84 
SIE B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
events which concur to produce a specified result, and that result alone, we shall endea- 
vour to arrive at a similar comprehension of the nature of those operations by which 
events occur, that is to say, of “ the causes of events.” The fundamental idea through 
which these operations will be conceived of in this Calculus is given in the following 
definition. 
(1) Definition : — 
If in any chemical event the change in the arrangement of the symbols by which the 
composition of the units of matter before and after the event respectively is symbolized 
be of such a nature that where in the arrangement before the event the symbol x 
appears the symbol a appears in the arrangement after that event, and where the 
symbol a appears in the arrangement before that event the symbol x appears in the 
arrangement after that event ( x and a being symbols of two among the prime factors by 
which the equation is expressed), so that the two arrangements differ in this respect, 
and in this respect alone, then that event is said to occur by the “ substitution ” 
or “ exchange ” of a for x, and that “ substitution ” is said to be the “ cause ” of that 
event. 
It is evident that, consistently with this definition, the same events may arise from 
more than one “ cause for it may be true that where, in the arrangement before the 
event, the symbol x appears the symbol a appears in the arrangement after that event, 
and that where the symbol x appears in the arrangement after that event the symbol a 
appears in the arrangement before that event, so that the two arrangements differ in 
this respect, and in this respect alone ; but it may also be true that where in the 
arrangement before the event the symbol y appears the symbol b appears in the 
arrangement after that event, and where the symbol b appears in the arrangement 
before the event the symbol y appears in the arrangement after the event, so that the 
two arrangements differ in this respect, and in this respect alone. In this case the event 
may be referred to either of two “ causes,” namely, to the substitution of a for x or for 
b for y. These causes represent two alternative hypotheses as to the ways in which the 
event may have occurred. Similarly one and the same “ event ” may be referred to 
several alternative “ causes,” representing various hypotheses as to the modes of the 
occurrence of that event. 
(2) If, however, the two arrangements so differ that where the symbol x appears in 
the arrangement before the event a appears in the arrangement after the event, and 
where a appears in the arrangement before the event x appears in the arrangement 
after the event, and also differ in the circumstance that where the symbol y appears in 
the arrangement before the event b appears in the arrangement after the event, and 
where b appears in the arrangement before the event y appears in the arrangement 
after the event, then that event is said to occur by two substitutions, namely, by the 
substitution of a for x and of b for y ; and these two substitutions are said to be the two 
“ causes ” of that event for the production of which they concur ; and, similarly, if 
the arrangements referred to differ in the n circumstances that where x, y, z . . . 
