
(a - /3) 8 (a + ¡3) 1, -7, +20, -28, +14, +14, -28, +20, -7, +1 
1 bj — 8 ci + 28 dli — 5Qeg + 70/ 2 
+ 1 - 8 +28 - 56 
— b f lj — *7bi + 20ch — 28dq + 14eA 
U 1 - 7 +20 - 28 +14 ) 
+ c / li — 8bh + 28c$ — 56df + 70e 2 \ 
V+ 1 - 8 + 28 - 56 ) 
- - 14 
k 
h J 
+ 2-2 
0 
ci 
- 16 +2 
- 14 
+ 1 
dli 
+ 56 
+ 56 
- 4 
eg 
- 112 
- 112 
+ 8 
P 
+ 70 
+ 70 
- 5 
b% 
+ 14 
+ 14 
- 1 
bch 
- 40 - 16 
- 56 
+ 4 
bdg 
+ 56 
+ 56 
- 4 
bef 
- 28 
- 28 
+ 2 
c 2 g 
+ 56 
+ 56 
- 4 
cdf 
- 112 
- 112 
+ 8 
ce 2 
+ 70 
+ 70 
- 5 
± 23, 
which, in fact, exhibits the calculation of the sharp form ci go ce 1 . The disappearance 
°f the term in bj will be noticed, 
c. XIII. 
39