but with regard to all the other leading truths of Optics. The hypothesis of emission no more suggested to Newton the notion of the unequal refrangibility of the different colours, than that of undulation disclosed to Huyghens the law of double refraction proper to certain substances. Great discoverers like these observe a connection of facts, and then create a hypothesis to account for the connection; and then those who come after them conclude that the chimerical conceptions must be inseparable from the immortal discoveries. There is a use, as I have before asserted, in these imaginary conceptions, which, in regard to their one function, are indispensable. They serve, transiently, to develope the scientific spirit by carrying us over from the metaphysical to the positive system. They can do this and nothing more, and they accomplished their task some time ago. Their action can henceforth be only injurious, and especially in the case of Optics, as any one may see who will inquire into the state of this science,particularly since the almost universal adoption of the undulatory in the place of the emissive system.

Excessive ten- One more error must be noticed before we dency to sys- leave the subject of the unscientific pursuit tematize. of Optics. Some enlightened students imagine that the science acquires a satisfactory rationality by being attached to the fundamental laws of universal mechanics. The emission doctrine, if it means anything, must suppose luminous phenomena to be in analogy with those of ordinary motion; and if the doctrine of undulation means anything, it means that the phenomena of light and sound are alike in their vibratory agitation; and thus the one party likens optics to barology and the other to acoustics. But not only is nothing gained by the supposition, but if either was the case, there would be no room for imagination or for argument. The connection would be at once apparent to all eyes on the simple view of the phenomena. Such a reference of phenomena to those general laws has never been a matter of question or of conjecture. The only difficulty has been to know those laws well enough to admit of the application. No one doubted the mechanical nature of the principal effects of gravity and sound long before the progress of rational dynamics admitted of their

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exact analysis. The application powerfully tended, as we have seen, to the perfecting of barology and acoustics; but this was precisely because there was nothing forced or hypothetical about it. It is otherwise with Optics. Notwithstanding all arbitrary suppositions, the phenomena of light will always constitute a category sui generis, necessarily i irreducible to any other: a light will be for ever heterogeneous to a motion or a sound.

Again, physiological considerations discredit this confusion of ideas, by the characteristics which distinguish the sense of sight from those of hearing, and of touch or pressure. If we could abolish such distinctions as these by gratuitous hypotheses, there is no saying where we should stop in our wanderings. A chemical philosopher might make a type of the senses of taste and smell, and proceed to explain colours and tones by likening them to flavours and scents. It does not require a wilder imagination to do this, than to issue as a supposition, now become classical, that sounds and colours are radically alike. It is much better to leave such a pursuit of scientific unity, and to admit that the categories of hetereogeneous phenomena are more numerous than a vicious systematizing tendency would suppose.

Natural philosophy would no doubt be more perfect if it were otherwise; but co-ordination is of no use unless it rests on real and fundamental assimilation. -Physicists must then abstain from fancifully connecting the phenomena of light and those of motion. All that Optics can admit of mathematical treatment is with relation, not to mechanics, but to geometry, which is eminently applicable to it, from the evidently geometrical character of the principal laws of light. The only case in which we can conceive of a direct application of analysis is in certain optical researches in which observation would immediately #furnish some numerical relations: and in no case must the positive study of light give place to a dynamical analysis. These are the two directions in which geometers may aid the progress of Optical science, which they have only too E effectually impeded by prolonging the influence of antiscientific hypotheses through inappropriate and ill-conceived analyses.

The genius of Fourier released us from the necessity of

applying the doctrine of hypotheses, as previously laid down, to the case of thermology: and neither barology nor acoustics required it. As to electrology, there are abundance of chimerical conceptions preponderant in that department: but their absurdities are so obvious, that almost all their advocates acknowledge them. It is in Optics that the plausibility and consistence of such chimeras give them the most importance; and I have therefore chosen that department as the ground on which they should be judged.

Divisions of
Optics.

