352 PHILOSOPHICAL TRANSACTIONS. [aNNO ] 75p. 



account for the little advantage that arises from its impulse; and shall immedi- 

 ately see of how little consequence this impulse is to the effect of an overshot 

 wheel. However, as every thing has its limits, so has this ; for thus much is 

 desirable, * that the water should have somewhat greater velocity, than the cir- 

 cumference of the wheel, in coming on it;' otherwise the wheel will not only be 

 retarded, by the buckets striking the water, but thence dashing a part of it over, 

 so much of the power is lost. The velocity that the circumference of the wheel 

 ought to have, being known by the following deductions, the head requisite to 

 give the water its proper velocity is easily computed from the common rules of 

 hydrostatics ; and will be found much less than what is generally practised. 



III. Concerning the f^elocity of the Circumference of the IVheel, in order to 



produce the Greatest Effect. 



If a body is let fall freely from the surface of the head to the bottom of the 

 descent, it will take a certain time in falling ; and in this case the whole action 

 of gravity is spent in giving the body a certain velocity: but if this body in fall- 

 ing be made to act on some other body, so as to produce a mechanical effect, 

 the falling body will be retarded; because a part of the action of gravity is then 

 spent in producing the effect, and the remainder only giving motion to the fall- 

 ing body : and therefore * the slower a body descends, the greater will be the 

 portion of the action of gravity applicable to the producing a mechanical effect ;* 

 and in consequence the greater that effect may be. 



If a stream of water fall into the bucket of an overshot wheel, it is there re- 

 'tained till the wheel by moving round discharges it : of consequence the slower 

 the wheel moves, the more water each bucket will receive : so that what is lost 

 in speed, is gained by the pressure of a greater quantity of water acting in the 

 buckets at once : and, if considered only in this light, the mechanical power of 

 an overshot wheel to produce effects will be equal, whether it moves quick or 

 slow : but if we attend to what has been just now observed of the falling body, 

 it will appear that so much of the action of gravity, as is employed in giving the 

 wheel and water in it a great velocity, must be subtracted from its pressure on 

 the buckets ; so that, though the product made by multiplying the number of 

 .cubic inches of water acting in the wheel at once by its velocity, will be the 

 same in all cases ; yet, as each cubic inch, when the velocity is greater, does 

 not press so much on the bucket as when it is less, the power of the water to 

 produce effects will be greater in the less velocity than in the greater- and hence 

 we are led to this general rule, " That, caeteris paribus, the less the velocity of 

 the wheel, the greater will be the effect of it." A confirmation of this doctrine, 

 together with the limits it is subject to in practice, may be deduced from the 

 foregoing sf)ecimen of a set of experiments. 



