Professor Lorentz has not contented himself with thus explaining all the mechanism of the phenomena of emission and absorption. He has endeavoured to rediscover, by starting with the fundamental hypothesis, the quantitative laws discovered by thermodynamics. He succeeds in showing that, agreeably to the law of Kirchhoff, the relation between the emitting and the absorbing power must be independent of the special properties of the body under observation, and he thus again meets with the laws of Planck and of Wien: unfortunately the calculation can only be made in the case of great wave-lengths, and grave difficulties exist. Thus it cannot be very clearly explained why, by heating a body, the radiation is displaced towards the side of the short wave-lengths, or, if you will, why a body becomes luminous from the moment its temperature has reached a sufficiently high degree. On the other hand, by calculating the energy of the vibrating particles we are again led to attribute to these particles the same constitution as that of the electrons. It is in the same way possible, as Professor Lorentz has shown, to give a very satisfactory explanation of the thermo-electric phenomena by supposing that the number of liberated electrons which exist in a given metal at a given temperature has a determined value varying with each metal, and is, in the case of each body, a function of the temperature. The formula obtained, which is based on these hypotheses, agrees completely with the classic results of Clausius and of Lord Kelvin. Finally, if we recollect that the phenomena of electric and calorific conductivity are perfectly interpreted by the hypothesis of electrons, it will no longer be possible to contest the importance of a theory which allows us to group together in one synthesis so many facts of such diverse origins. If we study the conditions under which a wave excited by an electron's variations in speed can be transmitted, they again bring us face to face, and generally, with the results pointed out by the ordinary electromagnetic theory. Certain peculiarities, however, are not absolutely the same. Thus the theory of Lorentz, as well as that of Maxwell, leads us to foresee that if an insulating mass be caused to move in a magnetic field normally to its lines of force, a displacement will be produced in this mass analogous to that of which Faraday and Maxwell admitted the existence in the dielectric of a charged condenser. But M.H. Poincaré has pointed out that, according as we adopt one or other of these authors' points of view, so the value of the displacement differs. This remark is very important, for it may lead to an experiment which would enable us to make a definite choice between the two theories.