﻿1150 



Dr. G. Breit on the Propagation of a 



In this connexion^ it is of interest to point out that the 

 result of Gribbs can be understood without calculation in the 

 following manner : — 



Statement of Result. 



Consider the group drawn in fig. 1. The waves are 

 more crowded at A than at B. The medium is thus dis- 

 turbed at a higher frequency at A than at B, and the velocity 

 or propagation is therefore different at A and B. In spite of 

 this, as shown by Gibbs, the waves passing a point moving 

 with the group velocity — appertaining to the frequency of 

 the group at the point — pass that point always in the same 

 orientation. 



Thus it is required to show that at a given point of the group 

 the orientation of the elementary waves is constant. 



Proof in Special Case, 



Consider the special group of fig. 2, obtained by super- 

 posing the sinusoidal waves of wave-lengths \,, X 3 drawn on 



Fig. 2. 



Fisr. 3. 



fig. 3. The minimum P is the point at which X 1? X§ destroy 

 each other. Hence the lines LjM^ L 2 M 2 joining points of 

 opposite phase of X 1? X 2 on fig. 3 are vertical at P. If CD is 



