158 
MAJOR P. A. MACMAHON ON A CERTAIN CLASS OF 
In the fourth and fifth compartments we have simply and in each case the 
element selected is that in the 5^’" row and 5* column. Altogethei' we have obtained 
the product 
and we observe that the contacts 
X^Xp {q>p) 
are correctly indicated by the quantities 
^qp- 
Art. 64. The process is obviously a general one, and the rule of element selection 
to demonstrate the desired result may be set forth as follows :— 
If a compartment of the permutation be 
a, h, G, d, e being in descending order of magnitude, we take elements in 
row a, column h, 
5> 55 ^5 
c d 
5 5 ^5 5 5 '-^5 
d G 
55 55 a , 
and thus obtain the product, 
^ad^bc^rrl^de^a^d^c^dXf) 
wherein the contacts are correctly represented by the quantities X. 
If a compartmeut contain the single quantity x^, we take the element in the row 
and column. 
By the above process 
elements are taken from row 1, 
^ 9 
o2 5 5 5 5 5 5 "5 
55 55 55 
tAy j ^^2 
xhji . 
to form the product 
