These observations are particularly applicable to the philo- sophical history of Optics, — the department of Physics in which an imperfect positivism maintains the strongest con- sistence,— chiefly through the mathematical labours which are connected with it. The founders of this science are those who have done most towards laying the foundations of the Positive Philoso^ihy, — Descartes, Huyghens, and Newton; yet each one of them was led away by the old spirit of the absolute to create a chimerical hypothesis on the nature of light. That Newton should have done this is the most remarkable, considering how his doctrine of gravitation had raised the conception of modern philosophy above the point at which Descartes had left it, by estab- lishing the radical inanity of all research into the nature and mode of production of phenomena, and by showing that the great end of scientific effort is the reduction of a system of i3articular facts to one singular and general fact. Newton himself, whose favourite saying was, " O! Physics, beware of Metaphysics! " allowed himself to be seduced by old habits of philosophizing to personify light as a sub- stance distinct from and independent of the luminous body: a conception as metaphysical as it would have been to imagine gravity to have an existence separate from that of the gravitating body.
After what has been said about the philosophical theory of hypotheses, there can be no occasion to expose the ficti- tious character of the respective doctrines of philosophers on the nature of light. Each one has exposed the unten- ableness of those of others; and each explorer has confined himself to the evidence which favovxred his own conception. Euler brought fatal objections against the doctrine of emis- sion; yet, at the present day, our instructors conceal the fact that the advocates of the emission doctrine have offered equally fatal objections to that of undulations. To take the most simple instance — Has the fact of i)ropagation in all HYPOTHESES ABOUT LIGHT. 287 directions, characteristic of the vibratory motion, ever been reconciled with the common phenomenon of ni<?ht; that is, of darkness produced by the interposition of an opaque body? Does not the fundamental objection of the New- tonians about this matter hold its ground against the sys- tem of Descartes and Huyghens, untouched at this hour as it was above a century ago, after all the subterfuges that have been in use ever since? The case is made clearer by the fact that there are phenomena which the two theories will suit equally well. If the laws of reflection and refrac- tion issue with equal ease from the hypotheses of emission and undulation, it is pretty clear that our business is with the laws, and not with the hypotheses. The mathematical labours expended on the opposite theories will not have been thrown away; they will show, in a veiy short time, that the analytical apparatus is no certain instrument of truth, as it has served the purpose of both hypotheses equally well; as it would, quite as easily, of many others, if the progress of positivity was not excluding, more and more, this vicious method of philosophizing. It is true, the most enlightened advocates of both systems are ready to give up the reality of emission and of imdulation, and hold to them only as a matter of logical convenience, — as a rally- ing-point of ideas. But if we can pass from the one hypo- thesis to the other without affecting the science at all, it is clear that such an artifice is needless. We must admit, as we before said, that the combination of scientific ideas would be extremely difficult to minds trained under the prevalent habits of thought, if they were suddenly deprived of such a mode of connection as they here contend for; but it is not the less true that the next generation of scientific thinkers would combine their ideas more easily, and much more perfectly, if they Avere trained to regard directly the relations of phenomena, without being troubled by artifices like these, which only obscure scientific realities.
The history of Optics, regarded as a whole, seems to show that these hypotheses have not sensibly aided the progress of the theory of light, since all our important acquisitions have been entirely independent of them. This is true not only of the laws of reflection and refraction, which were discovered before these hypotheses were created.
288 POSITIVE PHILOSOPHY.
but with regard to all the other leading truths of Optics. The hypothesis of emission no moi'e suggested to Newton the notion of the unequal refrangibilitj of the different colours, than that of undulation disclosed to Huyghens the law of double refraction proper to certain substances. Grreat 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 im- mortal discoveries. There is a use, as I have before asserted, in these imaginaiy 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 im- dulatory 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 teniatize. ^f Optics. Some enlightened students imagine that the science acquires a satisfactoi-y 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 svipposi- tion, 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 pheno- mena. 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 TENDE^'CY TO SYSTEMATIZE. 289 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. Not- withstanding all arbitrary suppositions, the phenomena of light will always constitute a category siii goieris, necessarily irreducible to any other: a light will be for ever hetero- geneous to a motion or a sound.
Again, physiological considerations discredit this con- fusion of ideas, by the characteristics which distinguish the sense of sight from those of hearing, and of touch or pres- sure. If we could abolish such distinctions as these by gratuitous hypotheses, there is no saying where we should stop in our wanderings. A chemical 2:)hilosoi>her might make a type of the senses of taste and smell, aiad 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 fancifidly connecting the phenomena of light and those of motion. All that Optics can admit of mathematical treatment is with rela- tion, 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 effectually impeded l)y prolonging the influence of anti- scientific hypotheses through inappropriate and ill-conceived analyses.
