SIR B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 101 
This equation may be thus expressed, 
«g(aV | + aV£ 2 - 2)(ax 2 | - 1) = 0, 
whence 
of (aV|- l)(«x s | - 1) +a£(«V§ 2 - l)(a* 2 f- 1)=0, 
the constituents of the event being 
a£(a 2 ?c 2 £ — l)(a;f 2 £ — 1 ) = 0, 
a£(aV£ 2 - l)(a* 2 £_l)=0. 
In these events af is constant ; the two events may be referred to a common cause, 
namely the transference of ax 2 £. The resulting identities are 
aVf 3 +«f=a 3 * 2 £ 2 +aV| 2 , 
These phenomena have been realized, the unit aV£ 3 , which together with a unit of 
acetic acid is formed by the decomposition of a unit of diacetic glycol and a unit of 
water, is the unit of monacetic glycol, which has been prepared by the simultaneous 
decomposition of a unit of bromide of ethylene, a unit of acetate of potash, and a unit 
of water. 
(5) A unit of suberic acid is identical with a unit of the hydride of hexyl and two 
units of carbonic acid ; this relation is given in the equation 
2+ a V£W* 6 +2*£ 2 . 
This equation may be thus expressed 
(aV^+aV- 2)(x| 2 -l)=0, 
whence 
(aV| 2 -l)(^ 2 -l) + ( a V-l)(^ 2 -l) = 0, 
the constituents of the event being 
(aV£ 2 - 1)(«| 2 -1)=0, 
(aV~l)(*r-l) = 0, 
which two events may be referred to a common cause, namely the transference of 
the results being 
aV£ 4 + 1 =aV£ 2 +x| 2 , 
a 7 ?£ 7 ^ 2 + 1 = a 7 * 6 -f- x£ 2 . 
The unit aV£ 2 , which appears in these events, but not in the original event, is the 
unit of cenanthylic acid, the existence of which unit and the properties by which it may 
be recognized are here pointed out. 
(6) A unit of terchloride of phosphorus and three units of water are resoluble into a 
unit of hydrated phosphorous acid and three units of hydrochloric acid, thus 
3a|= 3a^ +a 2 <p| 3 . 
