460 POPULAR LECTURES AND ADDRESSES. 



not merely the surface motion produced by the 

 force that you applied, but you have the water- 

 motion in the interior. You have the whole 

 essence of the thing discovered, if you can 

 mathematically calculate from a given motion 

 at the surface what is the motion that necessarily 

 follows throughout the interior ; and that can 

 be done, and is a part of the elements of the 

 mathematical results which I have to bring 

 before you. 



Now to find mathematically the velocity of 

 progression of a free wave, proceed thus. Take 

 your gutta-percha form and hold it stationary 

 on the surface of the water ; the water-pressure 

 is less at the crest and greater at the hollow ; 

 by the law of hydrostatics, the deeper down you 

 go, the greater is the pressure. Move your form 

 along very rapidly, and a certain result, a centri- 

 fugal force, due to the inertia of the flowing 

 water, will now cause the pressure to be greatest 

 at the crest and least at the lowest point of the 

 hollow. Move it along at exactly the proper 

 speed and you will cause the pressure to be 



