74 
Proceedings of Royal Society of Edinburgh. [sess. 
above. The writer, however, whose work that of Molins most 
closely resembled was Scherk, and very probably the two 
were unknown to each other. Both had the same purpose in 
view, and both used the method of so-called “ mathematical induc- 
tion.” The difference between them may most easily be explained 
by using a special example and modern notation. 
To make the solution of the set of three equations 
a 4 x + a 2 y + a 3 z = a 4 
b 4 x + b 2 y + b 3 z = b 4 - 
c 4 x + c 2 y + c 3 z = c 4 
dependent upon the already obtained solution of two, Scherk put 
the first pair of equations in the form 
a 4 x + a 2 y = a 4 - a 3 z j 
b,x + \y = \ - b z z f, 
solved for x and y , and substituted the values in the third equation. 
Molins, on the other hand, having used the multipliers m l , m 2 , 
1 , with the equations of the given set, performed addition, solved 
the pair of equations 
m 4 a 2 -1- m 2 b 2 + c 2 = 0 
m 4 a 3 + m 2 b 3 + c 3 = 0 
for m 1 and m 2 , and substituted the obtained values in the result 
_ m l a 4 + m 2 b 4 + c 4 
1 — m Y a Y + m 2 b 1 + c 4 
His exposition is laboured and uninviting. 
Boole, G. (1843). 
[On the transformation of multiple integrals. Cambridge Math. 
Journ ., iv. pp. 20-28.] 
Boole had to use in his paper the resultant of a system of n 
linear homogeneous equations, and he therefore thought proper, by 
way of introduction, to state a mode of forming the resultant, and 
