SIR B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 81 
event (1) is constituted, may themselves be compound events, and that in various ways. 
Thus, for example, the event 
1 + «Z 2 + °^ 2 = 2a Z + 
may be considered as the aggregate of the two events, 
2a*+a£ 2 =a;c 2 + 2 of, 
1 + 2a^ 2 + 2a| = 4a% + £ 2 ; 
in which case the event (1) will be the aggregate of three events — 
2a^ + a§ 2 = a^ 2 -f 2a|, 
l + 2 az 2 +2 a £=4a*+| 2 , 
2^=«+«/- 
Example (2). — Again, a unit of ammonia and three units of iodide of ethyl are iden- 
tical with three units of hydriodic acid and a unit of trie thy lamine. 
This event is thus expressed : 
a 2 v -j- 3a 3 J c 2 a— 3cwy-j- a 8 * 6 ?. 
Now this event may be regarded as the aggregate of the three following events : — 
a 2 v -f- a. 3 x 2 eu = aa + a 4 x 2 v, 
a 4 x 2 v -j- a 3 x 2 a =au- j- a?x 4 v, 
a 6 x 4 y -f - ol 3 x 2 oj = aco- j- a 8 x 4 v. 
Each of these events, too, may itself be regarded as a compound event ; thus the event 
a 2 v T a 3 x 2 a — ctu- j- a 4 x 2 v 
may be considered as constituted of the following events : — 
a, 3 x 2 co-\-axv^=a 3 x 3 v^-\-aco, (a) 
a 3 x 3 v^-\-u^=a 4 x 2 v- {-x£ 2 , ..(b) 
x% 1 -\-o?v=u,%-\-axvt'. ..(c) 
For if (a) we take a unit of iodide of ethyl and a unit of cyanic acid and transform 
them into a unit of hydriodic acid and a unit of cyanic ether, and then (b) take a unit 
of cyanic ether and a unit of water and transform these into a unit of ethylamine and 
a unit of carbonic acid, and also (c) take a unit of ammonia and a unit of carbonic acid 
and transform these into a unit of water and a unit of cyanic acid (3), the final result 
of these successive events will be to transform a unit of ammonia and a unit of iodide 
of ethyl into a unit of hydriodic acid and a unit of ethylamine, which is the event in 
question. 
Example (3). — The following equation expresses to us the transformation of two 
units of marsh-gas and a unit of oxygen into two units of methylic alcohol, 
2« 2 x+£ 2 =2a 2 x£+l. 
