216 LECTURE XXIIT. 



while the pipe discharges itself into a reservoir out of which the water runs 

 through a second pipe, placed horizontally, of exactly the same dimensions 

 with the first, the height at which the water in the reservoir becomes 

 stationary, will be very nearly equal to the height of the funnel above its 

 surface, so that the same height produces the same velocity in both cases. 

 (Plate XX. Fig. 259.) 



We may understand the action of the forces immediately concerned in 

 this experiment, by attending to the mutual effects of the water and of the 

 atmosphere. The water entering the orifice must immediately acquire a 

 velocity equal to that of the whole water in the pipe, otherwise there would 

 be a vacuum in the upper part of the pipe, which the pressure of the at- 

 mosphere will not permit ; and this pressure, considered as a hydrostatic 

 force, is equal to that which would be derived in any other way from a 

 column of the same height with the pipe, since the weight of the water in 

 the pipe is wholly employed in diminishing the counterpressure of the 

 atmosphere below, not only in the beginning, when it is at rest, but also 

 while it is in motion ; for that motion being uniform throughout its descent, 

 the power of gravitation is expended in producing pressure only : so that 

 the pressure of the atmosphere on the water in the funnel becomes com- 

 pletely analogous to the pressure of a reservoir of water, of the same height 

 with the pipe. The circumstance which causes the appearance of paradox 

 in this experiment, exists also in the simplest case of the discharge of 

 water ; for it may be shown that the portion of accelerating force actually 

 employed in generating the velocity with which a stream is discharged 

 through a small orifice, is twice as great as the pressure of the fluid on a 

 part of the vessel equal in extent to the orifice ; and in the same manner the 

 quantity of force exerted by the atmosphere on the water in the funnel, as 

 well as that with which the descending fluid impels the air below, is equal 

 to twice the weight of the quantity existing at any time in the pipe. 



There is, however, a limit, which the mean velocity in such a pipe can 

 never exceed, and which is derived from the magnitude of the pressure of 

 the atmosphere. For the water cannot enter the pipe with a greater 

 velocity than that with which it would enter an exhausted pipe, and which 

 is produced by the whole pressure of the atmosphere ; and this pressure 

 being equivalent to that of a column of water 34 feet high, the velocity de- 

 rived from it is about 47 feet in a second : so that if the vertical pipe were 

 more than 34 feet long, there would be a vacuum in a part of it near the 

 funnel. 



Wherever a pipe of considerable length descends from a funnel, if the 

 supply of the fluid be scanty, and especially if it approach the orifice ob- 

 liquely, the pressure of the amosphere, and the centrifugal force of the 

 particles which must necessarily revolve round the orifice, will unite in 

 producing a vacuity in the centre ; and when this happens, the discharge 

 is considerably diminished. 



In order that a siphon may run, it is obvious that it must first be filled ; 

 and when it is once filled, it will continue to run till the reservoir ia 

 exhausted, as far as the level of its upper orifice. And from this cir- 

 cumstance, the phenomena of some intermitting springs have been ex- 



