96 Scientific Intelligence. 



long, mathematical papers, one by A. Sommerfkld and the 

 other by L. Brillouin. 



To begin with, great care must be taken in defining the vari- 

 ous kinds of velocities which may be associated with the propa- 

 gation of transverse vibrations. If the train of waves is unlimited 

 in both directions, it is not possible in general to define the 

 velocity of propagation. In this case a phase velocity is obtained, 

 and this arises in interference experiments and in the majority of 

 optical phenomena. What is generally understood by the 

 " velocity of light " in an ordinary optical medium (velocity in 

 free space divided by the index of refraction, c/fx) is nothing but 

 this phase velocity. Only in a vacuum does the phase velocity 

 equal the velocity of propagation. In any other medium it only 

 shows how the phase of the light is retarded by the interaction of 

 the medium, but it teaches nothing about the process of propaga- 

 tion. In order to be able to state anything about the propagation 

 a limited train of waves must be considered. That is, the medium 

 is at rest up to a certain instant, then a uniform succession of 

 vibrations sets in, which either breaks off, after a time, or persists 

 indefinitely. Such a train of waves is called a " signal." The 

 velocity of the " head " of the wave-train must not be confused 

 with the signal velocity, that is, with the velocity with which the 

 main part of the light motion is propagated in a dispersing 

 medium. It turns out that as the signal progresses it does not 

 retain its original form. At a given depth in the medium a very 

 weak light-motion first arrives (the "forerunners") which grad- 

 ually increases to a value corresponding to the intensity of the 

 incident light. Brillouin proves that the signal velocity practi- 

 cally agrees with the group velocity when the period of the vibra- 

 tions is different from the natural period of the dispersing medium, 

 that is, outside of the region of anomalous dispersion. Sommer- 

 f eld shows that the " head velocity " is identical with the vacuum 

 velocity, c, under all circumstances, no matter whether the medium 

 disperses normally or anomalously, whether it is transparent or 

 absorbent, whether it is single refracting or double refracting. 

 Consequently, if white light falls normally upon a dispersing 

 plate, the less refrangible ("fast") components do not hasten 

 ahead of the more refrangible (" slow ") components, so that, at 

 the first instant of emergence the light is colored red. On the 

 contrary, the wave-fronts of all the components of the white light 

 traverse the plate with the same velocity c, and, at the first 

 instant, all contribute in the same manner to the energy of the 

 emergent light. Furthermore, the "forerunners" do not show 

 the colors of the constituents from which they have arisen, but 

 have an ultra-violet wave-length and an extremely small intensity 

 determined by the dispersive power and thickness of the plate. 

 During the passage of the light through the plate its character is 

 changed so fundamentally — while the ions are being set in vibra- 

 tion — that in general no similarity exists between the incident 

 and the first emergent light. Also so much energy is held back 



