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hypothetical principle of Fresnel and of n theoretic formula of 

 Cauchy. And quite recently M. Abria has made an elaborate 

 examination of uniaxial refraction for the purpose of testing the 

 truth of the construction of fluyghens. I may here remark that 

 it is much to be desired that some competent observer would 

 undertake the yet more difficult task of verifying experimentally 

 the wave-surface of Fresnel. 



But to revert to the general subject. If any physicist is in- 

 clined to agree with the views of Comte upon this subject, let 

 me propose to him the following test : — Let him strike out of 

 physical optics everything which that science owes to theories of 

 light, and then let him try to write a treatise on the subject, 

 excluding the language and the ideas of theory. Finally, let 

 him compare his work with some treatise in which these aids 

 have not been neglected, and judge himself of their relative 

 value. Theoretic science need not be afraid of the result. 



Naturally suggested by the subject which we have been con- 

 sidering, namely, the tendencyof scientific progress to a reduction 

 of all physical science under the power of mathematical analysis, 

 is the gradual development of connections between the different 

 members of that great group to which we give the name of 

 physical science. And among the instances of such growing 

 relationship I take, also suggested by the topics which have 

 engaged us, the connection between optics and chemistry. I 

 only say " suggested " by our former subject, for I do not desire 

 tu attach any undue significance to the fact that of these con- 

 nected sciences one may already be called a mathematical science. 

 As yet the connection between these sciences has consisted prin- 

 cipally in the introduction into chemistry of an analysis in some 

 respects more refined than any which has been hitherto known. 

 And this fact does not in itself indicate the extension to chemis- 

 try of the mathematical character which belongs to physical 

 optics. Still, if we hold the assumption of this character by 

 any science to be the mark of perfection, we shall be inclined 

 to regard every improvement in its instruments of research as 

 tending in that direction. 



In .speaking of the connection between optics and chemistry, 

 the topic which will occur first to everyone is the Spectroscope ; 

 but on this part of the subject it is not necessary that I should 

 dwell. It has so largely occupied the attention of physicists, 

 and has been so fully treated by those who have made it their 

 special study, that I could not hope to add anything to what they 

 have said. I would only observe that the spectroscope has enabled 

 chemistry to overleap a barrier which Comte pronounced to be 

 insurmountable, and which \\'ould have excluded from the objects 

 of chemical research anything lying without the limits of our 

 earth. Comte warned us that our knowledge of the planetary 

 worlds was necessarily limited to their geometrical and mecha- 

 nical properties — to the nature of their movements, and the forces 

 by which they are produced, — and that all inquiry into the con- 

 stituent elements of the planets or their atmospheres was for ever, 

 and by the necessities of the case, interdicted to us. But the 

 spectroscope has told quite another story. 



But there is another point of contact between optics and 

 chemistry, — another spot on the border-land between these two 

 sciences which, I think, promises also to be fertile in discovery, 

 — I mean the use of polarised hght as an instrument of chemical 

 analysis. It is true that the application of this instrument is 

 limited in its extent. The physical property on which this ap- 

 plication depends (namely, the power possessed by certain liquids 

 to change the plane of polarisation of a transmitted ray, or, a^ 

 it is commonly called, the rotatory power) is altogether confined 

 to the organic world, and is not universal even there. Still, 

 within this limited range, the application of polarised hght is 

 capable of solving, or aiding to solve, chemical problems which 

 chemistry proper would probably find very difficult. Let me 

 give you two examples. 



I . Is it trrre that an acid salt is decomposed by solution ? Or, 

 taking the question in another form : If to a solution of a neutral 

 salt there be added, atom for atom, a quantity of its own acid, 

 does that additional atom of acid enter into combination, or does 

 it remain free ? It has been usually inferred from the thermic 

 researches of Dr. Andrews, followed up by Favre, Silbermann, 

 Berthelot, and others, that the second alternative is the true one, 

 the solvent being water. Now, if the problem be varied a little 

 by making the solvent spirit, the application of polarised light 

 gives us this important information : — 



If to an alcoholic solution of the ordinary nitrate of quinia 

 there be aaded an additional equivalent of acid, this additional 

 equivalent does enter into combination with the nitrate. 



