1888.] Dr Muir on a Glass of pimple Alternants. 303 
where the symmetric functions of all variables except one occur in 
three out of the four columns. The principal term of the deter- 
minant is 
(cd +ca -1- da) 
X {d^a + d% -i- a^d -p a% 4 h^a -l- lAd) 
X ia%c^ + ah'^A + ah^d^) , 
which may be conveniently written 
a. 
h 
c 
d 
1 
1 
0 
1 
0 
1 
0 
1 
1 
X 1 
0 
3 
1 
3 
0 
3 
0 
1 
3 
1 
0 
0 
3 
1 
0 
1 
3 
X 4 
4 
1 
4 
1 
4 
1 
4 
4, 
where the first factor appears in 
1, 1, 0 placed under the letters a, 
the form of the permutations of 
c, d ; the second in the form of 
the permutations of 1, 0, 3 placed under the letters a, d and 
similarly for the third. Multiplying the first and third factors by 
adding each line of the one to each line of the other, we have 
a 
h 
c 
d 
5 
4 
2 
0 
5 
1 
5 
0 
2 
4 
5 
0 
5 
4 
1 
1 
5 
1 
4 
1 
2 
4 
4 
1 
4 
4 
2 
1 
4 
1 
5 
1 
1 
4 
5 
1 . 
VOL. XV. 25/10/88 • u 
