578 Dr. J. Larmor on the 



law of prismatic dispersive power as holds by the same 

 argument for a disturbance consisting of uniform trains of 

 simple waves, if the average wave-length of the latter 

 corresponds to this group-velocity. 



As these considerations relating to the mode of propagation 

 of pulses apply to both Prof. Schuster's and Prof. Ames's 

 arguments, it will not be superfluous to fortify them by the 

 following quotation from Lord Kelvin *, written in connexion 

 with the features exhibited near the beginning and end of a 

 regular gravitational train of surface-waves travelling on deep 

 water : — " Our present solution shows how rapidly the initial 

 sinusoidality of the head, and front of a one-sided infinite 

 procession, travelling right-wards, is disturbed in virtue of 

 the hydrokinetic circumstances of a procession invading still 

 water. Our solution, and the item towards it represented 

 in figs. 6 and 7, and in fig. 2 of § 6 above, show how rapidly 

 fresh crests are formed. The whole investigation shows 

 how very far from finding any definite c group-velocity ; we 

 are, in any initially given group of two, three, four, or any 

 number, however great, of waves. I hope ... to return to 

 this subject in connexion with the energy principle set forth 

 by Osborne Reynolds, and the interferential theory of Stokes 

 and Ray lei gh giving an absolutely definite group-velocity in 

 their case of an infinite number of mutually supporting 

 groups." 



It would appear then that there is no certain ground, on 

 the basis of the ideas pertaining to group-velocity, for con- 

 cluding that a prism is competent to disperse any isolated 

 sethereal pulse, or any series of pulses with absolutely irregular 

 statistics, into a series of simple wave-trains, in a regular 

 manner f, as an ideal grating could do, the number of undula- 

 tions in each train being in that case the number of rulings 

 in the grating or a sub-multiple thereof. 



But Lord Rayleigh in his recent paper has thrown fresh 

 light on the subject of the general action of dispersive media, 

 by examining the disturbance that follows an impressed 

 travelling aperiodic pulse, maintained at constant intensity, and 

 showing that such a pulse imitates in some respects closely 

 the behaviour of a wave-train %. He in fact points out the 

 analogy with the surface-waves produced by a boat travelling 

 with uniform velocity on a lake, which, as everybody has 



* Kelvin, " On the Front and Rear of a Free Procession of Waves in 

 Deep Water." Phil. Mag. vol. viii. 1904, p. 468. 



f What applies to a prism would probably also apply to colour- 

 perception by the eye. 



% A more direct investigation than that quoted from Lord Kelvin's 

 note of 1877 is given in Prof. Lamb's ' Hydrodynamics/ 1895, § 227. 



