SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 
37 
matter which we infer, from probable reasoning of various kinds, would occupy our 
measure, in the gaseous state, under certain normal conditions, if only we could thus 
estimate it. Hence undoubtedly our results are liable to be affected with very serious 
errors. So that it may be truly said that the theory of chemistry refers rather to an 
ideal world created by the reason of man out of the actual world than to the actual 
world itself. There is, however, a wide interval between the ideal creations of the 
reason and the figments of the imagination. In the long run the former correspond to 
realities, and the comparison of the results as to the densities of gases which have 
actually been anticipated by this mode of probable reasoning with those subsequently 
arrived at by conclusive experiments prove us to be on the right track. 
If it be asked why we do not, as is usually done, select a “ molecule ” as our unit, we 
reply, not that the molecular hypothesis is untrue (this would be going beyond the 
mark), but that it is unnecessary. We do not object to it, but we do not use it, for we 
do not want it for our present purpose. Having thus obtained the “ unit of matter,” the 
inquiry before us is, by what operations are these units of matter made! We begin 
by endeavouring to answer another question, namely, of what are they made 1 To this 
but one rational reply can be given. The units of matter are made of the matter of 
one another. But this is not all that can be said, for we may proceed to ask how, in 
particular cases, these units are thus made up. 
The matter of two units of water, 2C, is made up of the matter of two units of 
hydrogen, 2A, and one unit of oxygen, H, and is therefore identical with that matter. 
We may state this identity in an equation, thus — 
2C=2A+D; 
whence 
D=2C-2A, 
=2(C— A). 
Now we give a complete definition of the unit of oxygen, D, when we say that the 
matter of a unit of oxygen is identical with the matter of two units of water without 
the matter of two units of hydrogen ; but we may further, from the last equation, assert 
that the matter of a unit of hydrogen, A, is a part of the matter of a unit of water, C. 
If, then, in the above equation, making this assumption, we put C=Bff-A, we have 
D=2B. 
Further, assuming the matter of two units of water to be identical with the matter of 
a unit of hydrogen and the matter of a unit of binoxide of hydrogen*, and putting E 
as the matter of a unit of binoxide of hydrogen, we have 
2C=A+E, 
* The vapour-density of binoxide of hydrogen has not been experimentally determined. If this vapour- 
density should prove to he other than that here given, we should he compelled to take a ditferent view of the 
constitution of water ; hut, from all we know, this is a highly improbable contingency. 
G 2 
