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NATURE 



{Aug. 20, 1874 



Is it true, for example, and do we feel it to be true, that in our 

 anxiety to being physical optics completely under the power of 

 mathematical science, we have abandoned the principles of the 

 inductive philosophy, and substituted mere hypotheses for true 

 knowledge ? And are we convinced, at least, that every chemist 

 is bound, as he values the truth and reality of his science, to 

 resist the introduction into chemistry of the methods of mathe- 

 matical analysis, if any such attempt should be made ? _ 



This latter is the opinion of Comte, whose severe strictures on 

 the application of mathematical analysis to physical optics I shall 

 have to consider further on ; for the present I would con6neyol!r 

 attention to the inquirj'. What indications on this subject are 

 presented by the actual progress of physical science? Does its 

 history exhibit a tendency to widen or to contract the field of 

 mathematical analysis ? 



In reviewing, with this purpose, the history of physical science, 

 we may leave out of sight those sciences, or parts of a science, to 

 which the methods and language of mathematics are applicable 

 without the aid of hypotheses. No scientific man doubts the 

 advantage of applying, as far as our analytic powers enable us 

 so to do, the methods of mathematical analysis to such sciences 

 as plain optics or plain astronomy. Even physical astronomy, 

 although in strict logical precision not wholly independent of 

 hypothesis, has been long recognised as, in the most proper sense 

 of the word, a mathematical science. Wherever, in fact, the 

 fundamental equations rest either on direct observation (as in 

 plain optics) or {as in physical astronomy) upon an hypothesis, if 

 we may venture to call it an hypothesis, so entirely accepted as 

 universal gravitation, the extension of the methods of mathe- 

 matics is only limited by the weakness of mathematical analysis 

 itself. But there are other sciences, as, for example, physical 

 optics, to which mathematical analysis cannot be applied without 

 the intervention of hypotheses more or less uncertain. And if 

 we would appreciate the true character of scientific progress, the 

 question which we must put to scientific history is this. Is science 

 becoming more or less tolerant of such hypotheses ? A principle 

 is assumed, possessing in itself a certain amount of plausibility, 

 and capable of mathematical expression, from which we are able 

 to deduce, as consequences and by mathematical reasoning, 

 phenomena whose reality may afterwards be proved by direct 

 experiment. And from this experimental verification we infer, 

 with more or less probability, the truth of the original assump- 

 tion. The question, then, which we have to put to scientific 

 history is this. Do the records of science indicate a greater or a 

 Jess tolerance of this kind of logic ? Is the mode of physical in- 

 vestigation which I have shortly sketched gaining or losing the 

 favour of scientific men ? 



Passing over sciences like astronomy, which, though not 

 wholly free from hypothesis, do not give us very extended infor- 

 mation on this point, I come to a part of scientific history to 

 which we may put the question with every probability of obtain- 

 ing (so far, at least, as one science is concerned) a decisive answer 

 ■ — I mean, the history of physical optics. 



We have here a science whose basis is purely hypothetical. 

 The definition of light is an hypothesis, the nature of the ethe- 

 real motion is an hypothesis, even the very existence of the 

 ether is an hypothesis— hypotheses, indeed, which have led to 

 conclusions amply verified by experiment, but hypotheses still. 

 Does the history of optical science indicate a desire to discard 

 this hypothetical liase? Does the history of this science betray 

 a tendency on the part of scientific men to abandon or neglect 

 mechanical theories of light? Have pliysicists given up as 

 hopeless, or perhaps unphilosophical, the attempt to reduce, by 

 the intervention of a supposed ether, the phenomena of light 

 under the mathematical laws which govern motion ? Are they 

 even abandoning the reasoning or the pliraseology of the undu- 

 latory system ? Tlie answer to these questions is not doubtful- 

 Commencing with Fresnel, more than half a century ago, the 

 history of physical optics is a history of efforts, constantly re- 

 peated, to frame what M. de St. Venant has called "a really 

 rational theory of light." 



Take, for example, the repeated attempts to reconcile the 

 mechanical principle of continuity with the optical phenomenon 

 of double refraction. When the movement which we call light 

 passes from one medium to another, if the molecular movement 

 be continuous, it is hard to see how the elastic force of the ether 

 can be different at different sides of the plane of separation. It 

 would seem, then, that tlie principle requires that the elastic 

 force of the etlier should be the same in all media. But if it 

 be the same in a crystalline ^as, in an uncrystalline^ medium, it 



ought to be the same in every direction ; and if it be the same 

 in every direction, how are we to account for the phenomenon 

 of double refraction ? The effort to overcome this difficulty may 

 be said to have engaged the attention of Cauchy during all the 

 latter part of his life. The same question was taken up after 

 his death by other writers, among whom I may mention M. 

