Constitution of Natural Radiation. 517 



attack would not be required in order to determine it. At 

 any rate, such questions of mathematical validity can arise 

 only in regard to the presence o£ selective or anomalous 

 dispersion*. 



The argument of Prof. Schuster (Phil. Mag. Jan. 1904, 

 p. 6 t) arrives at the conclusion that a single pulse is split up 

 regularly into a spectrum by a prism. It appears to start 

 from an implied hypothesis that even an abrupt pulse travels 

 unchanged across the dispersive medium, with the velocity 

 appropriate to a group of waves. If for a pulse is substituted 

 a train of waves with wave-lengths variable within the narrow 

 limits X and \-f 8\, so that the train is very nearly simple 

 harmonic, this statement will be sensibly exact except near 

 the beginning and end of the train : and Prof. Schuster's 

 representation of the emergent radiation, as consisting of 

 groups of waves, most concentrated in the neighbourhood 

 of surfaces which are oblique to the wave-fronts, then affords 

 an instructive view of the process of dispersion, whether 

 prismatic or diffractive. But if this argument is to be pressed 

 so as to include a single sharp pulse, what value of X are we 

 to take as applicable to it ? The theorem of definite group- 

 velocity is demonstrated only for the compound disturbance 

 arising from the superposition of simpler trains of some 

 common type but with slightly differing parameters, — the 

 trains being unlimited and of simple harmonic type in the 

 usual Stokes-Rayleigh theory. A single pulse will thus not 

 have any definite group-velocity with which it can travel ; 

 or, what comes to the same, the different parts of it will 

 travel in the dispersive medium with widely different 

 velocities, so that it will spread out and be dissipated. An 

 argument which assigns a definite velocity to a complex dis- 

 turbance can thus be applicable only to very special types of 

 disturbance t : for them it must of necessity lead to the same 



* I fear that I have on previous occasions orally assigned to them a 

 wider importance. It is only the fate of the constituent wave-trains 

 that are near the free period that is undetermined. 



f The paper, as its title indicates, is concerned mainly with a "brilliant 

 application of groups of undulations to the instantaneous explanation of 

 Fox Talbot's interference hands. In connexion with § 6 it may he 

 remarked that the dynamical relations require that a limited disturbance, 

 travelling in a transparent medium, must consist of compensating 

 positive and negative parts. 



X Formation of the differential equation for the forms of disturbances 

 that are propagated without change of type shows that, when simple 

 wave-trains possess this property, there are in general no other solutions ; 

 the existence of a wave-group in fact implies the existence of the wave- 

 train through which it travels. 



Phil Mag S. 6. Vol. 10. No. 59. Nov. 1905. 2 R 



