WAVES 



107 



Consider the motion of the partiales of water. Every 

 particle reyolves with uniform speed in a circular orbit, and 

 complètes a révolution during the period in which the wave 

 advances through its own length. Assume the circles repre- 

 sent the position at successive eighths of a whole révolution. 

 Let PPP be particles on the upper surface, then the wave of 

 the radii of the ôrbits is OP, OP, etc. Assume one-eighth of 

 a révolution to be accomplished, then the points P occupy the 

 position R, and RRR will be a trochoid identical in form with 

 PPP, but with its crest and hollow farther to the left. The 

 motion of the particles in the direction of the advance is limited 

 by the diameter of their orbits, and they move to and fro about 

 the centres of the orbits. 



ff rp 





Direction oF Advance 

 FiG. 18.— The Advaxce of a Wave. 



The diagram shows how, on the trochoidal theory of 

 wave-motion, the wave-form advances very rapidly, while the 

 individual particles hâve little or no advance. 



It will be noticed that on the ridge of the wave the particles 

 move in the same direction as the advancing wave, in the 

 trough of the wave in the contrary direction. 



When a cork is dropped overboard from a ship it does not 

 travel away on the wave on which it falls, but simply sways 

 backwards and forwards, following the line of motion of the 

 particle P in the above diagram. 



The disturbance caused by the passage of a wave must 

 extend for some distance below the surface, until at length at 

 great depths the disturbance will hâve ceased. 



The trochoidal theory expresses the law of decrease, and 



