Frederick Guthrie on Stationary Liquid Waves. 37 9 



pendently of one another) at Fl S- 4 - 



the same rate and at the 

 rate of the original system. 

 The experiment which illus- 

 trates this relation most di- 

 rectly is Y(/= 619 millims.) 

 of the binodal, where n = 

 94-5,andW(/=308)ofthe 

 mononodal, where n= 94'0. 

 Such a material diaphragm 

 cannot satisfy the ideal con- 

 ditions; for if at rest, ad- 

 ditional friction i s introduced 

 by the motion along its sur- 

 faces of pairs of particles at 

 each side exerting equal and 

 opposite pressures. These, 



in the absence of the diaphragm, exert no friction on one 

 another, since they move at the same rate. 



§ 23. General comparison with Pendula. — As the amplitude 

 of the wave produces no sensible effect on its rate of progression, 

 and the latter varies for small wave-lengths directly as the square 

 root of the wave-length both in circular and rectangular troughs, 

 the oscillation of water may be closely compared with that of a 

 pendulum, which for small circular arcs is isochronous, whatever 

 be the amplitude of displacement ; height of wave : height of 

 pendulum-bob = v(l — cos^#). The mean velocity of the pen- 

 dulum-bob varies as the arc for the same radius ; for the same 

 small angular displacement inversely as the square root of the 

 radius. We have then the analogous cases : — 



Pendulum. 



Water-wave. 



velocity 



velocity 



path ' 



R path ' 



a/~ 



vr 



3 



r 



~ I ' 



1 



1 



vr 



" W 



The moving force in a simple pendulum is always equal to its 

 weight, though this force is always applied partly to the point 

 of suspension. In the moving water the to-and-fro motion is 

 due to the action of a variable difference of pressures (heights). 

 The law of oscillation, however, is preserved, although the un- 

 dulations are the result of particle-motion in the mass of the 

 liquid, and although these particles in the case of stationary 