This information leaves to us the alternative of supposing that 

 the ordinary nitrate, sulphate, &c., of quinia are not neutr.il but 

 basic salts, or of admitting that an acid salt is not always decom- 

 posed by solution, at least in spirit. 



2. When an acid is added to a solution containing two bases, 

 the salts formed being also soluble, does the acid divide itself 

 between the bases ? and if so, what is the law which governs the 

 division ? 



The application of polarised light enables us to solve this 

 question for some of the organic bases, proving that there is a 

 continuous partition of the acid, aird enabling us in one case, and 

 probably in many others, to assign the law according to which 

 the partition is made. 



One more instance may suffice to exemplify the advantage 

 which chemistry proper has already derived from its union with 

 optics. I take this instance from the general problem of saccha- 

 rometry. 



We have long known how to analyse, both optically and 

 chemically, a solution which contains two kinds of sugar, one 

 of which is sucrose ? lint as each of these methods gives but 

 two equations, it is plain that neither is suflicient where the un- 

 known quantities are more than two. If, then, as is very com- 

 monly the case, there are present in the solution three kinds of 

 sugar, we cannot obtain a complete analysis, either from optics 

 or from chemistry. But, as Dr. Apjohn has recently shown, 

 this problem, insoluble by either method taken alone, is readily 

 solved by a combination of both methods. An important step is 

 thus made in the application of optics to chemistry. Instead of 

 merely giving to chemistry a new solution of a problem which 

 chemistry could solve without any assistance, 0]itics has aided 

 chemistry to solve a problem which chemistry unaided might 

 have found very difficult. 



But it is time that I should bring these remarks to a close, and 

 I recur, in conclusion, to a thought which my subject has already 

 suggested. 



Let none presume to fix the bounds of Science. "Hitherto 

 shalt thou come, but no further" — that sentence is not for man. 

 Not by our own powers, not by the powers of our generation, 

 not even by the conceptions of possibility, may we linrit the nrarch 

 of scientific discovery. To us, labourers in that great field, it is 

 given to see but a few steps in advance. And when at times a 

 thicker darkness has seemed to gather before them, men liave 

 recoiled as from an impassable barrier, and for a while that ] atlr, 

 has been closed. But only for a while. Some happy acc'dent 

 some more daring adventurer, it may be time itselt, has shown 

 that the darkness was but a cloud. The light of Science has 

 pierced it ; the march of Science has left it behind ; and the 

 impossibility of one generation is for the next but the record ol a 

 new triumph. 



If seeming plausibility could give to man the right to dr.iw 

 across any path of scientific discovery an impassable line, surely 

 Comte might be justified in the line which he drew across the 

 path of chemistry. Filty years ago it might seem no unjust re- 

 striction to say to the chemist. Your field of discovery lies within 

 the bounds of our own earth. You must not hope to place in 

 your laboratory the distant planet or the scarce-visible nebula. 

 You must not hope to determine the constituents of their atmo- 

 spheres as you would analyse the air which is around your own 

 door; and you wdl never do it. Frfty years ago no chemist 

 would have complained that chemical discovery was unjustly 

 limited by such a sentence ; perhaps no chemist would have 

 refused to join in the prediction. Yet even thofe who heard it 

 uttered have lived to see the prediction falsified. They have 

 seen the barrier of distance vanish before the chemist, as it has 

 long since vanished before the astronomer. They have seen the 

 chemist, like the astronomer, penetrate the vast abyss of space 

 and bring back tidings from the worlds beyond. Comte might 

 well think it impossible. We know is to be true. 



We have learned from this, episode of scientific history that 

 the attempt to draw an impassable line between the domain ol 

 the chemist and the domain of the astronomer was not justified 

 by the result. Another generation may learn to obliterate as 

 completely the line between the domain of the chemist and the 

 domain of the mathematician. When that shall be, when 

 Science shall have subjected all natural phenoweua to the laws 

 of Theoretical Mechanics, when she shall be able to predict the 

 result of every combination as unerringly as Hamilton predicted 

 conical reiraciion or Adams revealed to us the existence of 

 Neptune — that we cannot say. That day may never come, and 

 it is certainly far in the dim future. We may not anticipate it — 



