44 
SIB B. C. BEODIE ON THE CALCULUS OE CHEMICAL OPEEATIONS. 
and 
ri'm— 2q, 
n"'m= tr. 
2 p ... 
n=^ a positive integer. 
m 
hi tr 
It appears from these equations that m is either a factor of p, q>', and q, or is of the 
form 2 ml, where m 1 is a factor of and q. 
Further, since m is a factor of tr , if m be a factor of and q, m is prime to r, and 
m is a factor of t. If m=2m 15 since m 1 is prime to r , m l is a factor of t. If we assume, 
therefore, in conformity with the results arrived at as to the symbol of carbon (I. Sec. 
VII. (2)), t = 1 and t = 2 as the most probable assumptions in the case of that symbol, 
we have in the former case, 
t— 1, n!"=-^ and m=l, 
in the latter case, 
t=2, n"'~ ; 
whence either m—\ or is of the form m=2m I , where m x is a factor of r. But m is prime 
to r; therefore we have on these assumptions only two values for m, m= 1 or m=2>. It 
is, however, to be borne in mind that this limitation of the value of m implies a more 
definite knowledge of the hypothetical density of carbon than we possess. These results 
are the only consequences to be here deduced from the joint hypotheses that the units 
of ponderable matter are made up of an integral number of simple weights, and that 
the unit of hydrogen is constituted of two identical simple weights. The application of 
these principles will be readily seen in a particular case, For example : — 
One unit of trichloracetic acid weighing 7 - 308 grms. is identical with half a unit of 
hydrogen, three halves of a unit of chlorine, one unit of oxygen, and some unknown 
number of units of carbon (to be hypothetically determined) weighing F072 grm. 
Putting the symbol of carbon as where t is an undetermined integer, we will 
R 
call this unknown number of units — . Expressing this identity in an equation, we have 
m, «c 3 | 2 » 2 =^ « 2 +~u 1 c 2 +m 1 | 2 +Ex < 
