IMPROVED sy J. RUMSEY. 18% 
The centrifugal force. 
Let x=diftance of any point in the radius from 
the centre of motion in feet 
r=radius or length of the arm, . 
a and w as before, 
t=time of a revolution in feconds. 
Then a will alfo be the area of a fection of the water paf- 
fing through the tube, at right angles to its dire@ion (or 
of fo much of it as we muft compute the centrifugal force 
for) which multiplied by the fluxion of x, and by w will 
be wax=the Wt. of the evanefcent quantity or moving 
plane a x, which is the fluxion of the current water in the 
tube; and, by the dotrine of central forces, as t?: 
1.228awx x 
1,.226x::aw x:——-—-—= the centrifugal force thereof at 
t? 
x Ft. from the centre of motion, or the fluxion of th 
whole centrifugal force of the quantity pafling through 
either brachium at any time; the fluent of which, when 
76.7 5ar” 
x=r, being doubled, is —--—---—— =the central force of the 
. 
water in both arms; which is equal to the augmentation 
of power thereby occafioned at the apertures, becaufe fluids 
prefs equally in all direCtions. But this force is greatly 
counteracted by 
The Inertia of the Fluid. 
The Inertia of the rotatory tube, with the contained 
fluid, would not continue to refift the moving power, af- 
ter the velocity became uniform, werethe fame fluid re- 
tained therein to which the motion had been at firft im- 
parted; but as this paffes off, and there is a continual 
fucceflion of new matter acquiring a motion in the direGion 
of the rotatory, there muft be a conftant rea&tion again{t 
the infide of the tube, by the inertia of the fluid, equal 
to the communicating force. Now this reaction is very 
Aa 2 different 
