SIR B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
103 
These three equations inform us of the origin and properties of the units of the 
chlorhydrins of the sulphur-derivatives of glycerin, a 4 x 3 dy 2 , a 4 x 3 (Py, which substances 
have been procured by Carius*. In these three events a is constant, and the three 
events may be referred to one cause, namely the substitution of 6 for y. 
(8) A unit of glycerin and three units of acetic acid are resoluble into three units of 
water and a unit of triacetin, whence 
a 4 x 3 ^ 3 -f- 6a 2 x 2 ^ 2 = 3a£ -f- a 7 x 9 £ 5 . 
This equation may be thus expressed 
-a|(a 3 x 3 | 2 +a 4 « 5 | 3 +aV| 4 -3)(a« 2 ^-l)=0. 
Proceeding as in the last example, we arrive at the following constituents of the 
event : — 
aVg 3 +aV| 2 =a£+aV§ 4 , 
a 5 * 5 £ 4 +aV£ 2 =a£ + aV| 5 , 
a 6 x 7 % 5 -f-a 2 x 2 £ 2 =a£- \-a 7 x 9 £ 6 . 
In these events a|, the unit of water, is constant. The three events may be referred to 
one cause, namely the transference of ax 2 %. These events have been severally realized, 
the experiments by which Berthelot procured the units of the three acetates of 
glycerin, monacetin a 5 « 5 | 4 , diacetin a 6 x 7 %\ and triacetin a 7 x 9 % 6 , being recorded in these 
three equations. 
(9) Three units of iodide of ethyl and a unit of ammonia are identical with three 
units of hydriodic acid and a unit of triethylamine, 
6a x co-\-a v = oaco -J - a x v. 
This equation may be thus expressed 
a( Zed — a 5 x 4 v — a 3 x 2 v — av)(a 2 x 2 — 1) = 0 ; 
whence we have the following constituents of this event : — 
a(o- a 5 x 4 v)(a 2 x 2 — 1) = 0, 
a{u — a 3 x 2 v)(a 2 x 2 — 1 ) = 0, 
a{u — av)(a?x 2 — 1 ) = 0 . 
In these events a is constant ; the three events may be referred to a common cause, 
namely the transference of a?x 2 . The results of these events are given in the following 
equations : — 
a 3 x 2 cu -J- a 6 x 4 v —aw- f- a s x 6 v, 
a 3 x 2 a -j- a 4 x 2 v =au-\- a 6 x V, 
a 3 x 2 a-\-a 2 i> —au-\-a 4 x 2 v. 
The three phenomena of which the above event is the aggregate, the realization of 
* Annalen der Chemie, cxxiv. 221. 
