30 Mr. Vince's Observations on the Theory 
widely from matter of fact, as to render it very doubtful 
how far the principles here applied can be admitted. And if 
we were to grant the application of the principles here as- 
sumed, so far as regards the determination of the velocity, yet 
the time of emptying a vessel can by no means be deduced 
from it. 
In order to determine the time of emptying a vessel, we 
must know both the area of the orifice c d, and the velocity at 
that orifice. Now the theory gives only the velocity at m n ; 
and as it gives not the ratio of m n to c d, the velocity at the 
orifice cannot be deduced from thence, and therefore we can- 
not find the time of emptying. No theory whatever has at- 
tempted to investigate the ratio of inn to cd ; it is well known 
that that is only to be determined by an actual mensuration. 
When the orifice is very small, Sir Isaac Newton found the 
ratio to be that of 1 to v~\ when the orifice is larger, the 
ratio approaches nearer to that of equality. We cannot there- 
fore, even in the most simple case, determine, by theory alone, 
the time in which a vessel will empty itself. 
If ABCD (fig. 2.) be a vessel filled with a fluid, and 
a pipe in nr s be inserted at the bottom, m n being very 
small in respect to B C, then, according to the theory of D. 
Bernouilli, the fluid ought to flow out of the pipe at r s with 
the same velocity it would out of a vessel A L M D through 
the orifice r s . Now in this latter case, the velocity, according 
to his own principles, varies as the square root of L A, and 
therefore it varies in the same ratio in the former case ; hence 
if the length m r of the pipe bears but a very small proportion 
to A B, the velocity with which the fluid flows out of the pipe 
will be very nearly equal to the velocity with which it would 
