[ 35 ] 
II. The Calculus of Chemical Operations ; being a Method for the Investigation , by 
means of Symbols, of the Laws of the Distribution of Weight in Chemical Change . — 
Part II. On the Analysis of Chemical Events. By Sir B. C. Brodie, Bart., F.B.S., 
late Professor of Chemistry in the University of Oxford. 
Received January 13, — Read May 18, 1876. 
“ The Observer is not he who merely sees the thing which is before his eyes, but he who 
sees what parts that thing is composed of. ” — J. Stuart Mill. 
Contents. 
Introduction. — O n the Law of Even Numbers. 
Section I. On Chemicae Equations. — ( 1) Multiplication and division of chemical equations. — (2) Cases in 
which this is admissible. Definition of a “ normal chemical equation.” Examples. — (3) Transformation 
of chemical equations. Examples. Equation 1 -\-xy=x+y. — (4) Proof that (x—a)(y — 6)=0. — (5) Coin- 
cidence of chemical and numerical equations. — (6) Equation 2a. m v m i=3oc+a. n v n i, considered as a nume- 
rical equation. — (7) Interpretation of normal equations. Identity as regards space and matter. — (8) Sub- 
stitutions admissible in chemical equations. 
Section II. On “ Simple ” and “ Compound Events.” — ( 1) Equations the records of events. Definition of a 
chemical event. — (2) Aggregates of events. Definitions : a “ compound event,” a “ simple event.” 
Section III. On t he “ Causes ” of Chemical Events. — ( 1) Definition of an event occurring by one substitution 
and so occurring in several ways. Substitutions, the Causes of events. — (2) Events occurring by 2, 3, 
. . . n substitutions and so occurring in any number of ways. — (3) Definitions : “ Variables,” “ Values.” — 
(4) “Constants.” — (5) Vanishing of chemical equations. — (6) Event A(x— a)(y — 6)=0. — (7) Examples. 
— (8) Special forms of this event. — (9) Term “Transference.” — (10) Reverse events. — (11) Event 
A(x—d)(y—b')(z—c)=Q. — (12) Forms of this event. Examples. — (13) Events A(#—a)(y—&)(z—c)(z—c) 
( v — d)= 0. Examples. 
Section TV. Examples of the Elementary Analysis of Events. 
Section V. On the Theoretical Analysis of a Chemical Event. — (1) x—a , y — b. Symbols of “ substitutions.” 
Orders of events. — (2) Definition of “Congruous Functions.” Terms “Residue,” “Modulus,” Intro- 
duction of the symbol of chemical congruence =. — (3) Conditions satisfied by chemical functions congruous 
to a given residue for a given modulus. — (4) Relation of chemical to numerical congruity. — (5) Definition. 
“ Theoretical Analysis of a chemical event.” Development of f(x) in ascending powers of the modulus 
x—a. Development of f(x,y ) in ascending powers of the moduli x — a, y — b. Application of this deve- 
lopment to the analysis of events. — (6) Further definition of a “ Chemical Equation.” — (7) Theory of 
chemical phenomena as aggregates of events of various orders. — (8) Interpretation of x—a, xy—ab , as 
aggregates of transferences. 
Introduction. — ON THE LAW OF EVEN NUMBERS. 
The first part of this Calculus was devoted to the construction of those rudimentary 
tools of analytical investigation termed Chemical Symbols. I have there given expres- 
MDCCCLXXVII. G 
