SIR B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
89 
analogous to the fundamental hypothesis which is the base of the system constructed 
in Part I., namely, that the unit of hydrogen is itself a simple weight and expressed 
by a single letter a. This is not the place for the further discussion of this question, 
which I shall hereafter have occasion to consider in some detail ; but I have made the 
preceding remarks to prevent any misapprehension arising in the mind of the reader in 
reference to the examples of chemical events given in this and the following Section, in 
which the equations are expressed by various sets of prime factors. These are not, as 
a matter of fact, mere arbitrary expressions (although, indeed, such would have 
sufficiently served the object in view), but I have not entered on the reasons which 
justify them, as being beside my purpose. I need only further observe that the 
equations are not to be considered collectively as representing systems of events (although 
they may be selected from such systems), but as individual equations, where a system is 
reduced to its simplest form, namely to a single event which from some unexplained 
reason is represented in the way given. 
(7) The following event is an example of this class of phenomena. A unit of chloride 
of benzoyl and a unit of potassium alcohol are identical with a unit of chloride of 
potassium and a unit of benzoic ether, 
+ a 5 * 9 £ 2 - 
This equation may be expressed by means of the prime factors a, %, (aV£), 
(aV£), and thus written 
a(a V|) x + a(aV§)a. = a X ^ + a(a V£)(aV£), 
whence 
a(aV£ - p){% ~ «V§) = 0. 
By which equation we are informed that a in this event is “ constant ” and that a the 
event occurs in one of two ways, namely, either by the exchange of the “weight” 
aV£ for [jb or of % for aV£. It is to be borne in mind that these hypotheses are purely 
relative to this equation alone, and involve the assumption that in this event the 
“ weights ” a, aVf , aV£, % are not distributed. If this restriction be removed, 
other views may be taken of the nature of this occurrence. 
(8) It is desirable to notice certain special forms of this fundamental phenomenon. 
If ci=b so that the “ values ” of y and x become identical, the equation becomes 
A(x—o){y—a)=0, 
and 
Kxy + Aa 2 = A ay + A ax. 
Such an event, for example, is the following:— 
Example : — A unit of acetate of chlorine and a unit of iodine are identical with a unit 
of acetate of iodine and a unit of the chloride of iodine ; thus 
+ a<y 2 =aV| 2 a; + au X , 
