322 



NATURE 



S^Aug. 20, 1874 



One of these signs is the appearance of time as one of the 

 elements of a chemical problem. And in recognising the 

 necessity of a certain time for the production of a chemical effect, 

 chemists are now pointing not obscurely to the analogy of me- 

 chanical science. "Time," says Berthdot, "is necessary for 

 the accomplishment of chemical reactions, as it is for all the other 

 mechanical phenomena." This might not in itself be very sig- 

 nificant ; but chemists have not merely recognised the necessity 

 of time as a condition for the production of chemical phenomena, 

 they have also undertaken to measure it ; or rather, taking the 

 converse problem, they have undertaken to measure the amount 

 of chemical effect produced in the unit of time ; and the law of 

 this phenomenon announced by Berthelot take; (necessarily, 

 indeed) a mathematical form quite analogous to equations which 

 present themselves in dynamical science. The next step has 

 followed as a matter of course, and chemists now speak as 

 familiarly of the velocity of chemical reactions as engineers do of 

 the velocity of a cannon-ball. 



Still more important in its bearing on the future of chemistry, 

 and tending distinctly in the same direction, is the theory of 

 chemical combination, which science owes to Prof. Williamson, 

 and according to which this phenomenon, like so many others, 

 ought to be regarded as in great measure a mode of motion. 

 We suppose the normal condition of the atomic constituents of a 

 body to be motwii, not rest ; and when we say that a molecule 

 of one substance enters into comlnnatioii with a molecule of 

 another substance, we do not mean that the same molecules con- 

 stantly adhere together, but that the union between the molecules, 

 whatever be its nature, is continually dissolved and as continually 

 re-formed. According to this theory, chemical equilibrium does 

 not denote molecular rest, but a system of molecular motion, in 

 which these decompositions and recompositions balance each 

 other. 



If I may venture to add anytliing to that which comes from 

 such an authority, I would say that this theory leads us naturally 

 to regard the chemical properties of bodies as, if not wholly 

 modes of motion, yet largely dependent upon the nature of the 

 movements which take place among their constituent atoms. 

 Hence, if two bodies incapable of chemical action are brought 

 into chemical presence of each other, we may suppose that their 

 atomic movements, and therefore their properties, remain un- 

 altered. If, on the other hand, these bodies be capable of acting 

 chemically on each other, their atomic movements are modified 

 by their mutual cliemical presence ; and therefore the chemical 

 properties of the compound, as we call it, may be wholly diffe- 

 rent from those of either of the bodies which have entered into 

 combination. 



Now we are not yet prepared to consider chemical combina- 

 tion as a problem of molecular dynamics. We have not suffi- 

 ciently clear ideas (even hypothetical ideas) of these atomic 

 movements, and of the modifications wl\ich are caused by the 

 chemical presence of another body, to place the investigation of 

 these phenomena 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 theo- 

 retical 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 impor- 

 tant application ot 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 theo- 

 retical mechanics to biological science recently made by Prof. 

 Haughton. 



The first example which I shall notice is the establishment of a 

 principle governing 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 gi'eatest amount 

 of work under the given external circumstances. If this principle 

 be admitted as an a priori truth, the arrangement of any given 

 muscle may be mathematically deduced from it ; but many, no 

 doubt, will prefer to regard it as an inductive truth establislied 

 by the number of instances which Professor Ilaughton lias 

 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. 



Prof. Ilaughton 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 Prof. Haughton is a remarkable 

 example of the increasing use of mathematical methods in the 

 investigation of physical problems. 



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 pro- 

 bable, not only that we shall improve the mathematical instru- 

 ment as applied to those sciences which are already recognised 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 independent of its 

 authority ? And to this question I think that scientific history 

 must answer. Yes, it is 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 pro- 

 bable, 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. 



I hare thus far endeavoured to show to you the light which is 

 thrown on the connection between physical science and mathe- 

 matical analysis by actual scientific history ; and I have given 

 you soma reasons for believing, so far as it is permitted to us to 

 read the future, that this connection 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 bemg likely to extend 

 our real knowledge of nature ? Or will its result be merel)- to 

 encourage the formation of vain hypotheses, recommended only 

 by their capability of mathematical expression, and deeply injurmg 

 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 I have noticed before. 



Now, I believe that the advocate of the mathematical method 

 of investigation might be, and would be, perfectly content to 

 fight the battle of mathematical physics on the ground which 

 Comte himself has chosen. We have put one important question 

 to the history of science, let us put another. 



Has the effect of theories of light upon the progress of real 

 optical knowledge (knowledge which Comte himself would admit 

 to be real) been beneficial or injurious ? 



This question belongs to a class to which the answer is never 

 easy. It is never an easy task to abstract one from a group of 

 causes which concur in the production of an effect, and then 

 determine how the effect would have been changed by such 

 removal. Still we may succeed in obtaining at least a partial 

 answer to the question. 



It has been frequently remarked as one of the benefits con- 

 ferred upon physical science by theory, that it suggests experi- 

 ment. Nowhere is this principle more strongly exemplified than 

 in the liistory of perhaps the greatest name in optical science — I 

 mean Fresnel. He is an experimentalist, certainly ; but he is ar 

 experimentalist because he is a theorist. His most valuable ex- 

 periments had their origin in the desire to test the truth of a tlieory. 

 The experiment with the two mirrors were devised to test Young's 

 principle of interference. His difTraction experiments were 

 devised at first to test the truth of Young's theory ; and when 

 that had been found to be inconsistent with fact, then to test 

 the truth of his own. And, not to multiply instances, the ex- 

 periments by which he established the existence of circular 

 polarisation, and ascertained the true nature of the light which 

 passes along jthe axis of a quartz crystal, were suggested by 

 theory. 



Among the motives which induced Jamin to undertake the 

 experimental researches which liave given to science such valu- 

 able results, not the least was the desiie to test the ti'Uth of an 



