92 Mb GREEN, ON THE MOTION OF WAVES IN CANALS, 



or neglecting (disturbance) 8 



c being the vertical depth of the fluid in equilibrium. 



Also at the upper surface p = 0, therefore by continuing to neglect 

 (disturbance) 2 (A) gives 



= St + 777 (when % = c). 

 Hence, by eliminating £, we get 



which by (c) becomes, when we neglect terms of the order y a and a 8 

 compared with those retained, 



= 2gc<t>, + ^. 



Or eliminating (p d by means of (C), 



_ d 2 (f> _ gc d\po 

 df 2 " dx % * 



The particular integral of which belonging to the wave that proceeds 

 in the direction of x positive is 



*.=/(*-* \/f) , 

 and hence the velocity of propagation of the wave is 

 (D) ** Vf . 



