SIE B. C. BRODIE ON THE CALCULUS OE CHEMICAL OPERATIONS. 
63 
result produced by the original object considered. Thus in mechanics the fundamental 
theorem of the parallelogram of forces is an analytical method, by which it is demon- 
strated that a force of a given magnitude operating in a given direction may always be 
theoretically resolved, in an infinite variety of ways, into two or more forces of certain 
specified magnitudes operating in certain specified directions, the result of which, taken 
together, is in magnitude and direction identical with the result of the force thus analyzed. 
Or, again, take the case of the analysis of vibratory movements. Defining the vibration 
of a point as “ motion in a curve which returns into itself with a velocity which is 
always the same at the same point of the curve,” it may be demonstrated that any given 
vibration of a point in a plane may be analyzed into two component rectilinear vibrations 
in an infinite variety of ways, and that every vibration of a point, whether plane or not, 
may be similarly resolved into three component rectilinear vibrations*. 
Now precisely as forces are compounded of forces, as vibrations, are compounded of 
vibrations, so chemical events are compounded of chemical events ; and from the point 
of view of this Calculus the theoretical analysis of a chemical event consists in the 
theoretical determination of a certain special system or systems of such events, the total 
result of which, as regards the transformations of ponderable matter, is identical with 
that of the original event. 
When we say that a chemical event is thus constituted of other events into which it 
may be resolved, the question arises, what view we take of the nature of such an event 
to justify this statement, and of what kind of events it is to be regarded as made up. 
The reply is given through the peculiar representation of a chemical event, afforded by 
the method of this Calculus, by which this fundamental conception is suggested. This 
representation is brought under our notice through the development of the method 
itself when we express dynamical facts by it, and consider how we are to reason upon 
them through its instrumentality. I shall therefore treat the subject in this natural 
order, considering first the construction of the “ Organon ” or Instrument of reasoning, 
then the ideas suggested to us by that Instrument, and to which that Instrument is 
applicable. When the nature of a chemical event has been thus defined so that we 
clearly see what we have to do, the further inquiry lies before us of the theoretical 
solution of the problem, namely, given a chemical event, how are we to determine the 
events of which that event is compounded 1 This problem may in all cases be solved. 
The solution is effected by means of a peculiar theorem, which occupies in theoretical 
chemistry a position analogous to that held in theoretical mechanics by the theorem 
of the parallelogram of forces. Lastly, I shall give examples of the application of this 
theorem to actual events and things, when the chemist will have an opportunity of 
estimating the bearing of this theory upon facts and its practical utility. 
* ‘ Acoustics, Theoretical,’ by W. F. Donkin. Oxford, 1870. Chapter III. On the Composition of Vibrations. 
