SIR B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
83 
(3) Formation of alcohol from olefiant gas and water, 
«V+a£=«V£+ 1. 
(4) Oxidation of alcohol with the formation of acetic acid and water, 
aV£+£ 2 =a|+aV£ 2 . 
(5) Decomposition of acetic acid into marsh-gas and carbonic acid, 
l+aV^=a^+^ 2 . 
(6) Resolution of carbonic acid into carbon and oxygen, 
1 +*£■=*+£*. 
For if we write down these equations in order, and add the corresponding members 
of those equations, we arrive at the equation required, 
2x-j-a=ax 2 -\-2, 
coi 1 + a = a 2 x 2 -f- 1 , 
a V+a|=aV£+l, 
aVf+| 2 =a£ + aV| 2 , 
l+aV| 2 =a 2 x+*f 2 , 
l+xf 2 =*+| 2 . 
Now we have seen in the last example that the event (2) may be considered as con- 
stituted of 8 events, and the event (3) as constituted of 6 events, each of which is 
repeated twice in the “ compound event ” (1), which therefore is to be regarded as con- 
stituted of 20 distinct “ occurrences ” or “ events.” This last example is derived, with 
certain modifications, from the work of the distinguished chemist Berthelot, ‘ Chimie 
organique fondee sur la Synthese,’ where numerous similar illustrations of the aggrega- 
tion of phenomena may be found. “ C’est ainsi,” says Berthelot, “ que l’on parvient 
a la synthese d’un alcool par une succession reguliere de reactions definies ” (Chimie 
organique fondee sur la Synthese, ed. 1860, vol. i. p. 97). 
The synthesis of an alcohol thus effected by Berthelot is undoubtedly brought about 
by the aggregation of phenomena, and so far affords an illustration of a compound event. 
But this aggregate of phenomena is an accidental collection of events selected to 
attain a particular end, which, although concurring to produce the result in question, are 
yet marked by no regular order or sequence and are characterized by no common pro- 
perties. Such aggregates are not to be confounded with the aggregates subsequently 
considered in this Calculus. 
Section III.— ON THE “ CAUSES ” OF CHEMICAL EVENTS. 
Having thus arrived at the conception of the nature of that complex phenomenon 
which is here termed “ a compound chemical event ” as an aggregate or collection of 
MDCCCLXXVII. N 