 Boussinesq as the most recent, and is to this day a question of 

 great interest to mathematical physicists. I am not now inquir- 

 ing whether the reasoning which I have just stated be valid, or 

 whether the difficulty, which some writers do not appear to have 

 felt, be real. I allude to it only as a proof of the anxiety felt 

 by men who have borne the greatest names in optical science to 

 have a complete mechanical theory of light. It would be easy 

 to multiply instances, affecting all the great phenomena of optics, 

 which evince the same anxiety. 



Another and even stronger proof of the firm footing which the 

 undulatory theory has obtained in the world of science, is the 

 familiarity with Vi'Iiich we use the terms of that theory, as if they 

 denoted actual physical realities. When, not long since, much 

 labour was expended in calculating the wave-lengths for the 

 several rays of the spectrum, there does not appear to have been 

 among physicists any consciousness that they were discussing, 

 and even professing to measure, things which had no existence 

 but in tlie fancy of mathematicians. On the contrary, we have 

 come to speak of wave-lengths quite as freely and as familiarly 

 as we speak of indices of refraction. Nor is this true only of 

 detached memoirs, which might be supposed to represent only 

 individual opinion. The language and the principles of the 

 undulatory theory have found their way into our ordinary text- 

 books — a sure proof that these principles have been generally 

 accepted by the scientific world. I am not now discussing the 

 question whether, regarded as an indication of scientific progress, 

 this fact is favourable or unfavourable. I only say that it is a 

 fact. M. Comte has done all that the hard words of a man 

 of great genius could do to banish theories of light from the 

 dom.ain of science, but his greatest admirer will hardly say that 

 he has been successful. 



I pass to the consideration of another branch of science, 

 closely connected with, and indeed including, physical optics, 

 and exemplifying, even more strongly, the desire of scientific 

 men to extend the sway of mathematics over physical science — 

 I mean, Molecular Mechanics. This branch of mechanical 

 science (if, indeed, it be not more correct to say, this science), is 

 altogether modern. Fifty years ago it had hardly begun to 

 exist, and even now it is in a very imperfect condition. Imper- 

 fect as it is, however, it has advanced far enough to mark the 

 progress of science in the direction which I have indicated. And 

 as it is a science more general than physical optics, the indica- 

 tions which we can gather from it are more important. Physical 

 optics does not take us outside our own Section ; molecular 

 mechanics shows a marked tendency to carry mathematical analysis 

 into the domain of chemistry. If it shall ever be possible to 

 establish an intimate connection between this latter science and 

 theoretical mechanics, it is probably here that we shall find tlie c j; ; 

 necting link. In truth, it is impossible to contemplate the ever- 

 growing tendency of science to see in so many natural phenomena 

 varieties of motion, without anticipating a time when mathe- 

 matical dynamics (the science which has already reduced so 

 many of the phenomena of motion beneath the power of mathe- 

 matical analysis) shall be admitted to be the universal interpreter 

 of nature, as completely as it is now admitted to be the inter- 

 preter of the motrons of the planets. I do not say that it will 

 ever be. I do not even say that it is possible. It is no true 

 philosophy which dogmatises on the future of science. But it is 

 certain that the current of scientific thought is setting strongly in 

 that direction. The constant tendency of scientific thought is, 

 as I have said, to increase the number of tliose phenomena which 

 are regarded as mei'e varieties of motion. Sound — tliat we have 

 placed on the list long since. Light, though here our conclusions 

 are more hypothetical, we have also long regarded as belonging 

 to the same category ; and heat may now be fairly added ; and 

 we have almost learned, under the guidance of Professor Wil- 

 liamson, to regard chemical combination as a phenomenon of the 

 same kind. All these phenomena (of sound, of lifiht, of heat, 

 and perhaps even of chemical combination) we now regard as 

 produced by the movements of systems of exceedingly small 

 particles — whether of known particles, as in the case of sound, 

 or of the hypothetical ether, as in the case of light ; and a 

 science wliich proposes to itself the mathematical discussion of 

 the laws which govern the movements of such .systems can hardly 



