ON THE THEORY OF HYDRAULICS. 217 



plained,* which only begin to run when the reservoirs from which they 

 originate have been filled by continued rains, and then go on to exhaust 

 them, even though the weather may be dry. From a combination of 

 several such siphons and reservoirs, a great number of alternations may 

 sometimes be produced. (Plate XX. Fig. 260.) 



Since the velocity of a stream or jet issuing in any direction, out of a 

 simple orifice or a converging one, is nearly equal to that of a heavy body 

 falling from the height of the reservoir, it will rise, if directed upwards, 

 very nearly to the same height, excepting a slight difference occasioned by 

 the resistance of the air, and by the force which is lost in producing the ve- 

 locity with which the particles must escape laterally, before they begin to 

 descend. The truth of this conclusion is easily confirmed by experiment. 

 (Plate XX. Fig. 261.) 



If a jet issue in an oblique or in a horizontal direction, its form will be 

 parabolic, since every particle tends, as a separate projectile, to describe the 

 same parabola in its range : and it may be demonstrated, that if it be 

 emitted horizontally from any part of the side of a vessel, standing on a 

 horizontal plane, and a circle be described, having the whole height of the 

 fluid for its diameter, the jet will reach the plane, at a distance from the 

 vessel twice as great as the distance of that point of the circle, through 

 which it would have passed, if it had continued to move horizontally. 

 And if the jet rise in any angle from the bottom of the vessel, the utmost 

 height of its ascent will be equal to that of the point in which it would meet 

 the same semicircle, if it continued to move in a right line, and the hori- 

 zontal range will be equal to four times the distance, intercepted between 

 the same point and the side of the vessel. This law is equally true with 

 regard to simple projectiles : but the experiment is most conveniently ex- 

 hibited in the motion of a jet. (Plate XX. Fig. 262.) 



We have hitherto considered the motions of fluids as continued princi- 

 pally in the same direction ; but they are frequently subjected to alternations 

 of motion, which bear a considerable analogy to the vibrations of pendu- 

 lums ; thus, if a long tube be immersed in a fluid, in a vertical direction, 

 and the surface of the fluid within the tube be elevated a very little, by 

 some external cause, the whole contents of the fluid will be urged down- 

 wards by a force which decreases in proportion to the elevation of the 

 surface above the general level of the vessel, and when both surfaces have 

 acquired the same level, the motion \vill be continued by the inertia of the 

 particles of the fluid, until it be destroyed by the difference of pressures, 

 which now tends to retard it ; and this alternation will continue until the 

 motion be destroyed by friction and by other resistances. It is also obvious, 

 that since any two vibrations in which the forces are proportional to the 

 spaces to be described, are performed in equal times, these alternations 

 will require exactly the same time for their completion, as the vibrations 

 of a pendulum of which the length is equal to that of the whole tube ; for 

 the relative force in the tube is to the whole force of gravity as the elevation 



* Regnault, Philosophic Conversations (English edition), ii. 125. Dechales, De 

 FontibusNaturalibus, Tr. 7, Prop. 15. Desaguliers, Ph. Tr. No. 384. Atwell, Ph. 

 Tr. xxxvii. 301. 



