CHAPTER IV 



WAVES 



WHEN the surface of the sea is disturbed, waves are produced. 

 The chief characteristic of such wave-motion is that while the 

 waves pass over the surface at considerable speed, the water 

 itself simply rises and falls with a slight to-and-fro motion of 

 a rhythmic character. The theory of wave-motion establishes 

 by mathematical calculation a relation between the length of 

 the wave (the distance between consecutive crests), its velocity, 

 and the depth of the water, and thus affords an explanation of 

 the difference in behaviour of waves in the deep sea and the 

 same waves when they reach shallow water. 



There is a simple relation common to all types of wave- 

 motion where waves follow one another in trains, either in the 

 air, ether, or water, and it is expressed by the formula 



where L is the length of the wave, V its velocity, and T the 

 period of oscillation of the particles which are effected by 

 successive waves. 



It must be borne in mind that in a typical deep-sea wave it 

 is not the mass of water which is being bodily transferred, but 

 the energy. 



Let OR be a straight line under which the circle with radius 

 OQ rolls. The length OR being made equal to a semi-circum- 

 ference, the rolling circle will have made a semi-revolution 

 during its motion from Q to R; and if QR and the semi- 

 circumference QR' are each divided into the same number of 

 equal parts, then as the circle rolls the points with correspond- 

 ing numbers come into contact successively. Now take a point 



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