The genius of Fourier released us from the necessity of I. u 290 POSITIVE PHILOSOPHY.
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 abun- dance of chimerical conceptions preponderant in that depart- ment: 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.
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 OiiYicT"^ ^ naturally divided into four departments, as light, whether homogeneous or coloured, is direct, reflected, refracted, or diifracted. These elementary effects usually co-exist in ordinary phenomena; but they are distinct, and must therefore be sejiarately considered. These four parts comprehend all optical phenomena which are rigorously universal; but we must add, as an indispens- able complement, two other sections, relating to double refraction and polarization. These orders of phenomena are pi'oper 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 depart- ments either to natural historv, as in the niatterr*^ 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.
For the same reasons which have led us to visfon^ ^ condemn theories of hearing and utterance, in connection with Physics, we must now refuse to include am.oni^ optical phenomena the theory of vision, which certainly belongs to jihysiology, When phy- THEORIES OF VISION AND COLOUR. 291 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 incom- plete, and therefore illusory. There is scarcely a single law 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 metaphy- sicians, 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 liad 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 physi- cists for solutions which they could not furnish, our con- dition in regard to this important subject would be some- what less deplorable than it is.
Another study which must be excluded -f, r from Optics, and from all natural philosophy, louToHjoflies is 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 292 POSITIVE PHILOSOPHY.
the molecules, are more difficult to conceive thau the fact itself, and are, in truth, as absurd as the explanations that Molicre 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 exj^lain 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 mei'ely 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, proj^erly so called, or the study of direct light. This and catoptrics are the only part of the science culti- vated by the ancients; but this braiich is as old as the knowledge of the law of the rectilinear propagation of light in every homogeneous medium. This primary law malces purely geometrical questions of problems relating to the theory of shadows; questions difficult to manage in many cases, but not in the most imjjortant, — 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 tlie illuminated body. — What- ever its real antiquity may be, this first part of Optics is still very imperfect, regarded from the second point of . r. • view; that is, with regard to the laws of the intensity of light, or what is called pho- tometry. Important as it is to have a clear knowledge, our notions are as yet either vague or j^recarious as to how the PHOTOMETRY. 293 intensity of light is modified by such circumstances as its direction, whether emergent or incident; its distance; its absorption by the medium; and, finally, its colour. We are met by a grand difiiculty at the pi, <. outset. We have no photometrical instru- ments that can be depended on for enabling us to verify oiir conjeet^^res on the different modes of gradation of light. All our photometers rest on a sort of vicious circle, being devised in accordance with the laws which they are destined to verify, and generally according to the most doubtful of all, in virtue of its metaphysical origin, — that which relates to distance. We have called light an emanation; have calculated its intensity by the square of its distance; and then, Avithout confirming this conjecture by any experiment whatever, we have proceeded to found the whole of photo- metry upon it. And when this conjecture was replaced by that of undulations, we accepted the same j^hotometry, neglecting the consideration that it must require revision from its very basis. It is clear what our jireseut photo- metry must be, after such treatment as this. The law relating to direction, in the ratio of the sine of the angle of emergence or of incidence, is no better demonsti'ated than that of distance, though it comes from a less suspicious source. It has nothing about it at present like Fourier's labours on radiating heat; and yet it seems as if it would admit of an analogous mathematical elaboration. The only part of photometry which has, as yet, any scientific con- sistency is the mathematical theory of gradual absorption of light by any medium. Bouguer and Lambert have given us some interesting knowledge about this: but even here we are on unstable ground, for want of precise and unques- tionable experiments. Again, the photometrical influence of colour has been the subject of some exact observations; but we are not yet in possession of general and precise con- clusions, unless it be the fixing of the maximum of bright- ness in the middle of the solar spectrum. Thus, to sum up, in this first, oldest, and simjilest department of optics, phi- losophers have scarcely outstripped popular observation, — leaving out what belongs to geometry, and the measurement of the velocity of the propagation of light, which is fur- nished by astronomy.
294 POSITIVE PHILOSOPHY.
SECTION II.
CATOPTEICS.
It is otherwise with regard to catoptrics, and yet more, dioptrics, if we discard questions about the first causes of reflection and refraction. Scientific studies have largely extended and perfected universal ideas about those two orders of general phenomena; and the varied effects be- longing to them are now referred with great precision to a very small number of uniform laws, of remarkable sim- plicity.
