IMPROVED sy J. RUMSEY. 189 
time of its acquiring that velocity, z.¢. of pafiing from 
Cto P,= X: now the accelerating force neceilary to com- 
Vv 2cx 
municate a velocity of—--feet per fecond, toa body weigh- 
° t CWavx 
ing awx lb, in § feconds will be —1b.=the fluxion of 
16t 
the inertia, and the fluent, when x becomes =r, will be 
12.272avr 
——-—— b.=the refiftance oppofed to either brachium, to 
t 
be eftimated as if accumulated at 1 r from the centre of 
motion ; confequently equal to the effect at both apertures 
when reduced to their diftance, Q.EF. 
This may be obtained independently of fluxions; by 
confidering, that the whole cuantity of water (r wa) in 
r 
the time (—) of its pafling through the rotatory, acquiresa 
2crv 
velocity (—-)equal to, and in the direction of, the aper- 
t 
tures, as it is carried with the tube out of its natural courte; 
12.272avr 
> as 
to produce which the neceflary force will be 
t 
before. 
Acquired velocity of the water. 
The velocity of the water through the apertures at the 
beginning of rotation is 8yh (by the eftablifhed principles 
of hydroftatics) and,as 2 wah; 8yn\*7=64h:: 2awh 
76.7 5a 39,296r- 
4+— —: 6ah4+—--——=the fquare of the augment- 
eS t* O14r* 
ed velocity; the fquare root of which is 8y¥(h+——)= 
the acquired velocity of the water, t* 
| Proportion 
