96 
SIE B. C. BEODIE ON THE CALCULUS OE CHEMICAL OPEEATIONS. 
Example : — A unit of methylethylamylamine and a unit of methylamine and a 
unit of ethylamine and a unit of amylamine are identical with a unit of methylethyl- 
amine and a unit of methylamyl amine and a unit of ethylamylamine and a unit of 
ammonia ; thus 
a w x 8 v + a 3 x v -f- cc 4 x 2 v + aJx h v = a s x 3 v -f- a 8 x 6 v + a 9 x 7 v -f- arv, 
which equation may be written thus, 
(a 2 v)(ax)(a 2 x 2 )(u 5 x 5 ) -\-(a 2 v)(ax) +(ci 2 (')(a 2 « 2 ) -f- (a 2 v)(ef 5 j< 5 ) = (u 2 v')(ax)(ct 2 x 2 ) 
+ (a 2 v)(ax)(a 5 x 5 ) -)- (a 2 v)(u 2 x 2 )(a s x s ) ( a 2 v ), 
whence 
«X«*- l)(aV-l)(aV-l) = 0 ; 
a 2 v (the unit of ammonia) is constant, and the event occurs by the transference of ax, 
and by the transference of a 2 * 2 , and by the transference of a 5 x 5 . 
If a=b the equation becomes 
A(#— a)(y —a)(z—c)= 0, 
and 
Axyz + A acx -f A acy + A a 2 z = A cxy + Aaxz -j- A ayz -f A <tfc. 
Example : — A unit of the acetobromochlorhydrine of glycerine and a unit of mon 
acetine and a unit of the monobromohydrine of glycerine and a unit of the monochlor 
hydrine of glycerine are identical with a unit of glycerine and a unit of the bromo 
chlorhydrine of glycerine and a unit of the acetobromohydrine of glycerine and a unit 
of the acetochlorhydrine of glycerine, whence 
a V£ 2 / 3*+ «V£ 4 + «V£ 2 |3 + a VI 2 * = aV| 3 + a 4 x% 3 + a V| 3 /3 + a V| 3 Z . 
This equation may be written thus, 
(a 4 x 3 |)(ax 2 |)^ + (a 4 « 3 ^)(a« 2 |)| 2 +(a 4 x 3 |)/3|+(a 4 x 3 |)^=(a 4 « 3 |)^ 2 
+ (« 4 x 8 g)/3* + 
whence 
We are thus informed that in this event a 4 x 3 % is constant, and that there are three 
causes of the event, namely, the “ transference ” of ux 2 %, the substitution of £ for and 
the substitution of £ for /3. 
(13) By reasoning analogous to that previously employed, it may be readily demon- 
strated that if a chemical equation be expressed by four factors of the form x—a, so that 
A(x-a)(y-b)(z-c){v-d)= 0, 
the event symbolized in that equation may occur by one substitution, and may thus 
occur in four different ways ; that is to say, there are four alternative “ causes ” of that 
event, to one or the other of which the event must necessarily be referred, namely, the 
