62 
SIE B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 
properties of these substances and *£ which it was necessary to assume, this need be noi 
matter of surprise at all, for chemical substances (as everybody knew) existed in groups 
characterized by such similarities. When it was further urged that it would be very odd 
for such things to be found there and nowhere else in the world, they replied that on this 
point they really were incompetent to judge, but that, at any rate, many things as 
strange had more than once happened before, as in the case of the elements caesium, 
rubidium, and lithium, three out-of-the-way things found all together in one mineral 
water, and the mineral gadolinite, which presented many curious problems which no one 
had yet fathomed. However, they added, “We always measure out our belief according 
to the evidence, and you are mistaken if you imagine us to be speaking over-confidently 
on such a subject.” 
Now we certainly cannot say that any Laputian chemists were placed in the position 
or reasoned in the way we have described ; but we may say that if they had been placed 
in this position and reasoned thus they would have reasoned correctly, and their reasoning 
would have been fully justified by facts. 
This argument is greatly strengthened by the numerous analogies connecting the 
elements v and z. It is impracticable at this stage of our inquiries to bring these pro- 
perly forward ; hut the reader will hereafter have the conclusion forced upon him that the 
element v is, so to say, but a less potent carbon. At any rate, pursuing this train of 
thought, I have, as I must frankly confess, been brought to the opinion that by far the most 
probable explanation to be given of the anomalies presented by the densities of the 
binoxide and tetroxide of nitrogen is that the two gases which pass under this name are 
not homogeneous gases at all, but in each case are constituted of two gases which, taken 
together, are made up of the matter of oxygen and nitrogen, but which separately are 
not so made up. This is undoubtedly a speculation ; but it is not a mere speculation, 
but one founded upon reasonable grounds, which explains difficulties for which no other 
explanation has ever been propounded, and suggests experiments by which it may he 
verified or disproved. I proceed to another subject. 
The analytical construction of the symbols of the units of matter can be regarded 
only as preliminary to the consideration of a more complicated problem, namely, how 
these units are transformed in the processes of chemical change. On this subject there 
has been much speculation ; hut it is not going beyond the truth to say that no general 
theory of the nature of chemical events has yet been devised which will bear the 
slightest criticism or which is even intelligible. This question also we shall here con- 
sider from the analytical point of view afforded by the methods of this Calculus. “ The 
mental,” or, as it may be better termed, the “ theoretical ” analysis of a complex pheno- 
menon into its elements is (it has been truly said) the first step of inductive inquiry*. 
This theoretical analysis of any object of our study is effected when we replace that 
thing by some system of things, the result of which, taken together, is equivalent to the 
* J. S. Mill, vol. i. c. vii. 1, p. 437 ; and also Contents to the same, p. xiv (ed. 1843). 
