SIR B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
97 
substitution of a for x, of b for y, of c for z, and of d for v. The same principle may be 
extended to any number of factors ; and generally, if a chemical equation be expressed 
by n such factors, so that 
A.(x—a)(y—b){z—c){v—d)(w—e) .... =0, 
the event symbolized in that equation may occur by one substitution, and may thus occur 
in n ways ; that is to say, there are n alternative “ causes ” of that event to one or other 
of which the event must necessarily be referred, namely, the n substitutions indicated 
by the n factors of that equation. 
As the complexity of chemical phenomena increases so do these phenomena, regarded 
as actual events, become more rare, and it is more and more difficult to give real examples 
of them. This arises mainly perhaps from the difficulty inherent in the way of their 
experimental realization, an event expressed even by four different factors requiring the 
construction of no less than sixteen different substances connected by a certain definite 
relation, but also from the circumstance that the efforts of chemists have never been 
directed to the realization of such phenomena as a definite problem. We have the 
strongest evidence in favour of the existence of these relations, but we cannot exhibit 
them in a complete form. Such events are, if we may so say, fragmentary and imperfect, 
like buildings in process of construction, some near to completion, others of which the 
plan and outline are visible to the eye of the architect alone. 
The following events are examples of this class : — 
Example : — A unit of tetrachloride of carbon together with six units of monomethyl 
chloride and a unit of marsh-gas are identical with four units of chloroform and four 
units of chloride of methyl ; thus 
(A)/+6(A)^+(A)=i(a^) x 3 + i(A) x , 
whence 
K*Xx-i) 4 =o. 
In this event cdx, the symbol of the unit of marsh-gas, is constant. The event occurs 
by the transference of and in four ways by that transference. 
Example: — A unit of tetrachloride of tin, a unit of stannic diethylchloride, four 
units of stannic ethylmethylchloride [unknown], a unit of stannic dimethylchloride, 
and a unit of stannic diethyldimethyl are identical with two units of stannic methyl- 
trichloride, two units of stannic methylchloridediethyl [unknown], two units of stannic 
ethylchloridedimethyl, and two units of stannic ethyltrichloride*, whence 
a2 * , K 4 + a6 * , *V 2 +4aV?£ 3 ;£ 2 + aV;s 2 ;£ 2 -J- a 8 x'?e 6 =:2aV^ 3 +2aV 
-f- 2aVx 4 ;£ -f- 2 cdx.'z 1 ^ 3 . 
This equation may be written thus, 
(a^^ 4 +(«V]( a V) Y+ 4 (aV)( a x)(« 2 « 2 ) z 2 + ( a 2 «')(««) Y + (“ V )(^) 2 (« 2 « 2 ) 2 
=2(a 2 K , )( a «Y+2( a ^ , )( a «)( a V) 2 ^+2( a 2 « , )(««) 2 (a 2 « 2 )z+ 2 (“ 2 ^)(^ 2 Y 5 
* Vide Kekuee, vol. i. 782, p. 505. 
