190 Dre. BARKER’s MILL 
Uh of the central force to the Inertia. 
<614r’* 12.272aVvr, 
By fubftituting 8 v(h4+———--)for Vy) in —— it be~ 
98.1 76ar* hey ie* t 
comes———-—-——x / (—-+ .6 14) =the inertia 5 and, as the 
Be 7 
56,7 5ar*_98.176ar*,. .. ht* 
central force— —:———— x V/( host ES 
is aS de 
ht” 1.63Sht* 
1,29 + +.614 =v 14+{(———--); that is, the 
aa Ts 
power gained by centrifugal force is to the obftrudtion oc-= 
cafioned by the inertia, in theproportion of 1 to v (1+ 
1.63Sht* 
——--—-); by which itappears that the latter is the great- 
os | 
ter, except whent or h=o, or r infinite; cafes nev- 
er occuring in practice; and that the longer the brachia, the 
lefs the fall of water, and the greaterthe velocity of ro- 
tation are, the nearer thefe forces approach the ratio of 
equality ; but as we always find fomething in praCical ma- 
chanics to prevent our “ running into infinitecimals,”” fo 
here we are particularly limited; for in the 
Adjufiment of the parts and motion. 
The centrifugal force fhould not exceed the gravity of 
the rotating WAG or this water would be drawn into the 
tube fafter than the natural fupply at its entrance, by the 
velocity proper to that dept : confequently muft lofe the 
prefure of the column above it: nor fhould the velocity 
of the apertures, be greater than half that of the water 
through them; for the apertures being ftill adapted to the 
vel< ocity, the effluent quantity or number of acting parti- 
cles is as the time; confequently ae momentum is in the 
{imple 
