186 Dr. BARKER's MILL 
bottom of the air veflel toward which the water is uni= 
formly accelerated, u=the height of any other part. 
If p=the preffure of the fluid by its gravity, at the depth, 
h, in a pipe, the area of which is every where=ey-, it 
will be, as eh: ue ¥2:: p: pv¥#,=the preflure or momen» 
tum at the depth u below H. 
Of the initial power of the machine or force with which; 
it begins to move.* 
fa=area of either aperture 
| h= height of the water above the cen- > in feet: 
4 tres of the apertures 
a. avoirdupois=the Wt. of a 
cubic foot of water, 
Required, [=the initial force, or that with which the ma-- 
chine begins to move; 
If we conceive the water preffing in the tube from O 
toward I, previous to the opening of the apertures, it 1s 
evident it will not produce any motion, becaufe the action 
againft each fide is the fame: wherefore the preflure a- 
gainft the part m, which is to be removed for an opening, 
is equal that oppofed to the fame area e in the oppolite 
direction; now, when the part m is opened, the re-a¢tion. 
thereof ceafes, and the equal impulfe remaining on the: 
contrary fide e, will be the force required. Viz. ah w for 
each brachium; confequently, I= 2hwa =the power with 
which the rotatory commences its motion. But, as the 
velocity of rotation increafes, the relative velocity of the 
water to that of the tube, and confequently the power, is 
diminished, notwithftanding what is gained by - 
Given, 
The 
® Benjamin Martin, in his Philofophia Britannica Vol. I. page 217, has attempted to 
compute the power of fuch a machine, by the weight and velocity of water emitted per fe- 
cond, &c. without finding the force neceffary to expel it; but it is not the force accumulat- 
ed during afecond, or any given times, we require, but the power acting continually or at. 
any infant confidered abfractedly trom the idea of time. 
