80 SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
l + 2a£ 2 =2 o|+§ f , (2) 
l + 2a|=2a+r (3) 
It is now in our power to take a different view of the nature of the event, 
l+ a £ 2 = a +£ 2 (1) 
For if we add together the right-hand and left-hand members of equations (2) and (3) 
and divide the result by 2, we constitute equation (1); that is to say, this event (1) 
may be regarded as a compound event, which is the aggregate of the two events, 
! + «! 2 =a§+-i£ 2 , 
!+«£ =a+|£ 2 ; 
for not only is equation (1) an algebraical inference from equations (2) and (3), but it 
is actually in our power to effect the chemical transformation of a unit of binoxide of 
hydrogen into a unit of hydrogen and a unit of oxygen by effecting two several trans- 
formations, namely, the transformation of a unit of binoxide of hydrogen into a unit of 
water and half a unit of oxygen, and also the transformation of a unit of water into a 
unit of hydrogen and half a unit of oxygen ; and the result of these events (whether 
they occur successively or simultaneously, or in whatever order) is the transformation of 
a unit of binoxide of hydrogen into a unit of hydrogen and a unit of oxygen, and no 
other occurrence or event — it being quite immaterial as regards the result whether we 
first transform a unit of binoxide of hydrogen into a unit of water and half a unit of 
oxygen, and then take that unit of water and resolve it into a unit of hydrogen and half 
a unit of oxygen, or whether we begin by resolving a unit of water into a unit of 
hydrogen and half a unit of oxygen, and then resolve a unit of binoxide of hydrogen 
into a unit of water and half a unit of oxygen, or whether the two events occur together. 
In each case the final result is precisely the same, namely, the conversion of a unit of 
binoxide of hydrogen into a unit of hydrogen and a unit of oxygen, and nothing else. 
Now as the equation 
l+«| 2 = a +£ 2 (1) 
is an inference which may be arrived at in many ways and from many systems of equa- 
tions, so may we regard this event as “ constituted” of other “ events ” in many ways. 
Thus, for example, a unit of chlorine and a unit of binoxide of hydrogen are identical 
with two units of hydrochloric acid and a unit of oxygen, and also two units of hydro- 
chloric acid are identical with a unit of chlorine and a unit of hydrogen, whence 
1 + a.% 2 +a§ 2 = 2a^ + 1 2 , 
2 ap£=a-J-ap£ 2 . 
The event (1) is also an aggregate of these two events. But these events, of which 
