90 Mr GREEN, ON THE MOTION OF WAVES IN CANALS. 



We see therefore, in this case, that the particles of the fluid by 

 the transit of the wave are transferred forwards in the direction of the 

 wave's motion, and permanently deposited at rest in a new place at 

 some distance from their original position, and that the extent of the 

 transference is sensibly equal throughout the whole depth. These 

 waves are called by Mr Russel, positive ones, and this result agrees 

 with his experiments, Vide p. 423. If however £ were positive, or 

 the wave wholly depressed, it follows from our formula, that the 

 transit of the fluid particles would be in the opposite direction. The 

 experimental investigation of those waves, called by Mr Russel, nega- 

 tive ones, has not yet been completed, p. 445, and the last result 

 cannot therefore be compared with experiment. 



V 



The value — which we have obtained analytically for the extent 



7 

 over which the fluid particles are transferred, suggests a simple phy- 

 sical 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 equilibrium. 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 % vertical and directed up- 

 wards, the general equations for small oscillations in this case become 



