276 NOTE ON THE MOTION OF WAVES IN CANALS. 



The value which we have obtained analytically for the 



extent over which the fluid particles are transferred, suggests 

 a simple physical reason for the fact. For previous to the 

 transit of a positive wave over any particle P, a volume of fluid 

 behind P, and equal to V, is elevated above the surface of equi- 

 librium. During the transit, this descends within the surface of 

 equilibrium, and must therefore force the fluid about P forward 

 through the space 



admitting as an experimental fact, that after the transit of the 

 wave the fluid particles always remain absolutely at rest. 



Mr Russel, p. 425, is inclined to infer from his experiments, 

 that the velocity of the Great Primary Wave is that due to 

 gravity acting through a height equal to the depth of the centre 

 of gravity of the transverse section of the channel below the 

 surface of the fluid. When this section is a triangle of which 

 one side is vertical, as in channel (H), p. 443, the ordinary 

 Theory of Fluid Motion may be applied with extreme facility. 

 For if we take the lowest edge of the horizontal channel as the 

 axis of x, and the axis of z vertical and directed upwards, the 

 general equations for small oscillations in this case become 



. 



we have, also, the conditions 



= () (when y = 0) .................. (a), 



w dz z . , z 



v=d$=y ( when - 



dy 



a being the angle which the inclined side of the channel makes 

 with the vertical. 



