PROCEEDINGS 
OF THE 
ROYAL SOCIETY OF EDINBURGH. 
vol. vi. 1866-67. No. 73. 
Monday , 1 %lh February 1867. 
Sir DAVID BREWSTER, President, in the Chair. 
The following Communications were read : — 
1. On an Application of Mathematics to Chemistry. 
By Dr A. Crum Brown. 
In this paper chemical substances are represented as “ operands,” 
and chemical processes as “ operators ” — thus, <j> • x is the sub- 
stance produced by acting on the substance x by the process (f > . 
When </>, y, if/, &c., act independently on x, this is indicated by the 
cf> 
notation ^ 
&c. 
£c. When they act one on another to produce a 
complex operator which acts on x, the notation <f> • y • if/ • x is used. 
It is shown that in the latter case the commutative law does not 
apply to operators. 
The meaning of the negative index applied to an operator is 
defined thus : <f> • (<£~' 1 *x) = x ; and it is shown that <f>~ 1 -x may 
have more than one value. ^|*as is written <£ 2) *a?, and generally 
cf> m) 
cf> n) 
x = <£ w + n) «£c where m and n are both positive or both nega- 
tive (i~ l r® n °t being necessarily = x^j. cf)'<fj-x is written 
F • x, and generally <£” • </> • x = </> n + 1 . x. 
The general series x, <f>’X, </> 2 • x, <£ 3 • x 
<f> n • x is shown to 
VOL. VI. 
M 
