>3j23 op the motions of fluids. 



of the two series, that is, by the mean between the eleva- 

 tion or depression of the two points supposed in the pro- 

 position. 



Corollary 1. The points, in which the similar parts 

 of the two opposite series of waves continue to meet, will 

 always be free from horizontal motion ; hence it follows 

 that a solid obstacle in a vertical direction might be inter- 

 posed without altering the phenomenon : and consequently 

 that any fixed obstacle meeting the waves would produce 

 precisely the same effect on the subsequent state of either 

 series, as is produced by the opposition of a similar series, 

 and would reflect it in a form similar to that of the oppo- 

 site series, which would have travelled over it, if it had 

 originated from a primitive cause of motion on the other side 

 of the obstacle. 



Scholium. It will appear, by considering the combi- 

 nation of the horizontal with the vertical motion, that each 

 particle of tlie surface will describe an oval figure, which it 

 will be simplest to suppose an ellipsis ; the motion in the 

 upper part of the orbit being direct with regard to the pro- 

 gress of the wave, and in the lower part retrograde : and 

 the orbit will be of the same form and magnitude for each 

 particle of the surface, when the canal is supposed to be 

 prismatic. 



379. Theorem. The divergence of a wave 

 makes no sensible difference in the velocity of 

 its propagation, and its height will vary as the 

 square root of the distance from the centre. 



The immediate horizontal force is the same for a diverg- 

 ing wave as for a prismatic canal, its measure being always 