We will now pass from these useless hypotheses to the real knowledge that we are in possession of about the theory of light. The whole of Optics is naturally divided into four departments, as light, whether homogeneous or coloured, is direct, reflected, refracted, or diffracted. These elementary effects usually co-exist in ordinary phenomena; but they are distinct, and must therefore be separately considered. These four parts comprehend all optical phenomena which are rigorously universal; but we must add, as an indispensable complement, two other sections, relating to double refraction and polarization. These orders of phenomena are proper to certain bodies; but, besides that they are a remarkable modification of fundamental phenomena, they appear in more and more bodies, as the study proceeds, and their conditions refer more to general circumstances of structure than to incidents of substance. For these reasons they ought to be exactly analysed. As for the rest, it is not our business to classify the application of these six departments either to natural history, as in the beautiful Newtonian theory of the rainbow, or to the arts, as in the analysis of optical instruments. These applications serve as the best measure of the degree of perfection of the science; but they do not enter into the field of optical philosophy, with which alone we are concerned.

Irrelevant matters.

Theory of vision.

For the same reasons which have led us to condemn theories of hearing and utterance, in connection with Physics, we must now refuse to include among optical phenomena the theory of vision, which certainly belongs to physiology, When phy

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sicists undertake the study of it, they bring only one of the special qualifications necessary, being otherwise on a level with the multitude; and, however important their one qualification may be, it cannot fulfil all the conditions. It is in consequence of so many conditions being unfulfilled, that the explanations hitherto offered have been so incomplete, and therefore illusory. There is scarcely a single Ĩaw of vision which can be regarded as established on a sound basis, even where the simplest and commonest phenomena are in question. The elementary faculty of seeing distinctly at unequal distances remains without any satisfactory explanation, though physicists have attempted to refer it to almost every part of the ocular apparatus in succession. This humbling ignorance is no doubt owing to scientific men, both physiologists and physicists, having left the theory of sensations in the hands of the metaphysicians, who have got nothing out of it but some deceptive ideology: but before this time we should have approached to something like positive solutions, but for the bad organization of scientific labour among us. If, from the time of these questions beginning to assume a positive character, anatomists and physiologists had occupied themselves with a theory of vision grounded on the materials furnished by Optical science, instead of looking to physicists for solutions which they could not furnish, our condition in regard to this important subject would be somewhat less deplorable than it is.

Another study which must be excluded from Optics, and from all natural philosophy, lour of bodies. Specific Cois the theory of the colour of bodies. I need

not explain that I am not referring to the admirable Newtonian experiments on the decomposition of light, which have supplied a fundamental idea, common to all the departments of Optics. I refer to the attempts made to ascertain, now through the theory of emission, and now through that of undulation, the inexplicable primitive. phenomenon of the elementary colour proper to every substance. The so-called explanations, about the supposed faculty of reflecting or transmitting such and such a kind of rays, or of exciting such and such an order of ethereal vibrations, in virtue of certain supposed arrangements of

the molecules, are more difficult to conceive than the fact itself, and are, in truth, as absurd as the explanations that Molière puts into the mouth of his metaphysical doctors. It is lamentable that we should have such comments to make in these days. Nobody now tries to explain the specific gravity proper to any substance or structure: and why should we attempt it with regard to specific colour, which is quite as primitive an attribute ?-In physiology, the consideration of colours is of high importance, in connection with the theory of vision; and in natural history, it may prove a useful means of classification: but, in optics, the object of the true theory of colours is merely to perfect the analysis of light, so as to estimate the influence of structure or other circumstance upon transmitted or reflected colour, without entering into the causes of specific colouring. The field of inquiry is vast enough, without any such illusory research as this.

SECTION I.

STUDY OF DIRECT LIGHT.

The first department is that of Optics,

Optics proper. properly so called, or the study of direct light.

This and catoptrics are the only part of the science cultivated by the ancients; but this branch is as old as the knowledge of the law of the rectilinear propagation of light in every homogeneous medium. This primary law makes purely geometrical questions of problems relating to the theory of shadows; questions difficult to manage in many cases, but not in the most important, those of very distant luminous bodies, or bodies of extremely small dimensions. The theory depends, both for the shadow and the penumbra, on the determination of an extensible surface, circumscribed at once by the luminous and the illuminated body.—Whatever its real antiquity may be, this first part of Optics is still very imperfect, regarded from the second point of view; that is, with regard to the laws of Imperfections. the intensity of light, or what is called photometry. Important as it is to have a clear knowledge, our notions are as yet either vague or precarious as to how the