98 
SIE B. C. BEODIE ON THE CALCULUS OE CHEMICAL OPEEATIONS. 
whence 
(“**)(*— «x) 2 (*— a V) 2 = 0. 
This event, therefore, is to be considered as occurring by the substitution of cws for £ 
and by the substitution of «V for %, and in two ways by each of these substitutions 
respectively. 
Section IY. 
We thus arrive at the interpretation of the chemical equation 
A (x-a){y-b)(z-c) ... =0, 
considered as the symbol of a “ simple chemical event.” From the consideration of such 
an equation we are led to refer the event thus symbolized to certain specified substi- 
tutions (indicated to us by the factors of the equation) as the causes of that event, by 
the enumeration of which causes, together with the constant A, the event is defined, 
there being only one possible event which will satisfy the conditions specified in the 
equation. Such equations constitute a class apart. The explanation of a chemical 
event consists in referring the event to the causes which concur to produce it. There- 
fore it is only those events which can be thus expressed which can, in any proper sense, 
he said to be explained, simple events, and such events admit of no further explana- 
tion of this kind. 
Now a chemical equation may not be of the above form, an equation to a “ simple 
event,” but yet may be expressed by means of rational factors. In this case the event 
indicated in the equation may be immediately resolved into some number of simple 
events occurring by one or more specified substitutions, of which that event is the 
aggregate. Such aggregates were the first actually discovered by me ; and although in 
the next section the whole question of the analysis of aggregates will be discussed in a 
far more complete manner, I shall yet invite the reader, with a view to a clear compre- 
hension of the subject, to follow the course actually pursued, and to consider a few of 
the simpler problems which such equations present to us. 
Examples. 
(I) A unit of chlorine and two units of hydriodic acid are identical with a unit of iodine 
and two units of hydrochloric acid, and therefore may be transformed into these units. 
The equation to this event is 
ct^ 2 J r 2aoo= 2a% -f- ecu 2 . 
which equation may be thus expressed, 
a(x+v—2)(x—u)=0. 
Now we cannot interpret the equation in this form ; for although, it is true, we know 
what is meant by the factor (■/_ — a) and can perform the substitution which it directs us 
to perform, the factor (^ + ^—2), which should express the alternative mode of the 
occurrence of the event, conveys no meaning to us. We can, how 7 ever, easily convert 
