glides along the convex surface, because it finds a readier .passage in the neigh- 

 bourhood of the solid, towards which it is urged by the: impulse. of the parti- 

 cles 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. 2/0, ^71.) 



From considerations similar to those by whichithe.V'clocity of a river tis de- 

 termined, 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 dia- 

 meter: but a part only of the force of gravity is now expended in overcoming 

 the friction, the rest being employed in producing the momentum 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 in- 

 creased 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, discharge about five times as much 

 water as the former, although of only twice the diameter; and this circum- 

 stance requires the attention of all those who are concerned in regulating the 

 distribution of water by pipes for domestic use, or for any other purpose. 



In such cases it becomes also frequently necessary to attend to the angle 

 in which a small pipe is inserted into a larger; whenever a pipe is bent, there 

 is a loss of force according to the degree of flexure, and to the velocity of the 

 Avater, which may be calculated, if it be required; hut if a pipe be fixed into 

 another through which the water is moving very rapidly, in a direction con- 

 trary to that of the stream, its discharge will not only be much smaller than 

 if the directions more nearly coincided, but sometimes such a pipe will dis- 



