gSa l,KGTUBK XXIII. 



Tlie 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 samt 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 vreve employed, some time would 

 be required before the velocity became uniform ;but in such cases the retardation, 

 arising from friction is so considerable, as to cause a still greater deviatioa tiom 

 the quantity which would be discharged by a shorter pipe in the same time. 



When the aperture, through which a tluid is discharged, instead of being 

 every way of inconsiderable magnitude, is continued throughout the height 

 of the vessel, and is every where of equal breadth, the velocity must be 

 materially different at different parts of its height; but we may fir^d the 

 quantity of the discharge, by supposing the whole velocity equal to two 

 thirds of the velocity at the lowest point. And we ma) find the quantity 

 discharged by an orifice not continued to the surface, but still of consider- 

 able height, by subtracting from the whole discharge of an orifice so con- 

 tinued, that which would have been produced by such a portion of it, as must 

 be shut up, in order to form the orifice actually existing. But in this case, 

 the result will seldom differ materially, from that which is found by consi- 

 dering the pressure, on the whole orifice, as derived from the height of the 

 fluid above its centre. 



When a cylindrical vessel empties itself by a minute orifice, the velocity of 

 the surface, which is always in the same proportion to the velocity of the fluid 

 in the orifice, is, therefore, uniformly retarded, and follows, in its descent the 

 same la\v as a. heavy body, projected upwards, in its ascent; consequently 

 the space actually described, in the whole time of descent, is equal to half of 

 that which would have been described, if the initial motion had been uni- 

 formly continued; and in the time that such a vessel occupies, in emptying 

 itgelf, twice the quantity of the fluid would be discharged if it were kept 

 full by a new supply. This may be easily shown, by filling two cylindrical 

 vessels, having equal orifices in their bottoms, and while the one is left to 

 empty itself, pouring into the other the contents of two other equal vessels, 

 in succession, so as to keep it constantly full; for it: will be seen that both 

 operations will terminate at the same instant. 



