104 
SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
which is here suggested to us, are the successive stages by which triethylamine has 
actually been formed in the investigations of Hofmann. 
(10) Lastly, take the familiar phenomenon of the decomposition of water into its 
elements. 
Two units of water are identical with two units of hydrogen and a unit of oxygen, thus 
l+2a£=2«+£ 2 . 
This equation may be thus expressed, 
( 2a — 1 — £)(£— 1 )= 0 ; 
whence 
(a-£)(£-l)+(«-l)(f-l)=0, 
the constituents of the event being 
(«-$)«- i)=o, 
( a -i)(!-i)=o. 
These two events may be referred to a common cause, namely the transference of £. 
Their results are given in the equations 
a§+l=£-|-a. 
The element § which appears in these phenomena has not been isolated, but its 
existence is indicated to us as an object of research not here alone, but also by the 
analyses of numerous other chemical events. 
The previous examples are offered to the consideration of the reader, not as illus- 
trations of the general treatment of the subject to he ultimately pursued, but as examples 
of the most elementary application of the principles of algebraical reasoning, according 
to the fundamental methods of this calculus, to the analysis of phenomena. By the 
application to chemical equations of purely formal processes, we elicit from them new 
and true information as to the chemical occurrences of which they express the results. 
From this point of view the preceding analyses have a special interest. So far as I am 
aware they are the very first application which has been made of what can be termed 
(in any exact sense) algebraical reasoning in chemistry. Such examples might he inde- 
finitely multiplied ; but there would be no object in proceeding further in this direction. 
The method here employed is obviously of but narrow application, being limited to such 
equations as can be expressed by rational factors (which is an exceptional case), and is 
superseded by the more general treatment of the subject developed in the following 
section, to which I will now proceed. 
Section Y. 
(1) We have now constructed, in accordance with the method of this calculus, a 
symbolical representation of simple chemical events, according to which these events are 
referred to a definite system of causes, and are conceived of as occurring by means of 
