In optics we had no less trouble. It is true that the general principles of the undulatory theory of light had been firmly established and physicists were justly proud of the success that had been achieved in the explanation of interference and diffraction, double refraction and polarization. Yet, when we tried to penetrate somewhat deeper, we were confronted with serious difficulties. When we wanted to account for the different optical properties of various substances, of air and water for instance, we had the choice between two assumptions. Fresnel had sought the cause of the difference in an inequality of the density of the ether in the two substances, the elasticity being the same in both. F. E. Neumann, on the other hand, had supposed the densities to be the same, but the elasticities to be different. On either of these suppositions, and in no other way, it had been found possible to deduce the right value for the ratio between the amplitude of the reflected and that of the incident light. You know that in this problem two principal cases must be distinguished, the vibrations being normal to the plane of incidence in the one case and parallel to that plane in the other. The two values for the ratio in question are sin (_i_ — _r_) / sin (_i_ + _r_) and tg (_i_ - _r_) / tg (_i_ + _r_), if _i_ is the angle of incidence and _r_ the angle of refraction; and it is remarkable that, of the two rival theories, one led to the expression with the sines when the other required that with the tangents, and conversely. In connexion with this Fresnel supposed the vibrations of plane polarized light to be at right angles to the plane of polarization, whereas Neumann wanted them to be parallel to that plane. Here was a problem that long baffled the efforts of physicists, and many attempts were made to determine experimentally the direction of the vibrations. One cannot say that the result has been very satisfactory and the question remained open until Maxwell's theory settled it once for all. I have enumerated some only of the difficulties with which we had to struggle. I could have mentioned similar problems that arose in the theory of double refraction and I may add that in some cases longitudinal vibrations intruded themselves and complicated the theory.