ON THE THEORY OF HYDRAULICS. 213 



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 the 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 Ber- 

 noulli'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, supposing 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 ex- 

 periments 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 ;t 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 effects of 

 this kind, and both VenturiJ and Dr. Matthew Young have observed, 

 that a short pipe has no effect, in 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 absence of atmospherical pressure, it might 

 be produced by an accidental cohesion, like that which sometimes causes a 

 column of mercury to remain suspended in similar circumstances. (Plate 

 XX. Fig. 257.) 



The effect of ajutages of different kinds, on the quantity of water dis- 

 charged through an orifice of a given magnitude, may be most conveniently 

 exhibited by placing them side by side at the same height in a reservoir, 

 and suffering the water to begin to flow at the same moment through any 

 two of them ; the quantities discharged in a given time will then obviously 

 indicate the respective velocities. If a very long pipe were employed, some 

 time would be required before the velocity became uniform ; but in such 



* Surla Communication Laterale du Mouvement dans les Fluides, Par. 1797. 



t Hydrodyn p. 47. See D'Alembert, Trait6 des Fluides, Art. 149. 



J Exp. 2 and 7. 



Transactions of the Royal Irish Academy, ii. 8} ; vii. 53. 



