SIB B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 99 
the equation into an interpretable form by resolving this factor. If this be effected 
the equation to the event becomes 
a (z- 1 Xz- a, )+ a ( <y - 1 )(z-")=°- 
From the principles demonstrated in Section I. (4) each of the terms of this equation 
may be equated to zero, and we are thus informed that this event is an aggregate of the 
two simple events, 
a (x~ 1 Xz“")= 0 ’ 
a(a>—l)(x—a)=0. 
Since these equations have a factor in common (% — u), the events expressed in them 
may be referred to a common cause, namely, the substitution of a for and may be 
regarded as members of a system of two events (in which a is constant) occurring by 
this substitution. At the same time we have in each case an alternative cause of 
the event, namely, in the former of the two events the transference of in the latter 
the transference of a , the original event regarded in its result being 
cq£ 2 -j- 2au—2a.-j(_ -j- aco 2 , 
and the constituents of that event similarly regarded being 
a X ^~ aM=a X^~ aiiJ X’ 
aa-fc-\-aa=au 2 -\-ot.%. 
The synthesis here indicated has been actually effected, the unit being no other 
than the unit of the chloride of iodine, which is formed, together with a unit of hydro- 
chloric acid, by the action of a unit of chlorine on a unit of hydriodic acid according 
to the former equation, and a unit of which, together with a unit of hydriodic acid, is 
resolved into a unit of iodine and a unit of hydrochloric acid according to the latter 
equation. 
(2) A unit of chlorosulphuric acid and two units of water are identical with a unit 
of sulphuric acid and two units of hydrochloric acid, thus 
-f- 2 a^=aO^ -j-2a.%. 
This equation may be thus expressed, 
a (^ 2 Z+^ 3 ~ 2 )(^-^) : = 0 - 
Here, again, we cannot interpret one of the factors of the equation, namely (^ 2 ^ + ^ 3 — 2) ; 
but proceeding as before we may resolve this factor, and bring the equation into an 
interpretable form, thus 
iX*-£H«(^-iX*-£)=o. 
Equating as before each term of this equation to zero, we are informed that the event 
is an aggregate of the two events 
a (^ 2 x-iX*-£)= 0 > 
a (^ 3 -iXx-£)=°- 
MDCCCLXXVJI. 
P 
