86 
SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
It is necessary to notice that every algebraical condition under which a chemical equa- 
tion may vanish does not necessarily correspond to some one among the “ causes ” of the 
event, or throw light upon such causes. For an equation may vanish under algebraical 
conditions which are chemically uninterpretable and unmeaning. But if an equation 
vanish under certain specified conditions, such as that x=a , when x and a are two of 
the prime factors of an equation constructed upon the principles before laid down 
(I. Sec. V., II. Sec. I.), these conditions are capable of interpretation, and inform us 
of the “real” causes of the event — the term “real” causes being here used to distin- 
guish such causes from “ imaginary ” causes, which may be defined as substitutions cor- 
responding to algebraical conditions which are uninterpretable. It is quite possible that 
the consideration of “ imaginary ” causes may hereafter find its place in the chemical 
Calculus and lead to true results, but we shall not now consider them. 
(6) I shall now proceed to the consideration of certain forms of equations corre- 
sponding to the events of which the definition has now been given, and the interpretation 
of those forms. 
I will commence with the equation already referred to (Part II. Sec. I. (4)), 
Axy + A ab = A ya-\- A xb . 
Now, if we compare the arrangement before the event, namely, Axy-\-Aab, with the 
arrangement after the event, namely, Aay-\-Axb, superposing those arrangements the 
one upon the other, thus — 
Axy-\-Aab, ............ I. 
Aay-\-Axb, . II. 
it will he seen that where x appears in the arrangement before the event, a appears in 
the arrangement after the event, and where x appears in the arrangement after the 
event, a appears in the arrangement before the event, and the two arrangements differ 
in this respect, and in this respect alone. Thence, according to the definition, the event 
symbolized in the above equation may occur by the substitution of a for x , and this sub- 
stitution is a cause of that event. 
But, since Aay J r Axb=Axb J s-Aay, we may compare these arrangements from another 
point of view ; for, writing the arrangements after the event as Axb-\-Aay , and again, as 
before, superposing the arrangements the one upon the other, thus — 
Axy-\-Aab, I. 
Axb-\-Aay, II. 
it will be seen that where y appears in the arrangement before the event (I.), b appears 
in the arrangement after the event (II.), and where b appears in the arrangement before 
the event (I.), y appears in the arrangement after the event (II.), and the two arrange- 
ments differ in this respect, and in this respect alone. Whence, according to the defini- 
tion, the event may occur by the substitution of b for y , which substitution is a real 
“ cause ” of that event. 
