W

3.

where a very slight separation of the ray into component parts at the first surface, throws them at different angles on the second, and thus each is then still more deviated, but each by the same invariable law, and to a constant amount peculiar to itself, w is the white light incident, r the red, v the violet, and g the green rays, with other intermediate tints, as they finally emerge from the prism. In other words, each of the primary component rays of light has a refraction different from the others; peculiar to itself; constant for the same medium; and differing from one medium to another. Thus, prisms of different substances refract the several rays in different degrees both absolutely and relatively. The general fact was the great discovery of Newton; the particular variations

in different substances have been traced by his successors.

4.

9

Newton observed, "that to the same ray ever belongs the same refrangibility," but he employed only prisms of flint-glass, and perhaps one or two other substances. His successors soon found, that among different media there existed a vast diversity in the extent to which the effects were displayed. It had been already found that similar prisms of different substances would produce a very different total amount of deviation: that is, they were said to have different refractive powers; thus, in fig 4, a prism is represented which produces a greater absolute deviation of the whole body of light than that in fig. 5. But it was not till some time afterwards discovered that the extreme rays

5.

of the spectrum are more widely separated, or there is a greater relative deviation in some media than in others, as in the prism of fig. 5, compared with fig. 4. This is called greater dispersive power: these two powers bear no fixed proportion to each other in different bodies, though it is true, among a considerable number of substances, that the more highly refractive are also the more highly dispersive; but this is by no means universally the case.

Besides these distinctions there was also another which was rendered manifest as observation extended: viz., this; that if two media differed in dispersive power, they did not by any means cause the different rays of the spectrum to deviate in degrees proportional to the

whole amount of dispersion. Thus, suppose one medium, as in fig. 6, caused the green ray g, to take a sition halfway between the

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dispersion in different substances; this was sometimes called "the irrationality of the coloured spaces."

The subject attracted the notice of several eminent philosophers, who devoted great attention and skill to determining by observation the amount and general character of the refraction and dispersion of a large number of transparent bodies. In this inquiry by far the most eminent for the extent and accuracy of his researches was Sir. D. Brewster; he devised the most ingenious methods of observation, and published extensive lists and tables of the indices of refraction for a long range of media, as well as of the differences in refraction between the extreme rays in each, and the ratio between this and the mean refraction; that is, in other words, their dispersive powers. No one can even inspect the tables in which the results of his labours are contained, without a conviction of the immense labour bestowed on the investigation, as well as of the curious insight which these very marked characters in different bodies, afford us of their specific peculiarities; of the unlimited variety which pervades nature in these properties; and of the extreme imperfection of our present knowledge of the causes on which it depends.

THEORIES OF LIGHT.

66

WHEN philosophers began to turn their attention to the theories which might be invented to explain the phenomena of light, they were easily able to devise principles which sufficiently well account for the ordinary, simple refraction of a ray, on passing out of one medium into another, and even express accurately the law of refraction. The two great rival theories were those which are called the "corpuscular" or emission" theory, and the "undulatory." The former was adopted by Newton, not as a real exposition of the principle of nature, but only as affording convenient mathematical methods of investigation. The latter was the idea of Huyghens, who illustrated it by the familiar comparison of the circles which spread themselves on the surface of still water when a stone is thrown into it. In this way he conceived extremely small motions, or waves, to be propagated through an excessively rarefied medium, or æther, which pervades all space and all bodies; these waves or pulsations, striking upon our organs, produce the sensation of sight. The former, or corpuscular theory, supposed extremely minute particles shot off from luminous bodies in straight lines in all directions.. Upon either of these theories it could be shown why a ray of light should deviate from its course on entering a new medium; but upon the undulatory hypothesis this was connected with a wider range of phenomena;

and even in the hands of its inventor, Huyghens, it had far outstripped the rival theory in its applications to important physical laws.

When, however, the unequal refrangibility of the primary rays of light was established, both theories seemed equally at fault; both seemed alike incapable of affording any explanation of the fact, even of the most general kind; indeed, in the then stage of the inquiry, no explanation but the most general could have been attempted; as no accurate knowledge of the facts, nothing like precise data, much less any mathematical laws had been obtained. Nay, even more than this was soon apparent; for the undulatory theory (as commonly conceived) not only did not explain, but seemed absolutely contradictory to the fact of unequal refrangibility. Upon that theory (in its ordinary form), the equal refrangibility of all rays was a necessary consequence. The rival theory was equally difficult to reconcile with the phenomena. But both theory and fact were as yet imperfecty developed.

The grand step (in reference to our present subject) in the improvement of the former, was made by M. Cauchy; of the latter, by M. Fraunhofer. Of the improvement and extension of the theory, we fear it would be an utterly hopeless task to attempt to convey any notice to our readers within the compass of an article like the present. We must satisfy ourselves by merely observing, that if the propagation of circular waves on the surface of still water be adhered to as an illustration, the velocity with which these circles succeed one another will depend on the density of the medium; and in the theory of light, the velocity with which the waves producing light succeed each other (though inconceivably great), is subject to certain changes, and is invariably diminished in more dense media. It is, indeed, owing to this diminished velocity, that refraction is shown to take place, and it is the measure of the refractive power. On the ordinary theory, whatever might be the lengths of waves, they would all have the same velocity in the same medium. M. Cauchy's grand improvement of the theory, consisted in so modifying it, that while it still continued to fulfil all the conditions it did before, it also assigned an explanation for a change in the velocity corresponding to a supposed difference in the length of a

wave.

Now, on the same theory, the characteristic difference of the several primary rays is, that they are produced by waves of different, but determinate, lengths. The relation, therefore, established by M. Cauchy, assigned a connexion between the velocity, that is, the refrangibility, of a ray, and the length of its wave, that is, its colour.

