TRANSACTIONS OF THE SECTIONS. 7 
nomena in the same category with the investigation of the phenomena of physical 
optics; and I am sure that any attempt to hasten unduly the affiliation of 
chemistry to theoretical dynamics would be productive of serious mischief. The 
drift of the remarks which I have made has been only to show that the current of 
scientific thought is setting in that direction; and while we may not predict such 
an affiliation, still less should we be justified in pronouncing it to be beyond the 
possibilities or even the probabilities of science. 
Time will only allow me to notice very briefly another important application of 
mathematics to a branch of science considered hitherto to be altogether beyond the 
limits of our Section,—I refer to the application of the methods of geometry and 
theoretical mechanics to Biological science recently made by Professor Haughton. 
The first example which I shall notice is the establishment of a principle govern- 
ing the animal frame, and quite analogous to the principle of “least action” in 
dynamics. This principle asserts that every muscle is so framed as to perform the 
greatest amount of work under the given external circumstances. If this principle 
be admitted as an @ prior? truth, the arranzement of any given muscle may be 
mathematically deduced from it; but many, no doubt, will prefer to regard it as an 
inductive truth established by the number of instances which Professor Haughton 
has adduced and discussed. Among these the work done by the human heart is 
considered ; and in order more fully to exemplify the principle of the economy of 
work, Professor Haughton has imagined a very obvious construction of the heart 
in which the principle would be violated, contrasting this with the actual con- 
struction in which, as he has shown, the principle is preserved. 
Professor Haughton has also made much use of the geometry of curved surfaces 
in estimating the action of the non-plane muscles. 
On the whole the work of Professor Haughton is a remarkable example of 
pe renting use of mathematical methods in the investigation of physical 
roblems. 
: We have put to scientific history the important question—Is it probable that the 
dominion of mathematics over physical science will be more widely extended than 
it is at present? Is it probable, not only that we shall improve the mathematical 
instrument as applied to those sciences which are already recognized as belonging 
to the legitimate province of mathematical analysis, but also that we shall learn to 
apply the same instrument to sciences which are now wholly or partially inde- 
pendent ofits authority? And to this question I think that scientific history must 
answer, Yes, it 7s probable. It is probable, because physical science is learning 
more and more every day to see in the phenomena of nature modifications of that 
one phenomenon which is peculiarly under the power of mathematics. It is probable, 
because science already indicates the path by which that advance will be made, 
because we already possess in molecular dynamics a method (the creation, I may 
almost say, of our own age, and still very imperfect) whose proper subject is 
motion not in any limited or abstract sense, but as widely as it really exists in 
nature. And it is probable, because we cannot look back on the history of 
science for the last fifty years without becoming conscious how large is the advance 
which has been already made. 
Thave thus far endeavoured to show to you the light which is thrown on the 
connexion between physical science and mathematical analysis by actual scientitic 
history ; and I have given you some reasons for believing, so far as it is permitted 
to us to read the future, that this connexion is likely to extend still more widely. 
But before we pass from this part of the subject, we are bound to ask the 
question, Are we to regard this indication as being favourable to the cause of 
scientific progress? Shall we regard the tendency to use, as far as possible, the 
mathematical instrument in physical investigation as being likely to extend our 
real knowledge of nature? Or will its result be merely to encourage the formation 
of yain hypotheses, recommended only by their capability of mathematical expres- 
sion, and ieesle injuring the cause of science by means of the facility with which 
men accept such speculations as real knowledge ? This latter opinion seems to be, 
on the whole, that of Comte, whose severe strictures upon physical theories of light 
T have noticed before. 
Now I believe that the advocate of the mathematical method of investigation 
