Mechanics.

which isbut just(XL).

equivalent to the Power, or willkeep the Machine in Equilibria

The

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(XL) i. To demonstrate this Proposition, I shall PlateX.chuse a Water-Wheel A D E F, driven round by a Cur- Fig. 6 ,rent of Water G A, striking the lower Float-Boards Ajn a perpendicular Direction, in the Manner of an un-dershot Mill. Now if the Wheel be not loaded orcharged with any Weight, but moves freely on theGudgeons of its Axis C, then the Water, coming onthe Floats, will put the Wheel in Motion, and actingupon it continually will soon accelerate its Motion sofar, as to give it a Velocity equal to its own.

2. But if the Axle of the Wheel C be charged witha Weight P, which it is obliged to raise, this will giveResistance to the Wheel, and diminish its Velocity, orcause it to move flower than the Water ; as the WeightP is increased, the Motion of the Wheel will be pro-portionably retarded; till the Weight P, coming tohave an equal Momentum with the Water, the Wheelwill lose all its Motion, or be reduced to a State ofEquilibrium.

3. Now let F — Force of the Water, V — its Ve-locity, v — Velocity of the Wheel, P — Weight thatholds the Wheel in Equilibria , z — Weight raised bythe Wheel in Motion. Then the Difference of thoseVelocities, viz. V — v will be that with which theWater strikes the Wheel; and since the Force of Strik-ing Fluids is always as the Square of the Velocity, (aswill hereafter be shewn) and Causes are proportional to

their Effects, we shall have V— v* always proportionalto z ; and when v — 0, we shall have z z P; andthen V 1 will be as P, lo that it will always be V 2 : P

-—* J . vsH

:: V —v : z ; and so - - — V — v and v 3

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4. But