24 Prof. Larmor, On Kundt's law of selective dispersion. 



Thus, to an observer travelling with velocity U , so that x — U t 

 remains constant, the aggregate disturbance in his neighbourhood 

 has the features of a simple disturbance of type y = GF (n Q x — p> i), 

 namely of form y=GF(n x) travelling with velocity p fn . This 

 resultant form y = GF (n x) is not the same as the original standard 

 form y = Af(n x), belonging to the components which make it up. 

 But if the component form is represented by a sine or cosine, the 

 resultant is also of that type ; and an observer travelling with 

 velocity U then keeps in touch with a steady aggregate dis- 

 turbance of the standard type, which travels as a group in 

 company with him. 



The generalised result is the proposition that the local 

 features of a train formed of disturbances of nearly identical types 

 travel with a definite velocity, different from the velocity of 

 propagation of the individual waves, and therefore travel through 

 the waves; but the travelling group is of the same type as the 

 individual disturbances which in the aggregate give rise to it, 

 only when these latter are simple harmonic trains represented by 

 sines or cosines. 



Thus, for example, we may for an instant imagine a radiation, 

 the aggregate of an indefinitely great number of similar discrete 

 radiant pulses shot out from the radiating molecules, each pulse 

 being propagated without change of type with a velocity de- 

 termined by the scale of its dimensions in space of time : in the 

 aggregate they would present the appearance of disturbances 

 travelling onward with the group-velocity determined above, 

 but there would be no similarity between these groups and the 

 original type of pulse. This illustration is however purely ideal, 

 for the dynamics of propagation require that it is only single 

 harmonic wave-trains that can travel unchanged in a dispersive 

 medium. 