The improvement in the investigation of the phenomena consisted in several particulars. In the first place; Dr. Wollaston, in 1802, had pointed out, that when the spectrum is formed, taking a very narrow line of light as the origin, the coloured spaces appear crossed by several parallel dark bands. M. Fraunhofer, in 1819, without knowing of Dr. Wollaston's discovery, observed the same thing, but with much superior apparatus; and thus was enabled greatly to extend the minute knowledge of the nature of the phenomenon. Instead of a few, he found, by a telescope, an almost infinite number of such lines or bands. What their nature might be, there was no means of conjecturing; but, from a variet

of experiments, they appeared something inherent in the nature of the light. Seven principal, and well-marked, lines, were fixed upon as identifying determinate points in the spectrum, and were called the standard rays.

DISPERSION. COMPARISON OF THEORY AND OBSERVATION.

THE observations of Newton and his successors had hitherto referred only to the different refrangibility of what were termed, in a general way, the red, blue, &c., rays. These increased in refrangibility as we advanced towards the violet-end of the spectrum. The differences in the effect produced by prisms of different substances, were estimated generally by taking the refractive indices for the red, violet, and mean rays: the latter only were observed; the extremes inferred and calculated. The determinations were necessarily of the most vague and uncertain kind, since there was no precision in the definition of the rays. It depended only on the judgment of the eye to say (for example) how far the red should be considered to extend, and where the yellow should begin; and what point of the red, yellow, &c., should be taken as the point of

ineasurement.

Fraunhofer, however, having obtained the means of more exact definition, by means of the fixed lines, proceeded to make use of them for affording a basis of exact measurement of refractive indices. He, accordingly, observed, with an extremely delicate apparatus, the deviations of these precise and well-defined parts of the spectrum, and thence deduced, by an easy calculation, the refractive index for each of the seven standard rays.

This he did for 10 substances, of which he formed prisms, viz.:— 4 kinds of flint-glass, 3 of crown-glass, water, solution of potash, and oil of turpentine. These determinations are justly esteemed as amongst the most valuable optical data we possess; and it is, on all hands, evident that to have such precise numerical results, is the first essential preliminary, before we can attempt any philosophical investigation of laws

or causes.

Further, there are several optical phenomena, by which not only the existence, but even the precise magnitude, of the waves, or lengths of undulations, are determined. These had been assigned, in a general way, for the red, blue, &c., rays by Newton. Fraunhofer determined them accurately for each of the seven standard rays. Now we thus possess two distinct sets of numbers belonging to the same standard rays,—their lengths of waves, and their refractive indices. And the first and obvious question which arose, was, Can any relation be traced between these two series of numbers? The first are independent of all particular media; the second are different for each different medium. An inquiry, then, into any relation which may be found between them, would be the first requisite before we attempted to venture on any theory.

Now such an attempt was made, in 1827, by M. Rudberg. He examined the sets of numbers given by Fraunhofer, and, upon trial, deduced a conjectural rule, or empirical formula, assigning an arithmetical relation between the length of a wave and the refractive index. found that the calculated numbers agreed very closely with observation

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throughout the whole of that particular series. These results, however, were simply empirical and unconnected with theory. And it still remained to see whether any such rule could be deduced from theory, which should stand the test of comparison with observation in the cases already determined, and still more, in the vast number as yet unexamined, but which constitute so fine a field for the researches of future observers.

Now, from what we have already said of M. Cauchy's investigations, it will be apparent that they contain the germ, as it were, of such a rule or formula. The deduction of it was suggested by Mr. Airy (now Astronomer Royal), and developed by Professor Powell, in some papers in the Journal of Science, in which he had given an abstract of M. Cauchy's researches, and still more recently, in the same journal, a continuation, containing the investigations of Sir W. R. Hamilton, to facilitate the application.

By pursuing the calculations from every one of the cases determined by Fraunhofer, Professor Powell succeeded in verifying completely the theory, as far as those cases are concerned: the results are given in a tabular form, in the Phil. Trans. for 1835, part I. Ten other cases had also been examined experimentally, and, in each, the seven refractive indices found, by M. Rudberg. These valuable data were also compared with theory, with as perfect success as the former, by the same author, and the results are printed in the Phil. Trans., for 1836. Thus for 20 media, including a considerable range of refractive and dispersive powers, a formula deduced from the undulatory theory as modified by M. Cauchy, is found to give a very close approximation between the indices calculated, and those determined by actual observation.

Now, among these substances, the highest in refractive and dispersive power are by no means the highest in nature. On casting the eye over such lists as those contained in Sir D. Brewster's optics (Cab. Cyclop.), or other works, it will be seen that there are many media of dispersive powers, much higher than any of those above alluded to. Again, those who examine the mathematical formula will see, from its particular form, that though it may apply well enough to low dispersive substances, it by no means follows that it will hold good for those of higher power. It therefore becomes a subject of the deepest interest, to carry on the research for those substances. The theory may yet have to be modified, before it can be truly applicable to the real case of nature in all its generality. The formula which has succeeded so well for the lower media, MAY be only a simpler case of some more complex formula, to which it may be necessary to resort for the higher. All this remains

to be investigated; and in this research Professor Powell is now engaged. The first thing to be done is obviously to obtain good measurements of the indices of the standard rays, for the several highly-dispersive media.

No such determinations are at present known to have been made. Should any such be ascertained, the publication of them will be a valuable contribution. The last-named author has investigated a few. At the Dublin meeting of the British Association, he mentioned some results of this kind, which he had then obtained (confessedly only rough approximations), for the very highly-dispersive substances, oil of Cassia, oil of aniseed, and sulphuret of carbon. These were hardly worthy of comparison with