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 difficulty at the

outset.

Photometry. ments that can be depended on for enabling us to verify our conjectures 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, without confirming this conjecture by any experiment whatever, we have proceeded to found the whole of photometry upon it. And when this conjecture was replaced by that of undulations, we accepted the same photometry, neglecting the consideration that it must require revision from its very basis. It is clear what our present photometry 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 demonstrated 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 consistency 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 unquestionable 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 conclusions, unless it be the fixing of the maximum of brightness in the middle of the solar spectrum. Thus, to sum up, in this first, oldest, and simplest department of optics, philosophers have scarcely outstripped popular observation,leaving out what belongs to geometry, and the measurement of the velocity of the propagation of light, which is furnished by astronomy.

We have no photometrical instru

SECTION II.

CATOPTRICS.

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 belonging to them are now referred with great precision to a very small number of uniform laws, of remarkable simplicity.

Great law of reflection.

The fundamental law of catoptrics, well known by the ancients, and abundantly confirmed 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 Tschirnhausen. 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.

tion not found.

Every luminous reflection upon any body Law of absorp- whatever is accompanied by an absorption of more or less, but always of a great part of the incident light; and this gives rise to a second interesting question in catoptrics. But our knowledge about it

amounts to very little, from our backwardness in photometry; 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 specific, and especially optical characters. These questions are not only untouched: they have never been proposed. All that we know is simply 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 transparent substances; but here, again, the laws are ill understood. In these bodies, reflection accompanies refraction, 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 inclination appears to be less in proportion as the substance is more refracting: but the supposed law of the case is connected 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 at the same time, under two distinct and equivalent forms, by Snellius and Descartes. It consists of the constant proportion of the sines of the angles that

Great law of refraction.

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, constitutes 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 gravity-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 comparison 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 different states of aggregation. These variations in the refracting 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 separating 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 actual character of the science itself doubtful to impartial minds.

0

NEWTON'S DISCOVERIES ON ELEMENTARY COLOURS. 297

Newton's discoveries of the unequal re- Newton's disfrangibility of the different elementary coveries on colours form an indispensable complement elementary of the law of refraction. From the fact of colours. the decomposition of light in a prism, it clearly follows that the relation of the sine of incidence, though constant for each colour, varies in the different portions of the solar spectrum. The total increase which it undergoes from the red rays to the violet measures the dispersion proper to each substance, and must complete the determination of its refracting power in the common tables, where only the mean refraction can be inserted. This estimate constitutes, from its minuteness, one of the most delicate operations of optics, and does not admit of so much exactness as that of the refracting action properly so called, especially in bodies which bend the light but little, as the gases; but it is ascertained for a considerable number of substances, solid or liquid. In comparing the changes of the dispersive power as we pass from one body to another, we discover that the variations are not, as Newton supposed, in proportion to the refracting power and indeed we find, in more than one case, that the light is least dispersed by substances which refract it most. The discovery of this discrepancy between two qualities which appear to be analogous was made by Dollond, about the middle of the last century. It is an idea of high importance in Optics, as it indicates the possibility of achromatism by the compensation of the opposite action pertaining to two different substances which, without that, could not cease to disperse the light but by ceasing to bend it.

The laws of refraction show us that there can be none but purely geometrical difficulties in the analysis of the effects of homogeneous media upon the light which traverses them. The great complication which might arise from the form of the refracting body is diminished in ordinary cases by our satisfying ourselves with plane, spherical, or cylindrical surfaces: but we should yet find the inquiry embarrassing, and especially in regard to the dispersion, if we did not confine it to an approximate estimate of the few commonest circumstances.