230 LECTURE XXV. 



tional to its square. This inference was first made in a more simple man- < 

 ner, from comparing 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 effect 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 motion, 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 dimensions of the reservoir containing the fluid, might pro- 

 duce 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, striking on the surface exposed to it with a certain 

 velocity ; and in this case the force must be considered as simply propor- 

 tional to the relative velocity, and not to its square. For want of this con- 

 sideration, the effects of water wheels have frequently been very erroneously 

 stated. 



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

 body forwards, in its own direction, is found to be very nearly proportional 

 to the height to which the jet would rise, if it were similarly inclined to the 

 horizon. But when a plane is situated thus obliquely with respect to a 

 wide stream, the force impelling it in the direction of the stream is some- 

 what less diminished by the obliquity, at least if we make allowance for its 

 intercepting a smaller portion of the stream : thus, if the anterior part of a 

 solid be terminated by a wedge more or less acute, the resistance, according 

 to the simplest theory of the resolution of forces, might be found by 

 describing a circle on half the base of the wedge as a diameter, which 

 would cut off* a part from the oblique side of the wedge that would be the 

 measure of the resistance, the whole side representing the resistance to the 

 same solid without the wedge : but the resistance is always somewhat more 

 than this, and the portion to be added may be found, very nearly, by 

 adding to the fraction thus found one ten millionth of the cube of the 

 number of degrees contained in the external angle of the wedge. (Plate 

 XXI. Fig. 274.) 



The pressure of a fluid striking perpendicularly on a plane surface, has 

 been found to be very different at different parts of the surface ; being 

 greatest at the centre, and least towards the edges ; so that if an aperture 

 be made in the centre of a circular plane, covering the mouth of a bent 

 tube, the fluid within it will rise half as high again as if the whole mouth 

 were open. It is also observable, that two bodies, equal and similar in the 

 form of the part meeting the fluid, undergo very different degrees of 

 resistance according to the forms of their posterior terminations, and that a 

 thin circular plate is much more retarded than a long cylinder of the same 

 diameter. These circumstances are utterly inexplicable upon the vague 

 approximation of supposing the resistance produced by the immediate im- 

 pulse of separate particles of the fluid on the solid ; but they are no longer 



