Compton and Debye have given a very interesting quantita tive theory of this phenomenon based on the fact that the energy of the incident quantum is divided into two parts, one represented by the scattered radiation and the other by kinetic energy com municated to the scattering electron. The conservation of energy and the conservation of momentum are assumed between the atoms of radiation and the scattering electron (it is known from Einstein's work that a quantum of radiation by possesses a quan tity of momentum Experiment has confirmed this theory remarkably. In particular the existence of the recoil electrons having velocities in accordance with the predictions of Compton and Debye has been demon strated by the cloud method of C. T. R. Wilson.
We have there one of the most striking examples of the success of the corpuscular theories of light; certain particulars are how ever still far from clear; the electrons always behave as though quite free (or firmly bound when the scattering takes place with out change of wave-length) and many points concerning the funda mental mechanism of scattering still remain obscure.
We shall mention two further experiments which Wilson's method has rendered possible and which illustrate very well these phenomena of the propagation of light in quanta.
The first is due to C. T. R. Wilson: a beam of X-rays, while passing through an expansion chamber, falls on a copper "target," and we are then able to find on the same photographic plate the trajectory of a photoelectron ejected from the copper and a little further on in the gaseous mass that of another photoelectron ejected from an atom of the gas by the fluorescent X-rays of the copper due to the first phenomenon. We cannot more directly watch the transference of energy by discrete entities.
A second experiment has been carried out by Compton and Simon: a beam of X-rays experiences scattering by an atom of gas with change of wave-length and expulsion of a recoil electron whose trajectory is recorded in the form of a "fish track"; the tangent of the angle which the trajectory makes initially with the direction of the beam can be calculated. At the same time
there is a chance that the scattered quantum may be absorbed in the vicinity and furnish a photoelectron; the origin of the trajec tory of this photoelectron joined to the origin of the fish track will furnish the angle of scattering, so that all the geometrical elements necessary for the verification of the Compton-Debye theory can be obtained on the one plate. Experiment has shown, that to a first approximation at least the verification is satisfactory.
Bragg's formula nX=2dsin0 appeared, at the outset, quite rigorous, but the very precise experi ments of Siegbahn and his collaborators showed that it was not so. Ewald pointed out that this divergence is explained by supposing a refraction of the waves in the crystalline medium with an index p= 1— 3 with d= 27r m N being the number of electrons per unit volume and v the is known that Raman has quite recently found evidence of a change in wave-length in the case of scattering of ordinary light by liquids.
frequency. This gives for the index of refraction a value just a few thousandths less than unity; in passing from air into the crystal an incident ray undergoes a perceptible refraction and in certain cases a total reflection.
The phenomenon of total reflection with grazing incidence has been utilized by Compton and Doan and by Thibaud to obtain X-ray spectra using ordinary optical gratings (gratings having even no more than 200 lines to the millimetre can be used).