4 Lam]',. Relation bctzveoi Wave- Velocity and Group- Velocity. 



(beyond a certain distance frcjm O), there are two values of 

 the wave-length corresponding to any prescribed value 

 of the ^r<?«/'-velocity U. I'hese two values of X coincide 

 when C/ has a certain (minimum) value, indicated by the 

 point where the tangent to the curve at the point of 



Fig. 2. 



inflexion cuts OV; and it may be easily shewn that 

 we then have 



^= v/(3 + 2 ^/3) = 2-542, 



where V„ is the minimum tcv/z'^- velocity. These points are 

 of some interest in relation to Poisson's and Cauchy's 



