SIR 3. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
41 
the several units being 
Unit of Hydrogen 2 X— , weighing 0"089 grm., 
„ Chlorine 2D „ 3-173 grms., 
,, Hydrochloric acid . . ^-f-D ,, 1-631 grm., 
the weight in grammes of the bits of matter — and D being respectively 0-044 grm. 
and 1*586 grm. This result corresponds to the view now generally received by chemists 
as to the constitution of these units, according to which the matter of the unit of hydrogen 
is regarded as constituted of two bits of matter in all respects identical. Were we to 
construct the symbols of these units on the principles of this Calculus, we should arrive 
at the following system, which corresponds to the assumption that the unit of hydrogen 
is constituted of two simple weights : — 
Symbol of the unit of Hydrogen .... a 2 , weighing (M)89 grm. 
„ ,, Chlorine . ... c 2 ,, 3-173 grms. 
„ „ Hydrochloric acid . ac ,, 1-631 grm. 
It is important to observe that there are only two such symbolic systems*, which, 
* Besides the systems originating in these two hypotheses respectively, there is also the general or indeter- 
minate system comprehending both, in which we have 
Symbol. 
Hydrogen aW 2 
Chlorine a'x" 
Hydrochloric acid a 
Nitrogen aV 3 
Ammonia a'V-nr 3 
If in this system of symbols we put tn — 1, it becomes the system on hypothesis a ; if we put a'= 1 , it becomes 
the system ou hypothesis a 2 . We may consider the system to originate in the following manner. Taking the 
equation 
2E=A + C, 
let X be the matter common to A and C, and Y and Z the other constituents of A and C respective 1 y, so that 
we have then 
and 
A=X+Y, 
C=X + Z; 
2E=(X+Y) + (X + Z) 
E=X + 
Y+Z 
Y Z 
Since Y and Z have no common part, — must be a “ simple weight,” and ~ also a simple weight, whence 
we have the units of hydrogen, chlorine, and hydrochloric acid constituted as follows: — 
