226 LECTURE XXIV. 



the water of the vessel, until its surface becomes level with the lowest part 

 of the stream. (Plate XXI. Fig. 269.) 



The effect of a jet of water, in drawing towards it a current of air, is in 

 some measure illustrated by an experiment which is often exhibited among 

 the amusements of hydraulics. A ball of cork, or even an egg, being 

 placed in the middle of a jet, which throws up a pretty large stream to a 

 moderate height, the ball, instead of falling or being thrown off, as it might 

 naturally have been expected to do, remains either nearly stationary or 

 playing up and down, as long as the experiment is continued. Besides the 

 current of air which Venturi has noticed, and which tends to support the 

 ball in a stable equilibrium, the adhesion of the water, combined with its 

 centrifugal force in turning round the ball, assists in drawing it back, 

 when it has declined a little on either side, so that the stream has been 

 principally in contact with the other side. A similar effect may be observed 

 in the motions of the air only, as I have shown by some experiments of 

 which an account is published in the Philosophical Transactions.* Thus, 

 if we bend a long plate of metal into the form of the letter S, and sus- 

 pend it in the middle by a thread, so that it may move freely on its centre, 

 and if we then blow on its convex surface with a tube directed obliquely 

 towards the extremity, instead of retreating before the blast, it will on the 

 contrary appear to be attracted ; the pressure of the atmosphere being 

 diminished by the centrifugal force of the current, which glides along the 

 convex surface, because it finds a readier passage in the neighbourhood of 

 the solid, towards which it is urged by the impulse of the particles of the 

 air approaching it on one side, and by the defect of pressure on the other 

 side, occasioned by the removal of a certain portion of the air which it 

 carries with it. (Plate XXI. Fig. 270, 271.) 



From considerations similar to those by which the velocity of a river is 

 determined, we may calculate the quantity of water discharged from a pipe 

 of any given dimensions, and in any position. The same expressions will 

 serve for estimating the magnitude of the friction in both cases ; the pipe 

 being considered as a small river of which the mean depth is one fourth of 

 its diameter : but a part only of the force of gravity is now expended in 

 overcoming the friction, the rest being employed in producing the momen- 

 tum of the water. We may obtain a sufficiently accurate determination of 

 the velocity, by supposing the height of the reservoir above the orifice of 

 the pipe to be diminished in the same proportion as the diameter of the 

 pipe would be increased by adding to it one fiftieth part of the length, and 

 finding the whole velocity corresponding to four fifths of this height. Thus, 

 if the diameter of the pipe were one inch, and its length 100 inches, we 

 must suppose the effective height to be reduced to one third by the friction, 

 and the discharge must be calculated from a height four fifths as great as 

 this, which may be considered as a reduction derived from the interference 

 of the particles entering the pipe, with each other's motions. If the diameter 

 of the pipe had been two inches, the height must only have been supposed 

 to be reduced to one half by the friction ; such a pipe would, therefore, 



* Outline of Experiments and Inquiries respecting Sound and Light, Ph. Tr. 

 1800, p. 106. 



