302 LECTURE XXV. 



ducing the v'elocity. And this result is confirmed by experiments: but it is 

 necessary, that the diameter of the plane be at least four times as great as 

 that of the jet, in order that the full effect may be produced. When also a 

 stream acts on an obstacle in a channel sufficiently closed, on all sides, to pre- 

 vent the escape of any considerable portion of water, its effect is nearly the 

 same as that of a jet playing on a large surface. But if the plane, opposed to 

 the jet, be only equal to it in diameter, or if it be placed in an unlimited 

 stream, the whole velocity of the fluid column will not be destroyed, it will 

 only be divided and diverted from its course, its parts continuing to move 

 on, in oblique directions; in such cases the pressure is usually found to be 

 simply equivalent to the weight of a column equal in height to the reservoir, the ^ 

 surface being subjected to a pressure nearly similar to that which acts on a 

 part of the bottom of a vessel, while a stream is descending through a large 

 aperture in another part of it. (Plate XXI. Fig. 273.) 



It is obvious that, in all these cases, the pressure varies as the square of the 

 velocity, since the height required to produce any velocity is proportional to 

 its square. This inference was first made in a more simple manner, from com- 

 paring the impulse of a fluid on a solid with that of a number of separate 

 particles, striking the surface of the body, each of which would produce an 

 tifect proportional to its velocity, while the whole number of particles, acting 

 in a given time, would also vary in the same ratio. If the solid were in mo- 

 tion, and the fluid either in motion or at rest, it is obvious that the relative 

 velocity of the solid and the fluid, with regard to each other, would be the only 

 cause of their mutual effects, and that the hydraulic pressure or resistance 

 must be dependent on this velocity alone, except so far as the limited dimen- 

 sions of the reservoir, containing the fluid, might produce a difference in the 

 internal motions of its particles in different cases. Thus, where the fluid is so 

 confined, that the whole of the stream acts on a succession of planes, each 

 portion into which it is divided may be considered as an inelastic solid, strik- 

 ing on the surface exposed to it with a certain velocity: and in this case the 

 force must be considered as simply proportional to the relative velocity, and 

 not to its square. For want of this consideration, the effects of water wheels 

 have frequently been very erroneously stated. 



When a jet .strikes a plane surface obliquely, its force, in impelling 



