[91] See MM. Arago and Biot’s Memoirs, Mém. Inst. for 1811; the whole volume for 1812 is a Memoir of M. Biot’s (published 1814); also Mém. Inst. for 1817; M. Biot’s Mem. read in 1818, published in 1819 and for 1818.
Young’s mode of accounting for the brilliant phenomena of dipolarization appeared in the Quarterly Review for 1814. After noticing the discoveries of MM. Arago, Brewster, and Biot, he adds, “We have no doubt that the surprise of these gentlemen will be as great as our own satisfaction in finding that they are perfectly reducible, like other causes of recurrent colors, to the general laws of the interference of light which have been established in this country;” giving a reference to his former statements. The results are then explained by the interference of the ordinary and extraordinary ray. But, as M. Arago properly observes, in his account of this matter,[92] “It must, however, be added that Dr. Young had not explained either in what circumstances the interference of the rays can take place, nor why we see no colors unless the crystallized plates are exposed to light previously polarized.” The explanation of these circumstances depends on the laws of interference of polarized light which MM. Arago and Fresnel established in 1816. They then proved, by direct experiment, that when polarized light was treated so as to bring into view the most marked phenomena of interference, namely, the bands of shadows; pencils of light which have a common origin, and which are polarized in the parallel planes, interfere completely, while those which are [107] polarized in opposite (that is, perpendicular,) planes do not interfere at all.[93] Taking these principles into the account, Fresnel explained very completely, by means of the interference of undulations, all the circumstances of colors produced by crystallized plates; showing the necessity of the polarization in the first instance; the dipolarizing effect of the crystal; and the office of the analysing plate, by which certain portions of each of the two rays in the crystal are made to interfere and produce color. This he did, as he says,[94] without being aware, till Arago told him, that Young had, to some extent, anticipated him.
[92] Enc. Brit. Supp. art. Polarization.
[93] Ann. Chim. tom. x.
[94] Ib. tom. xvii. p. 402.
When we look at the history of the emission-theory of light, we see exactly what we may consider as the natural course of things in the career of a false theory. Such a theory may, to a certain extent, explain the phenomena which it was at first contrived to meet; but every new class of facts requires a new supposition,—an addition to the machinery; and as observation goes on, these incoherent appendages accumulate, till they overwhelm and upset the original frame-work. Such was the history of the hypothesis of solid epicycles; such has been the history of the hypothesis of the material emission of light. In its simple form, it explained reflection and refraction; but the colors of thin plates added to it the hypothesis of fits of easy transmission and reflection; the phenomena of diffraction further invested the particles with complex hypothetical laws of attraction and repulsion; polarization gave them sides; double refraction subjected them to peculiar forces emanating from the axes of crystals; finally, dipolarization loaded them with the complex and unconnected contrivance of moveable polarization; and even when all this had been assumed, additional mechanism was wanting. There is here no unexpected success, no happy coincidence, no convergence of principles from remote quarters; the philosopher builds the machine, but its parts do not fit; they hold together only while he presses them: this is not the character of truth.
In the undulatory theory, on the other hand, all tends to unity and simplicity. We explain reflection and refraction by undulations; when we come to thin plates, the requisite “fits” are already involved in our fundamental hypothesis, for they are the length of an undulation; the phenomena of diffraction also require such intervals; and the intervals thus required agree exactly with the others in magnitude, [108] so that no new property is needed. Polarization for a moment checks us; but not long; for the direction of our vibrations is hitherto arbitrary;—we allow polarization to decide it. Having done this for the sake of polarization, we find that it also answers an entirely different purpose, that of giving the law of double refraction. Truth may give rise to such a coincidence; falsehood cannot. But the phenomena become more numerous, more various, more strange; no matter: the Theory is equal to them all. It makes not a single new physical hypothesis; but out of its original stock of principles it educes the counterpart of all that observation shows. It accounts for, explains, simplifies, the most entangled cases; corrects known laws and facts; predicts and discloses unknown ones; becomes the guide of its former teacher, Observation; and, enlightened by mechanical conceptions, acquires an insight which pierces through shape and color to force and cause.
We thus reach the philosophical moral of this history, so important in reference to our purpose; and here we shall close the account of the discovery and promulgation of the undulatory theory. Any further steps in its development and extension, may with propriety be noticed in the ensuing chapters, respecting its reception and verification.
[2nd Ed.] [In the Philosophy of the Inductive Sciences, B. xi. ch. iii. Sect. 11, I have spoken of the Consilience of Inductions as one of the characters of scientific truth. We have several striking instances of such consilience in the history of the undulatory theory. The phenomena of fringes of shadows and colored bands in crystals jump together in the Theory of Vibrations. The phenomena of polarization and double refraction jump together in the Theory of Crystalline Vibrations. The phenomena of polarization and of the interference of polarized rays jump together in the Theory of Transverse Vibrations.
The proof of what is above said of the undulatory theory is contained in the previous history. This theory has “accounted for, explained, and simplified the most entangled cases;” as the cases of fringes of shadows; shadows of gratings; colored bands in biaxal crystals, and in quartz. There are no optical phenomena more entangled than these. It has “corrected experimental laws,” as in the case of M. Biot’s law of the direction of polarization in biaxal crystals. It has done this, “without making any new physical hypothesis;” for the transverse direction of vibrations, the different optical elasticities of crystals in different directions, and (if it be adopted) the hypothesis of finite [109] intervals of the particles (see [chap. x.] and hereafter, [chap. xiii.]), are only limitations of what was indefinite in the earlier form of the hypothesis. And so far as the properties of visible radiant light are concerned, I do not think it at all too much to say, as M. Schwerd has said, that “the undulation theory accounts for the phenomena as completely as the theory of gravitation does for the facts of the solar system.”