48 
SIR B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
we have from these equations 
n! 2 p 1 
n p +p' 
Now the values of the fraction for all positive and integral values of p and p' 
(whatever be the value of m) are comprehended between the limits 0 and 2. 
if y=o, 
^7=0. 
If _p=o, 
p+p 
p+p' 
It hence appears that if the symbol is to satisfy the conditions given in the 
equation 
moi n x n '{; n "z n "' =pa +p'o&)f 
a restriction is placed by the conditions of the problem upon the values of the integers 
n' 
n and n', which must be so selected that - shall not be < 0 or >2. 
’ n 
Yll 
If M =0,y=0, and the equation becomes 
mot, n % n "x. n "' =pc& + q% 2 -\-rx. 
n' 
If -=2,^ = 0, and the equation becomes 
mcc n x tn {; n "x. n "'=v'cix t + q^ 2 + rx. 1 . 
No restriction exists on the values of n" and n'". We may notice the two forms : — 
(1) m=l, 
n=p+p', 
n’=2p', 
n"=2q, 
n"'=r, 
n"'=2r. 
(2) 
m= 2 , 
n- 
.P+P. 
n'=p', 
n"=q, 
tn" r =r , 
