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Of the mechanical P&werS*

acting at F, sive seet frorn the Center C, the poWef and weight will justbalance each other. A hamm^r drawing a nail is a lever of this fort.

2. The fecond mechanical power is the 'wheel and axle, in whic.h The «Wthe power iis applied to the circumference of the wheel, and the weight and axlt 'is raifed by a rope which coils about the axle as the wheel is turnedround. Here it is plain that the velocity of the power raust be to thevelocity of the weight, as the circumference of the wheel is to thecircumference of the axle: and confequently, the power and weightwill balance each other, when the intensity of the poWer is to the in-tensity of the weight, as the circumference of the axle is to the cir-cumference of the wheel. Let AB be a wheel, CD its axle, and Fig. 5.suppofe the circumference of the wheel to be 8 times as great as thecircumference of the axle; then, a power P equal to 1 pound h ang-ing by the cord I, which goes round the wheel, will balance a weightW of 8 pounds hanging by the rope X, which goes round the axle.

And as the friction on the pivots or gudgeons of the axle is but fmall,a fmall addition to the power will catife it tö defcend, and raife theweight: but the weight will rise with only ari eighth part of the velo-city wherewith the power descends, and confequently, through nOmore than an eighth part of an equal space, in the fame time. If thewheel be pulled round by the handles S, S, the power will be increafedin proportion to their length. And by this means, ariy weight maybe raifed as high as the operator pleafes.

To this fort of engine belong ali cranes for raifing great weights;and in this case, the wheel may have cogs all around it instead of han-dles, and a fmall lantern or trundle may be made to work in the cogs,and be turned by a winch ; which will make the power of the engineto exceed the power of the man who works it, as much as the nurii-ber of revolutions of the winch exceed thofe of the axle D, whenmultiplied by the excefs of the length of the winch above the lengthof the femidiameter of the axle, added to the femidiameter or halfthickness of the rope K, by which the weight is drawn up.—ThuS,suppofe the diameter of the rope and axle taken together, to be 12inches, and confequently, half their diameters to be 6 inches; so thatthe weight W will hang at 6 inches perpendicular distance from belowthe center of the axle. Now, let us suppofe the wheel AB, which isfixt on the axle, to have 80 cogs, and to be turned by means of awinch six inches long, fixt on the axis of a trundle of 8 staves orrounds, working in the cogs of the whe^l.-r-Here it is plain, that thewinch and trundle would make 10 revolutions for one of the wheelAB, and its axis D, on which the rope K winds in raising the weight W ;

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