LIGHT 605 curvature. Thus, if a set of rays be drawn perpendicular to any wave-front, they will after reflexion be perpendicular to a new wave-front ; and the lengths of all the rays, from wave-front to wave-front, will be equal. This is merely another way of stating that if a set of rays can be cut at right angles by a surface (of finite curvature) they will always be capable of being cut at right angles by such a surface, even after any number of reflexions at surfaces of finite curvature, provided they move in a homogeneous isotropic medium. This proposition will be seen to be capable of extension to refraction, provided always that both media are homo geneous and isotropic. For a plane wave, falling on a plane refracting surface, our construction (fig. 30) is as follows : Lot AB be, as before, a plane wave-front in the first medium, and AC the plane surface of the second medium. As before, let BC be perpendicular to AB. Also let CD be drawn parallel toBA. With centre A and radius AD equal to the space described in the second medium while BC is described in the first, let a sphere be described. The disturbance at A will have diverged in this sphere, while that at B has just reached C. The disturbance at any other point, as P, will have passed to Q, and then have diverged into a sphere of radius QT such that QT : QT : : AD : BC. Obviously all spheres so drawn ultimately intersect along CD, which is therefore the front of the refracted wave. The angles of incidence and refraction, being the in clinations of the incident and refracted rays to the normal, are the inclinations BAG and DCA of the incident and refracted wave-fronts to the refracting surface. Their sines are evidently in the ratio of BC to AD, i.e., they are directly as the velocities of propagation in the two media. Hence the law of refraction also follows from this hypothesis. But there will now be separation of the various homogeneous rays, because the ratio of their velocities in the two media is not generally constant. Besides, it is clear from the investigation above that, in the refracting medium, the rays are still perpendicular to the wave-front. Thus the proposition lately given may now be extended in the following form : If a series of rays travelling in homogeneous isotropic media be at any place normal to a wave-front, they will possess the same property after any number of reflexions and refraction?. And it is clear from the investigations already given that the time employed by light in passing from one of these wave-fronts to another is the same for every ray of the series. We now see how crucial a test of theory is furnished by the simple refraction of light. On the corpuscular theory the velocity of light in water is to its velocity in air as 4 : 3 nearly ; on the undulatory theory these velocities are as 3 : 4, since, as we have seen, the refractive index of water is about -. But Foucault s experimental method showed at once that the velocity is less in water than in air. This finally disposed of the corpuscular theory. Though it had been conclusively disproved long before, by certain interference experiments whose nature will presently be described, the argument from these was somewhat indirect and not well suited to convince the large non- mathematical class among optical students and experi menters. The true author of the undulatory theory is undoubtedly Huygens. Grimaldi, Hooke, and others had expressed more or less obscure notions on the subject, but Huygens in 1678 first gave it in a definite form, based to a great extent upon measurements of his own. It was read to the French Academy, but not published till 1690, when it appeared with the title Traite de la Lumiere. Huygens gives the explanation of the double refraction of Iceland spar, which had been described by Bartholinus in 1670. Unfortunately the remarkable step taken by Newton in explaining the law of refraction on the corpus cular theory the earliest solution of a problem connected with molecular forces had for some time been before the scientific world. The authority of Newton was paramount in such matters, and the work of Huygens produced no effect at the time. Even the genius of Young, who at the commencement of the present century recalled attention to this all-but-forgotten theory, and enriched it by the addition of the principle of interference, as well as by many important applications, failed to secure its recognition. It was not till 1815 and subsequent years that, in the Opposi hands of Fresnel, the undulatory theory finally triumphed, tion to and, even then, the battle was won against determined tlie u " resistance on the part of the upholders of the corpuscular th theory. Yitness what Laplace 1 said, in 1817, in the following excerpt from a letter to Young : "J ai regu la lettre que vous m avez fait 1 honneur dt m ecrire, et dans laquelle vous cherchez a etablirque, suivant le systeme des ondulations de la lumiere, les sinus d incidence et de refraction sont en rapport constant, lorsqu elle passe d un nrilieu dans un autre. Quelque ingenieux que soit ce raisonnement, je ne puis le regarder que comme un apergu, et non comme une demonstration geomet- rique. Je persiste a croire que le probleme de la propagation des ondes, lorsqu elles traversent differens milieux, n a jamais ete resolu, et qu il surpasse peut-etre les forces actuelles de 1 analyse. Des cartes expliquoit ce rapport constant, aumoyen de deux suppositions ; 1 une, que la vitesse des rayons lumineux parallelement a la surface du milieu refringent ne changeoit point par la refraction ; 1 autre, que sa vitesse entiere dans ce milieu etoit la meme, sous toutes les incidences ; mais comme il nerattachoit aucune de ces suppositions aux lois de la mecanique, son explication a ete vivement com- battue et rejettee par les pins grand nombre des physiciens jusqu a ce que Newton ait fait voir que ces suppositions resultoient de Faction du milieu refringent sur la lumiere ; alors on a en uue ex plication mathematique du phenomene dans le systeme de I emis- sion de la lumiere : systeme qui donne encore 1 explication la plus simple du phenomene de 1 aberration, que n explique point le systeme des ondes lumineuses. Ainsi les suppositions de Descartes, comme plusieurs apergus de Kepler sur le systeme du monde, ont ete verifiees par 1 analyse : mais le merite de la decouverte d une verite appartient tout entier u. celui qui la demontre. Je coriviens que denouveauxphenomenesde la lumiere sont jusqu a present tres difficiles a expliquer; mais en les etudiant avec un grand soin, pour decouvrir les lois dont ils dependent, on parviendra peut-etre un jour a reconnaitre dans les molecules lumineuses des proprietes nou- velles qui donneront une explication mathematique de ces pheno- menes. Remonter des phenomenes aux lois et des lois aux force*, est, comme vous le savez, la vraie marche des sciences naturelles." Poggendorff remarks that there is no other instance, in the whole history of modern physics, in which the truth was so long kept down by authority. Poggendorff further remarks that of the six chief phenomena of light known in Huygens s time he fully explained three reflexion, refraction, and the double refraction of Iceland spar at least so far as concerns the direction of the reflected or refracted rays. Phenomena such as diffraction, and the colours of thin plates, required the principle of interference for their explanation, which was first given by Young ; and dispersion (not yet quite satisfactorily disposed of) was first accounted for in comparatively recent times by Cauchy. Huygens himself was the discoverer of polariza tion, but he could not account for it. Even Young also, because like Huygens he supposed the undulations to be in the direction of the ray, failed to account for it ; and it was not explained till Fresnel reintroduced with the 1 Young s Works, ed. by Peacock, vol. i. p. 374. It is matter for curious remark that Laplace refers to Descartes only, and not to Huygens.
