SIR B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
45 
and 
2 m 1 ac 2 % 2 %?=m l a 2 -\-^m 1 c 2 + 2?^ £ 2 -{-2R;t'. 
Comparing this equation with the general equation given above, we perceive that it 
falls under the case m=2m{, where m 1 is a factor oip and yJ and q. 
If we assume #=1, which corresponds to the assumption that the weight of a unit 
(that is, of 1000 cub. centims.) of carbon vapour at 0° and 760 millims. is 0*536, 
^-=2, R=2, and m x — 1, the equation being 
2ac 3 f V=a 2 -|- 3e 2 +2f 2 -f 4*. 
If we assume t— 2, which corresponds to the assumption that the weight of a unitot 
R 
carbon vapour is 1-072 [I. Sec. VII. Group 2, III.], — =1, R=l, m t =l, the equation 
being 
2a& % z 2 =a 2 + 3c 2 + 2£ 2 + 2* 2 . 
Again, one unit of dichloracetic acid is identical with a unit of hydrogen, a unit of 
chlorine, a unit of oxygen, and (as before) R units of carbon. In this case m is a factor 
of p, y, q, the equation being 
m a 2 c 2 ? 2 =m dr-\-m c 2 -\-m £ 2 -j-R;A 
There are two forms of this equation, corresponding to the hypotheses £=1, t = 2 : 
t= 1, $ 2 c 2 |j 2 }i 2 =-cl 2 -\-c 2 -\-^ 
t= 2, a 2 c 2 % 2 z 2 =a 2 -{-c 2 -\-!; 2 -\-x 2 . 
No limitation whatever is imposed by this hypothesis on the value of n, n', n", n'". 
Two cases may be discriminated : 
(1) m— 1, n=2p, n'=2p', n"=2q, n'"=r, 
(2) m=2,n=p, n'=p', n"=q, n"'=r; 
it being always remembered that q , r have no common measure. 
It hence appears that every combination of the letters a, c, k of the form a n c n '% n "x. n '" 
is the symbol of a unit of ponderable matter capable of being resolved into some number 
of units of hydrogen, chlorine, oxygen, and carbon, on the assumption here made as to 
the constitution of those elements. 
Now the symbols of all known compounds of these elements are to be found among 
these combinations, with their density and composition correctly indicated to us. Hence 
the hypothesis that the symbol of hydrogen is a 2 covers the whole ground, and is suffi- 
cient for our purpose. If it be defective, it is not by reason of its insufficiency. But 
there are other points to be considered. 
II. On the hypothesis a, namely, that the symbol of hydrogen is to be expressed by 
one prime factor, we have : — 
H 2 
