Change of Form of Long Waves. 



43; 



Sinusoidal Waves. — This last result is easily verified by 

 direct application of (12) to the equation of a train of sinu- 

 soidal waves: 



A . 27T.V 



77 = A sin ^r— ; 



for, supposing 

 we obtain 



a = 



2ttV 

 A, 2 ' 



Airx 



dn 3(/ 7tA 2 . 



— - = ~ sin 



dt 21X \ 



and from this the change of form indicated in fig. 4 is easily 

 calculated. 



Fig. 4. 



More complicated Cases. — For the sake of curiosity, sve 

 represent by means of the following figures the change of form 

 for some more complicated cases. 



Fig. 5. 



Fig. 7. 



""*5~ (s,\nJv 



Phil Mag. S. 5. Yol. 39. No. 240. May 1895. 2 G 



