288 LECTURE XXIII. 



tion of a theorem similar to his, but perhaps still more general and explicit. It 

 appears from these determinations, that sui)posing the fluids concerned to be 

 infinitely elastic, that is, absolutely incompressible, and free from friction 

 of all kinds, any small impulse, communicated to a fluid, would be transmitted 

 every way along its surface, with a velocity equal to that which a heavy body 

 would acquire in falling th.ough half the depth of the fluid; and I have 

 reason to believe, from observation and experiment, that where the elevation 

 or depression, of the surface is considerably extensive in proportion to the 

 depth, the velocity approaches nearly to that which is thus determined, 

 being frequently deficient one eighth or one tenth only of the whole; iu 

 other cases, where a number of small waves follow each other at intervals- 

 considerably less than the deptli, I have endeavoured to calculate the retar- 

 dation which must be occasioned by the imperfect elasticity or compressibility 

 of the fluid; but it seems probable that the motion of small waves is still, 

 much slower than this calculation appears to indicate. 



Whatever corrections these detenninations of the velocity of waves may be 

 found to require, the laws of their propagation may still be safely inferred 

 from the investigation. Thus, it may be shown, supposing the waves to flow 

 in a narrow canal of equable depth, that, whatever the initial figure of the 

 waves may be, every part of the surface of the fluid will assume in succession the 

 same form, except that the original elevationsand depressions,extending their in- 

 fluence in both directions, will produce efi'ects only half as'great on each side, 

 and those effects will then be continued until they are destroyed by resist- 

 ances of various kinds. It may also be inferred, that the surface of a fluid 

 thus agitated by any series of impressions, will receive the effects of another 

 scries, in the same manner as a horizontal surface,and that the undulations, thus 

 crossing each other, will proceed without any interruption, the motion of each 

 particle being always the sum or diflterence of the motions belonging to the 

 separate series. 



Supposing two equal and similar series of waves to meet each other in such 

 a canal, in opposite directions, the point in which their similar parts meet 

 must be free from all horizontal motion, so that any fixed obstacle in an up- 

 right position would have the same effect on the motions of the fluid on 

 either side as the opposition of a similar series; and this effect constitutes the 



