FLU 



ta is distant from the orifice a little less than the radius of the orifice, and 

 its magnitude is about of the magnitude of the orifice. 



2. If a cylindrical or prismatic vessel, whose altitude is A, and the area 

 of whose section is A, empty itself through a very small orifice a at the 

 bottom, the time t of emptying itself 



= -|= X - *J~h = ,3526 X - VT. 

 Vg- a 



and the time that the surface takes to sink from the depth h to any other 

 depth h' 



= ,3526 X ^ (VT V^.) 



Cor. The construction of the clepsydra depends upon this Proposition. 

 If the whole depth through which the water sinks in 12 hours be divided 

 into 144 parts, it will sink through 23 of these in the first hour, 21 in the 

 second, 19 in the third, and so on according to the series of the odd num- 

 bers. 4 



Any vessel may serve for a clepsydra, but in order that the fluid may 

 descend (which is most commodious) through equal portions of the ver- 

 tical axis in equal portions of time, the vessel must be a paraboloid of 

 the fourth order. 



3. M. Prony deduces from actual experiment, the following formula 

 for computing the discharge due to any altitude, and with any given ori- 

 fice. Let Q = quantity of water discharged in cubic feet, d diameter 

 of orifice in inches, H height of the head of the water in feet, T = 

 time in seconds, then 



Q =: 3.9103 <ft T VH- 



If instead of the aperture a pipe of one or two inches in length be in- 

 serted, the discharge is increased in the ratio of 13 to 10 nearly ; in that 

 case 



Q 5.1086c?2T VH- 



4. Bossut has found that the discharges due to equal intervals of time," 

 through horizontal tubes of the same diameter, and under the same 

 height of water, but of different lengths, not differing greatly from each 

 other, will be very nearly in the inverse ratio of the square roots of these 

 lengths. 



5. To find the time of emptying vessels in general ; let g 32% feet, 

 x depth of fluid at any point of time, a area of surface at the depth 

 r, a area of orifice; then the velocity with which the surface de. 



