258 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



gain velocity and lose it again during the passage of the wave ? 

 A wave always consists of tivo elements which travel along together, 

 a local distortion of the medium and a local state of motion of the 

 medium, the forces which are associated with the distortion are the 

 forces which produce the motion ; this production of motion involves 

 acceleration and the reaction of the acceleration gives rise to the 

 forces which produce distortion. The distortion creates the mo- 

 tion and the motion creates the distortion as they both travel 

 along together. The two are mutually dependent. 



A consideration of the simplest kind of water waves in a canal, 

 namely, the kind in which the only perceptible motion of the 

 water in the wave is a uniform horizontal floiv, will serve better 

 than anything else as an introduction to the discussion of electric 

 waves. Consider a canal of rectangular section which is filled to 

 a depth x with still water. Imagine a gate to be moved slowly 

 along the canal at velocity v, as shown in Fig. 1 89. The water 

 next the gate is set in motion, and in being set in motion it heaps 

 up to a definite depth x -f h ; and a wave of starting W moves 



along the canal at a definite 

 velocity V. If the gate is sud- 

 denly stopped, the wave of 

 starting W continues to move 

 as before, the water next to the 

 gate, in being stopped, drops 

 to its normal depth x, and a 

 wave of arrest W moves along the canal as shown in Fig. 

 190. The elevation h of the water in the wave is supposed to 

 be small. 



The uniformly moving and uniformly elevated body of water 

 A, Fig. 190, constitutes what is called a complete wave, or simply 

 a wave. The water in front of the wave is continually set in 

 motion at velocity v and raised to the depth x -f h. The water 

 in the back part of the* wave is continually brought to rest and 

 lowered to the normal depth x of the water in the canal. 

 Thus, the state of motion which constitutes the wave A travels 



still water 



moving water 







