of the Motion and Resistance of Fluids . 31 
flow through an orifice at the bottom equal to r s or m n, the 
pipe being supposed to be cylindrical. To find how far this 
conclusion agrees with experiment, I made a cylinder 12 
inches deep, and at the bottom I made a small circular orifice, 
whose area was about the 130th part of the area of the bottom 
of the cylinder : I also put a cylindrical pipe into the bottom, 
whose internal diameter was exactly equal to that of the hole, 
and length 1 inch. Hence, according to the theory, the velo- 
city of the fluid out of the pipe ought to be to the velocity out 
of the orifice as vTi : viz, or as 26 : 25 nearly. But by ex- 
periment, the quantity of fluid which run through the pipe in 
12" ( the vessel being kept full) was to the quantity which run 
through the orifice in the same time, very nearly in the ratio 
of 4 to 3, and consequently that ratio expresses the ratio of the 
velocities ; a consequence totally different from that which 
the theory gives. I then took a vessel of a different base, but 
the same altitude, and altered the diameter of the orifice and 
pipe, still keeping them equal, and made the pipe only half an 
inch long ; in this case the velocities, by the theory, ought to 
have been in the ratio of ^12,5 to v'TI, or as 49 to 48 nearly ; 
whereas by experiment the ratio of the velocities came out 
the same as before, that is, as 4 to 3 nearly. I then reduced 
the pipe to the length of a quarter of an inch, and in that case 
the velocity did not sensibly differ from that through the ori- 
fice. Upon examining the stream, in consequence of this great 
difference in the two cases, when the lengths of the pipes dif- 
fered by so small a quantity, I found that in the latter case the 
stream did not fill the pipe, as it did in the former case, but 
that the fluid was contracted as when it run through the 
simple orifice. At what length of pipe the stream will cease 
