60 
SIR B. C. BROD1E ON THE CALCULUS OE CHEMICAL OPERATIONS. 
gas at the lower temperature is essentially different from its constitution at the higher 
temperature. But in what does this difference consist 1 
If we are to discuss such questions with advantage, we must be content to advance 
from the known to the unknown, and base our reasoning upon analogous cases with 
which we are already acquainted. Here, again, I shall venture to give an illustration 
of the subject from the chemistry of Laputa. 
The Laputians, like ourselves, had their chemical difficulties. Two problems espe- 
cially had perplexed the heads of their philosophers (although, indeed, some of their 
chemists saw no difficulty in them at all). They had in their possession two chemical 
substances, to the units of which they had for various reasons assigned the symbols a« 2 | 2 
and a« 2 | 4 , and of which they had confidently predicted the densities (or weights of the 
units) on their hydrogen standard to be respectively 29 and 45. When, however, their 
best experimentalists came to take the density of these gases, this density was found to 
be in each case only half that at which it had been estimated, namely 14 '5 in the case 
of a» 2 | 2 , and 22 -5 in the case of a« 2 | 4 . 
The difficulty was serious enough ; for hitherto in the construction of the units of 
matter from acetylene a* 2 , oxygen £ 2 , hydrogen a, and the other elements, the operations 
a, x, | . . . had been sufficient for every requirement, hundreds of things had been made 
with these tools. But if these statements were to be unreservedly accepted, these 
operations would be inadequate to the purposes of the science ; for the symbols of the 
units of these substances, as expressed by the letters a, |, would be c&k% abs| 2 , neces- 
sitating in their construction the performance of an operation of, of which they had no 
experience whatever. 
The unit ajs 2 P is the unit of a substance which the Laputians had, but which we have 
not. It goes in our language under the name of the radical of formic acid. «^ 2 | 4 is the 
symbol we assign to the unit of oxalic acid. I proceed to explain how the Laputians 
dealt with this question. 
“ The accuracy of our experimentalists,” said they, “ is beyond suspicion, and we 
accept all the statements of fact made by them. But there is one point as to which it 
is necessary to inquire. How do they know, as their objections imply, that the gases of 
which they have taken the densities are really homogeneous gases \ If at the tempe- 
rature at which the experiment has been made these gases are really split in two, it is 
not necessary to modify, in this sense, our views. 
“ Now similar impediments have frequently stood in the way of our theories. But 
wherever it has been possible to look into the matter, as in the case of the pentachloride 
of phosphorus, and even hydrated sulphuric acid, theory has come out triumphant. 
This case is not strictly similar to those previously dealt with, but yet is not so dissimilar 
as to lead us to look for a totally different account of the matter. That we should dis- 
cover a new tool a v does not, we must confess, appear to us very likely. But that we 
should be able to do more, with our old tools a, x, |, than we have hitherto done is by 
no means out of the question. For the sake of argument let us assume, then, that the 
