32 Mr. Vince's Observations on the Theory 
to fill it, is a circumstance to which no theory has ever been 
applied, but the determination thereof must be a matter of ex- 
periment entirely. 
I next inserted pipes of different lengths, and found that 
when the length of the pipe was equal to the depth of the 
vessel, the velocity of the effluent fluid by theory was to that 
by experiment as about 7 to 6; and by increasing the length 
of the pipe, the ratio approached nearer to that of equality. 
In long pipes, therefore, the difference between theory and ex- 
periment is not greater than what might be expected from the 
friction of the pipes, and other circumstances which may be 
supposed to retard the velocity. 
If the pipe be conical, increasing downwards, the velocity, 
by theory, is still the same, and consequently the quantity run 
out will be in proportion to the magnitude of r s. As long as 
the expelling force can keep the tube full, this appears to be 
the case ; but by increasing the orifice rs, the pipe will, at a 
certain magnitude, cease to be kept full ; at what time this 
happens must depend entirely upon experiment. But if the 
pipe decrease, having its orifice r s equal to that of a cylindri- 
cal pipe of the same length, the velocity through the former 
appears, from the experiment I made, to be greater than 
through the latter in the ratio of 14 to 11. 
If the pipe in r (fig. 3.) be inserted horizontally into the 
£ide of a vessel, the velocity at the orifice rs, by theory, is 
always in proportion to the square root of the altitude C D, 
the orifice being still supposed to be very small compared with 
the bottom of the vessel. By trying the experiment with 
pipes of different lengths and of the same diameter, beginning 
with the shortest and increasing them, it appears that the 
