YMPROVED’ sy J. RUMSEY. Lok 
fimple ratio of the relative velocity as before demonftrat= 
ed {at page 146) for the underfhot wheel: hence, the 
greateit effet will be produced when the central force = 
gravity, and the velocity of the apertures—! that of the 
water; that is, 22s" _2war; and, 2 _4Vvh-+r. from 
which equations we have the following. 
40 == ot . 
Viz. Bossa sea nearly, where we find,. 
== yore oh nits, Set? ,-about’ the 
conftant ratio of 5, 3 and 1. 
Yet we may obferve here, that whiler and t are pre- 
7637 5ar* 12.272ave 
fervedinaconftant ratio, the valueof — and 
i ji 
z. €. the central force and inertia muft remain the fame; 
fo that the brachia may be made to.any length at pleafure 
(not lefs than-+ h) if the time of revolution be proportion- 
al, viz. if t= 7.6141, 2. e. if the velocity of the apetures 
be not varied; for a double radius, rotating in a double 
time, or with + the angular velocity, has the fame abfo- 
lute velocity at the extremity; and, with the fame power, 
there applied, will produce the fame effet. Wherefore, 
to find,, 
The moving force and velocity of the Machine, when the 
effect 1s a Maximum. 
If we put. 614r for t* and 3r for h, as before, in the ex- 
1.638ht* 
preffion y (1+ --—)itbecomes y 143 = 2; inwhich cafe 
ee 
the refiftance of inertia is juft double * the central force, or 
the: 
* It iscemonftrable, that the centrifugal force will be to the inertia, as the velocity of 
the apertures, isto that of the fluent water; hence allo, in the prefent cafe, they bear the 
proportion above itated, exactly, 
