SIR B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
91 
but simply does not appear at all, every chemical event being necessarily referred in it 
(without any forcing) to the operation of one and the same law of “ substitution,” a 
generalization due to the introduction of the chemical symbol 1. The meaning of a 
remark made in the first part of this Calculus (I. Sec. III. (3)) and there left unexplained, 
to the effect that the matter of an empty unit of space, although not an object to be 
presented to the imagination, must nevertheless, if we would reason correctly, be 
“ treated as a reality in the order of ideas,” will now be apparent. 
Example : — The following event is of the above form, 
a 3 x 2 co -f- a 2 v —aco -f- a. 4 x 2 v, 
which equation may be written thus 
ol{u — av)(a 2 x 2 — 1) = 0. 
The event here symbolized is the transformation of a unit of iodide of ethyl and a 
unit of ammonia into a unit of hydriodic acid and a unit of ethylamine, which event 
may be referred to one of two causes, namely, either to the substitution of av for u, 
or to the transference of a 2 x 2 , as is seen on inspecting the above equation. 
Example : — Again, 
a| 2 +a=2a|, 
or 
«(£-i) 2 =o. 
This equation expresses the event of the transformation of a unit of hydrogen and a 
unit of binoxide of hydrogen into two units of water. 
This event occurs by “ the transference ” of |, and in two ways by that “ transference.” 
Example : — Again take the equation 
aV£-fccf==2aV£, 
as expressed by the prime factors a, £, (aV), 
a£(aV) 2 + a £=2a£( a V), 
or 
a|(aV-l) 2 =0, 
which symbolizes the event of the transformation of a unit of ether and a unit of water 
into two units of alcohol. 
In this event a£ (the unit of water) is necessarily to be regarded as constant. The 
event occurs by “ the transference ” of a 2 * 2 , and in two ways by that “ transference. 
If in the equation A(#— a){y— £)=0, A=l, so that 
{x-a){y-b)= 0, 
“ no weight ” is constant, the event being fully defined when we say that the event 
occurs by the substitution of a for x or of b for y. 
Example : — Such an event, for example, is the transformation of a unit of hydrogen 
MDCCCLXXVII. 
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