FORM GIVEN TO THE SURFACE OF THE FLUID. (57 



Fig. 6. 

 (at 7| miles an hour.) 



The form given to the fluid in a channel ahout 8 feet deep, having a wave of 

 the velocity of 10 to 11 miles an horn-, is given in Plate 11. fig. 1, the velocity of 

 the vessel being about 7 mUes an hour. 



When the velocity of the sohd is greater than the velocity of the wave of the 

 fluid, the nature of the motion communicated to the fluid is totally different from 

 that which is given to it by a lower velocity. The anterior wave no longer presses 

 forward before the vessel, but the prow enters water that is smooth and undis- 

 turbed. The displaced fluid does not now accumulate at the prow, but is left on 

 either side, forming a lateral elevation of fluid, which has the effect of increasing 

 the depth of the fluid around the sides of the vessel, and fonning a wave, on the 

 summit of which the vessel may be poised in a position of eguihbrium. This is 

 in fact the wave formed by the displaced fluid, but moving with a less velocity 

 than the vessel, and therefore posterior to the prow of the vessel instead of an- 

 terior to it, as in the former case, where the velocity of the vessel was less than 

 that of the wave. It constitutes, therefore, a great central wave of displacement. 



At velocities greater than that of the wave the stem surge has now disap- 

 peared. The wave of displaced fluid, instead of being sent forward, was to leave 

 a vacancy in that part of the channel from which it was displaced, remains heap- 

 ed up on the sides of the vessel untU it has passed, and then collapses into the 

 space which it had previously flUed. The channel is therefore merely rendered 

 fuUer for the time being than it had formerly been. 



Since, therefore, it appears that the form of the fluid is changed by the pro- 

 trusion of a sohd floating upon its surface, and is no longer boimded by horizon- 

 tal plane ; since, also, the form of the fluid is different when the velocity is less 

 than that of the wave of the fluid, from its form when induced by a velocity in 

 the soUd greater than that of the wave ; since, also, the mode of displacement and 

 replacement are different, it may be expected that the law of resistance will ex- 

 hibit a very important change at the point of transition. This will form the sub- 

 ject of the ensuing section. 



