2 Lam r., Relation between Wave- Velocity and Group- Velocity. 



from different {joints of view, by Sir G. Stokes and Prof. 

 Osborne Reynoldsf ; and the problem has been further 

 generaHsed by Lord Rayleigh:[:, who has shewn that in 

 any medium where the wave-velocity F(Russeirs 'velocity 

 of wave-transmission ') is a functicjii of the wave-length A, 



V 



p 



Fig. I. 



the group-velocity U (Russell's ' velocity of wave-propa- 

 gation ') is given by the formula 



This result admits of a simple geometrical represen- 

 tation. If a curve be constructed with A as abscissa and 



mentioned, that a difference exists between the velocity of transmission and 

 the velocity of propagation. From this it results, that after the eye has 

 followed the apparent ridge of a wave, moving with a given velocity of trans- 

 mission, it will outrun the velocity of propagation, and the wave will appear 

 lo cease. This I have continually observed at sea. The eye follows a large 

 wave, and suddenly it ceases to pass on, but on looking back we find it 

 making once more an appearance on the same ground along which we formerly 

 traced its ridge ; this arises from the cause just mentioned." 



t Nattire, vol. xvi., p. 343 (1S77). 



% I'heory of Sottnd, § 191. 



