CHAPTER VII. 



WAVES IN LIQUIDS. 



146. Any disturbance which is propagated from one part of a 

 medium to another, whilst the particles of the medium do not 

 themselves share in the progressive motion of the disturbance, 

 but only deviate slightly from their original positions, is called a 

 wave. 



In the case of a liquid under the action of gravity, the disturb 

 ance manifests itself by the production of elevations and de 

 pressions which travel over the surface (originally, of course, plane 

 and horizontal). That the particles of the fluid do not follow the 

 motion of the waves, but always remain in the neighbourhood of 

 their undisturbed positions, may in this case be readily ascertained 

 by watching the motion of a small floating body. 



The present chapter is devoted to the study of waves in liquids. 

 We shall suppose for the most part that the liquid is uniform in 

 depth, that it is unlimited horizontally, and that the motion takes 

 place in two dimensions (one horizontal, the other vertical), so 

 that the elevations and depressions of the surface present the 

 appearance of a series of parallel straight ridges and furrows. 



Waves of Small Vertical Displacement*. 



147. We take first the case where the maximum horizontal 

 motion is so large compared with the maximum vertical motion, 



* Stokes, Camb. and Dublin Matli. Journal, Vol. rv. 



