of the Motion and Resistance of Fluids . 23 
of the fluid at the orifice and its depth cannot from thence be 
determined in all cases. If the magnitude of the orifice be in- 
definitely less than that of the surface of the fluid, the equation 
gives the velocity of the eflluent fluid to be equal to that which 
a body would acquire by falling in vacuo through a space equal 
to the depth of the fluid. But the velocity here determined is 
not that at the orifice, but at a small distance from the orifice % 
for the fluid flowing to the orifice contracts the stream, and 
the velocity being inversely as the area of the section, the ve- 
locity continues to increase as long as the stream, by the ex- 
pelling force of the fluid, keeps diminishing, and when the 
stream ceases to be contracted by that force, at that section of 
the stream called the vena contracta, the velocity is that which 
a body would acquire in falling through a space equal to the 
depth of the fluid. If, therefore AB ci EF (Tab. II. fig. 1.) 
be the vessel, cd the orifice, cmnd the form of the stream till 
it comes to the vena contracta, then this investigation sup- 
poses AB cmnd EF to be the form of the vessel, and m n 
the orifice, the fluid flowing through cmn d just as if the ves- 
sel were so continued. But as the proposition is to find the 
velocity of the fluid going out of the vessel, it may perhaps ap- 
pear an arbitrary assumption to substitute the orifice m n in- 
stead of c d, when no such a quantity as mn appears in the 
investigation. If, however, we grant that the expelling force 
must act without any diminution until the fluid comes to m n , 
it seems that from the principles here assumed we ought to 
substitute m n instead of c d, as otherwise we get the velocity 
generated by the action of only a part of the force. The con- 
clusion here deduced agrees very well with experiment ; but 
an application of the same principles to another case differs so 
