SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
47 
In the case m= 2, 
P+P 1 
ri=p’, 
n"=q, 
n'"=r. 
II. m is of the form 2m, , where m, is a factor oip! and q. In this case we have 
m tr 
W = 2 ^ 
(1) If ^=1, w'"= sir, w,= 1, and 
_P+P' 
n'=p', 
n"=q , 
»'"=4 
(2) If t— 2, m,= 1, and 
n'=p', 
n"=q, 
n"'=r. 
It appears therefore that, in the case of the hypothesis that the symbol of hydrogen 
is expressed by one prime factor a, m (as in the case of the previous hypothesis) may 
have two values and two values only, m=l, m=2. If m=l no restriction is placed on 
the values of the integers p,p', q, r; but if m=2, p+p 1 must be an even number. 
Referring again to the system of equations 
nm—p-\-p\ 
n'm=2p\ 
n"m=2q , 
n'"m=tr, 
