ON WAVES. 361 



Thus it was determined that along the axis of maximum intensity, the 

 height of the wave tiiere being the greatest, there was a corresponding acce- 

 leration of the wave motion. On each side of this axis the magnitude of the 

 wave diminishes rapidly, being at 30° diminished to y, and at 60° to ^ of its 

 height along the axis, and as this diminution was attended with a corre- 

 sponding retardation of propagation, so the ridge of the wave became some- 

 what elliptical, having for its major axis the axis of maximum intensity of 

 the wave. At right angles to the principal axis of propagation the wave is 

 scarcely sensible, a height of one-tenth part of that in the axis being the 

 greatest that was observed ; and that indeed was, in the circumstances of 

 observation, scarcely sensible. 



Concluding Remarks and Application. — There are several great applica- 

 tions of our knowledge of waves of the first order, which give value to that 

 knowledge beyond that which belongs to truth for its own sake. The phae- 

 nomena of the wave of translation are so beautiful and regular, that as a 

 study of nature it possesses a high interest. The velocity of the wave is one 

 of the great constants of nature, and is to the phsenomena of fluids what the 

 pendulum is to solids, a connecting link between time and force ; as a phse- 

 nomenon of hydrodynamics, it furnishes one of the most elegant and inter- 

 esting exercises in the calculus of the wave mathematics. 



But besides its importance in these aspects, there are others in which it is 

 capable of being regarded, each of which gives it value both in art and in 

 science:-^ 



1 . The wave of the first order is to be regarded as a vehicle for the trans- 

 mission of mechanical force (geological application). 



2. The wave of the first order is an important element in the calculation 

 and phaenomena of resistance of fluids (form of ships, canals, &c.). 



3. The wave of the first order is identical with the great oceanic wave of 

 the tide (improvement of tidal rivers). 



4. The water-wave of the first order presents some analogy to the sound 

 wave of the atmosphere (phaenomena of acoustics). 



Table XVIII. 



The Velocity of the Wave of the First Order, calculated for various depths 

 of the fluid in a channel of uniform depth, extending a depth from 0"1 of 

 an inch to 100 feet. 



Column A contains the depths of the fluid in decimal parts of an inch. 



Column B the corresponding velocities in feet per second. 



Column C gives the depth in inches. 



Colunm D the corresponding velocities in feet per second. 



Column F gives the depths in feet. 



Column G the corresponding velocities in feet per second. 



Columns of Differences, E and H, will assist in extending the table. 



