324 OF THE MOTIONS OF FLUIDS. 



becomes considerable : and the second part of the expres- 

 sion will become a small disturbing force, depending on the 

 tangent of the inclination of the surface, which represents 

 the fluent of the curvature, or of the accelerating force, and 

 being therefore proportional to the velocity : so that like 

 the resistance of a pendulum proportional to the velocity, it 

 will not sensibly affect the whole period of the alternate 

 motion, or the propagation of the wave depending on it. 

 We obtain the law of the diminution of the height of the 

 waves in diverging, from the principle of the preservation 

 of impetus (319), since the mass affected at once by the 

 similar velocities increases directly as the distance from the 

 centre x, when the depth is equable, consequently all the 

 velocities concerned must decrease as the square root of or, 

 in order that the sum of the masses, multiplied by the 

 squares of the velocities may remain constant. There will 

 always be a continual but insensible reflection, which will 

 preserve the centre of gravity immoveable, though it con- 

 sumes no considerable part of the impetus ; except at the 

 very origin of the wave, where there seems to be some- 

 thing like a vibratory motion from this reflection, for a short 

 space, at the beginning of the motion. 



Scholium. It is obvious that the surface of a wave so 

 diminishing cannot be supposed to glide on unaltered, but 

 the demonstrtition shows that the motion of each point of 

 the surface is the same as that of a surface, affected by a 

 series of equal waves, of the magnitude of the actual wave 

 at the given point, which is the condition supposed in the 

 comparison of the force with the curvature. 



380. "400." Theorem. All minute im- 

 pulses are conveyed through a homogeneous 