The fundamental law of catoptrics, well reff&etioiT ° known by the ancients, and abundantly con- firmed by experiment, is that whatever may be the form and nature of the reflecting body, and the colour and intensity of the light, the angle of reflection is always equal to the angle of incidence, and in the same normal plane. Under this law, the analysis of the effects produced by all kinds of mirrors is reduced to simple geometrical problems, which might, it is true, involve some long and difficult calculations, according to the forms of some bodies, if it were not usually sufficient to examine the simple forms of the plane, the sphere, and, at most, the circular cylinder. If we pretended to absolute precision in the analysis of images, we might encounter considerable geometrical difficulties: but this is not necessary. This analysis depends, in general, mathematically speaking, on the theory of caustic curves, created by Tschirnhavisen. But even in the application of this theory, some conjectures are hazarded; and the want of direct and exact experiments, and the uncertainty which attends almost all the parts of the theory of vision, prevent our depending too securely on the reality of the remote results of any general principle that we can yet employ.
., Every luminous reflection upon any body tion not found ""''I'^tever is accompanied by an absorption or more or less, but always of a great part of the incident light; and this gives rise to a second interest- ing question in cato^jtrics. But our knowledge about it DIOPTRICS. 295 amounts to very little, from our backwardness in photo- metry; so that we have not yet laid hold of any law. We do not know whether the loss is the same in all cases of incidence: nor whether it is connected with the degree of brightness: nor what is the influence of colour upon it: nor whether its variations in different reflecting bodies are in harmony with other sj^ecific, and especially optical characters. These questions are not only untouched: they have never been proposed. All that we know is simj>ly that the absorption of light appears to be always greater (but to what degree we are ignorant) by reflection than by transmission. From this has resulted, in recent times, the use of lenticular beacons, introduced by Fresnel.
A more advanced kind of inquiry belongs to the study of transj^areut substances; but here, again, the laws are ill understood. In these bodies, reflection accompanies refrac- tion, and we have the opportunity of inquiring by what laws, general or special, the division between transmitted and reflected light takes place. We only know that the last is more abundant in proportion as the incidence is more oblique; and that reflection begins to become total from a certain inclination proper to each substance, and measured exactly with regard to several bodies. The incli- nation appears to be less in proportion as the substance is more refracting: but the supposed law of the case is con- nected with chance conjectures upon the nature of light, and requires to be substantiated by direct experiment.
SECTION III.
DIOPTRICS.
Of all the departments of Optics, dioptrics is at present the richest in certain and exact knowledge, reduced to a few simple laws, embracing a large variety of phenomena. The fundamental law of refraction was wholly,,,, unknown to the ancients, and was discovered i-gfraction at the same time, under two distinct and equivalent forms, by Snellius and Descartes. It consistsi of the constant proportion of the sines of the angles that 296 POSITIVE PHILOSOPHY.
the refracted ray and the incident ray, always contained in the same normal plane, form with the perpendicular to the refracting surface, in whatever direction the refraction may be. The fixed relation of these two sines, when the light passes from a vacuum into any medium whatever, consti- tutes the most important optical coefficient of every natural body, and holds a real rank in the aggregate of its physical characteristics. The philosophers have laboured at its determination with much care and success, by ingenious and exact processes: they have prepared very extensive tables, which may rival, as to precision, our tables of specific gi-avity— the uncertainty not exceeding a hundredth part of the numerical value of the refracting power. If the light passes from one medium to another, the relation of the refraction depends on the nature of both: but in every case, the inverse passage gives it always a precisely reciprocal value; as experiment has constantly shown. Again, while a body undergoes no chemical change, and becomes only more or less dense, the relation of refraction which belongs to it varies in proportion to the specific gravity; as may be easily shown, especially with regard to liquids, and yet more to gases, in which we can so extensively modify density by temperature and pressure. This is why philosophers have adopted, in preference to the proper relation of refraction, its quotient by the density, which they have named refracting power; in order to obtain more fixed and specific characters in the dioptric com- parison of different substances. There is substantial ground for this distinction, though its origin was suspicious. But it must be observed that the refracting power varies when the substance does not undergo any chemical change, but passes, as we have seen in the case of water, through diffe- rent states of aggregation. These variations in the refract- ing power have given occasion to conflicts between the advocates of the two hypothetical systems,— each of which requires an invariability in the refracting power which we do not know to exist: and the difficulty of sej^arating what is really established from what they require is one of the mischievous consequences of anti-scientific hypotheses, and one which may well render the acitual character of the