46 
SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
Symbol of Hydrogen a, 
„ Chlorine o% 2 , 
„ Oxygen £ 2 , 
„ Carbon 
the symbol of a unit of matter as expressed by the prime factors a, %, z being 
From the conditions of the problem we have 
whence 
and 
ma n y^ l "z n '" =pa -\-p'ay ? ; 
mn=p-\-p’, 
n'm=2p', 
n"m=2q, 
n'"m=tr , 
p-\-p' . . 
a positive integer, 
n'=~ 
On 
n "= ^ 
m 
There are two cases. 
I. m is a factor of p, p\ q and is prime to r. 
If t— 1, and wi=l, since p, p\ q , r are so taken as to have no common 
measure, and 
n=p+p', 
n’—2p', 
n"=2q, 
n"'=r. 
If t= 2, n'"=--^. In this case m may have one of two values, m — 1 and m= 2. In 
the case m=l, we have 
n=p-\-p\ 
n'=2p', 
n"=2q, 
n"'=2r. 
