SIE B. C. BEODIE ON THE CALCULUS OE CHEMICAL OPEEATIONS. 93 
being an event in which a is constant, and which occurs in two ways by the transference 
of 
Now the resolution of hydrochloric acid into its elements is thus expressed, 
2 a^=a+a^ 2 , 
the symbol of which, regarded as a substantive event, is 
Instead of attempting to interpret the factor (1— we may write this event thus, 
+[-“(*— 1 «= 0 ; 
in which case we do not attempt to explain the “ causes ” of the event itself, but instead 
of so doing, we say that the event is the reverse of an event of which both causes are 
intelligible to us. 
The events which we have now considered are completely defined by their symbolical 
expression. They are events which may be referred to two alternative “ causes,” and 
to two such “ causes ” alone ; that is to say, they are events which necessarily occur by one 
or the other of two specified substitutions, and by this property are, as a class, separated 
from all other phenomena. This great class of events is, however, only one, and that 
the very simplest, instance of an indefinite number of such systems to the conception 
and consideration of which we are brought by the development of the methods of this 
Calculus, and to the explanation of which I shall now proceed. Of these systems, also, 
I shall lay before the reader a sufficient number of examples to invest these conceptions 
with reality, and to satisfy him that we are not dealing simply with algebraical forms, 
but with algebraical forms corresponding to real occurrences. It will not, however, be 
necessary to dwell at equal length upon this portion of the subject ; for the reader 
who has accompanied me so far will readily appreciate what I have now to submit to 
him. 
(11) If an equation be expressed as the continued product of three factors each of 
the form x— «, so that 
A (x-a)(y-b)(z-c)=0, 
the event may be conceived of as occurring by one substitution and, as thus occurring, 
in three different ways, namely, by the substitution of a for x and of b for y and of 
c for z, which three “ substitutions ” are to be regarded as three alternative “ causes ” of 
that event, to the one or the other of which that event must necessarily be referred. 
For the result of this event is expressed in the equation 
A xyz + A cibz-\- Kaye + A xbc— Axyc -f - Aab c + A ayz -f Axbz ; 
and if, proceeding as before, we institute a comparison between the arrangement before 
the event and the arrangement after the event, with the view of ascertaining experi- 
o 2 
