228 LECTURE XXV. 



pinasse and Frisi on do. Rozier's Journal, ix. 145, 398 , xi. 58. Fabre sur les 

 Torrens and les Rivieres, 4to, Paris, 1797. Silberschlag, Theorie des Fleuves. Ro- 

 bison's Mechanical Philosophy, art. Rivers. Eytelwein's Experiments with the 

 Hydraulic Quadrant. Sammlung zurBaukunst 1799. Girard, Essai sur le Mouve- 

 ment des Eaux courantes, 1804. Recherches sur les Eaux Publiques, &c. Prony, 

 Mem. des Savans Etrangers, 1815. Tadini, Del Movimento delle Acque correnti, 

 4to, Milan, 1816. Hachette, De 1'Ecoulement des Fluides Aeriformes, Annales de 

 Chimie. 1827, and Paris, 1830. Genieys, Essai sur les Moyens de conduire, d'ele- 

 ver, et dedistribuer les Eaux, 4to, 1839. 



LECTURE XXV. 



ON HYDRAULIC PRESSURE. 



THE mutual effects of fluids and moveable solids on each other depend 

 principally on the laws of hydraulic pressure, and of the resistance of fluids, 

 which have been considered by Bernoulli as constituting a separate depart- 

 ment of hydrodynamics, under the name of hydraulicostatics, and which 

 are of the utmost practical importance, since the application of the powers 

 of wind or water to the working of mills, and to the navigation of ships, are 

 wholly dependent on them. The impulse of a fluid differs very materially 

 from that of a solid, for in the motions of solids, the least possible finite 

 momentum must overpower the strongest possible pressure; but since the 

 particles of fluids are supposed to be infinitely small, the momentum of a 

 fluid stream may always be balanced by a certain determinate pressure, 

 without producing motion in the solid opposed to it ; so that this division of 

 the subject of hydraulics has nothing analogous to it in simple mechanics. 

 It is true that when a certain quantity of a fluid is made to concentrate its 

 action almost instantaneously, its effect is nearly similar to that of a solid, 

 for here the essential distinction derived from the successive action of the 

 particles no longer exists. Thus, when a stream of fluid filling a pipe acts 

 suddenly on an obstacle at the end of it, it requires to be resisted by a force 

 far greater than that which originally caused its motion, unless the action 

 of the force be continued through a considerable space ; and for this reason 

 the strength of the pipe ought to be so calculated as to be able to resist 

 this action ; its intensity may, however, be easily diminished by means of 

 an air vessel communicating with the pipe, which will allow the motion 

 to be changed in a less abrupt manner. But in the principal cases which 

 we are about to consider, the action of the fluid on the solid is supposed 

 to be confined to such of its particles as are nearly in contact with the 

 surface. 



When a part of the weight of any fluid is expended in producing a motion 

 in any direction, an equal force is deducted from its pressure on the vessel 

 in that direction : for the gravitation employed in generating velocity, 

 cannot at the same time be causing pressure ; and when the motion produced 

 is in any other direction than a vertical one, its obliquity must be imme- 



