OF THE MOTIONS OF FLUIDS. 321 



the horizontal velocity thus determined, or in other words, 

 that the wave will actually advance with that velocity. 



But in this form the solution is limited to the case 

 of a wave already in progress. It may, however, readily 

 be exteilded to all possible cases. For since the actions of 

 any two or more forces are always expressed by the addi- 

 tion or subtraction of the results produced, in any given 

 time, by their single operations, it may easily be understood 

 that any two or more minute impressions may be propa^ 

 gated in a similar manner through the canal, without im- 

 peding each other ; the inclination of the surface, which is 

 the original cause of the acting force, being the joint effect 

 of the inclinations produced by the separate impressions, 

 and producing singly the same force, as would have resulted 

 from the combination of the two separate inclinations ; and 

 the elevation or depression becoming always the sum or 

 difference of those which belong to the separate agita- 

 tions. If then we suppose two similar impulses, waves, 

 or series of waves, to meet each other in directions pre- 

 cisely opposite, they will still pursue their course : and at 

 the instant when they meet in such a manner as to destroy 

 completely each other's horizontal and vertical motions, the 

 elevation and depression of each series will coincide and 

 be redoubled, and the fluid will be quiescent, with an undu- 

 lated surface : but in the next instant the two series will 

 proceed uninterrupted, as before : consequently the fluid 

 being supposed to be initially in the same state, its pro- 

 gressive changes will be represented by the effects of the 

 two series of waves meeting each other, and the place of 

 each point will be determined by the middle between the 

 two places which it would have held by the separate eflect* 



Y 



