ON THE THEORY OF HYDRAULICS, 281 



water separates from its sides, so that it is no longer filled by the stream: 

 since there is then nothing to distinguish its motion from that of a stream 

 passing through a simple orifice: but the increase is not owing merely to the 

 cohesion of the water to the sides of the pipe; for the effect, as I have found 

 by experiment, is nearly the same in tlie motion of air as in- that of water. 

 The contraction caused by the motion of the water at the entrance of the 

 short pipe, may be considered simply as a contraction in the pipe itself, and 

 the subsequent part of the pipe either as cylindrical or as nearly conical: for 

 in this case it follows, from the general law on which Bernoulli's calculations 

 are founded, that as long as the fluid remains in one mass, the discharge will 

 be nearly the same, as if the mouth of the pipe were the only orifice, suppos- 

 ing that no force is lost: and the exceptions which Bernoulli has made to the 

 general application of the principle in such cases, although partly supported by 

 experiments, have been extended somewhat further, both by himself and 

 by other authors, than those experiments have warranted. In the case of a 

 diverging conical pipe, or of a pipe with a conical termination, the discharge 

 is found to be considerably greater than that which a cylindrical pipe would 

 produce, but not quite so great as would be produced on the supposition that' 

 no force is lost. (Plate XX. Fig. 256.) 



This analogy between the effects of a cylindrical and conical pipe is 

 strongly supported by the experiments of Venturi, compared with those of 

 Bernoulli. Bernoulli found that when a small tube was inserted into any 

 part of a conical pipe, in which the water was flowing towards the wider end, 

 not only none of the water escaped through the tube, but the water of a 

 vessel, placed at a considerable distance below, was drawn up by it; Venturi' 

 observed the same, when the tube was inserted into the side of a cylindrical 

 pipe, near to its origin; and in both cases air was absorbed, as well as water,, 

 so that cohesion could not be in any manner concerned. But the pressure of 

 the atmosphere is generally necessary for all eff'ects of this kind, and both' 

 Venturi and Dr. Matthew Young have observed, that a short pipe has no 

 effect, ill increasing the discharge through an orifice, in the vacuum of an air 

 pump: but even if the difference were sometimes found to exist in the ah-- 

 sence of atmospherical pressure, it might be produced by an accidental co- 

 hesion, like that which sometimes causes a column of mercury to remain sus<-- 

 pended in similar circumstances. (Plate XX. Fig. 25?.) 

 VOi. J. oo 



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