of the Motion and Resistance of Fluids. 33 
velocity first increases and then decreases ; and this is a cir- 
cumstance which has been before observed. If r s be greater 
than C m, the quantity of fluid which flows out in a given 
time (the vessel, being kept full) appears to be increased in 
proportion to the increase of r s, as long as the expelling force 
is able to keep the pipe full ; but at what magnitude of rs this 
effect ceases must be determined by experiment. If rs be less 
than C m, the quantity which flows out is greater than if the 
pipe were cylindrical, and of the same diameter as rs. 
The velocities of fluids spouting upwards through an orifice 
or pipe has not been considered by Bernouilli ; but the fol- 
lowing experiments will show the effects in this case. Let 
A B C D E F (Tab. II. fig. 4.) be a vessel filled with a fluid, 
r an orifice, x, y, z, three pipes each an inch long, having 
their tops on an horizontal line with the orifice ; x is cylin- 
drical, of the same diameter as that of the orifice ; y is conical, 
increasing upwards, of the same diarfteter at the bottom as the 
orifice ; % decreases upwards, of the same diameter at the top 
as the orifice. In 12", the quantities which run out through 
the orifice and pipes x, y, z, (the vessel being kept full) were 
found to be in the ratio of 7, 9.4, 11.2 and 10.7. Hence the 
ratio of the velocities through the orifice and pipe x appears to 
be very nearly in the ratio of 3 to 4, agreeable to what was 
found to take place for an orifice and short pipe at the bottom. 
The quantity which run out of the pipe y increased by in- 
creasing the diameter at the top, in proportion to that area as 
nearly as'could be ascertained, as long as the expelling force 
could keep it full ; and a greater quantity run out of the pipe 
z than through the orifice. All this is agreeable to what was 
found to take place under similar circumstances when the 
mdccxcv. F 
