Mechanics.

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\ / 2 R H — H% which, since H is given, will be asv/R — 1 ; but \/ R — 1 will be greater in ProportiontoR when R is small than when it is greater. Thusif R = 2, then / R — 1 - 1 = \ R; but if R = 5,then R —• 1 — 2, w hich is less than f R ; and ifR — 10, then R — i — 3, which is less than 4 R ;so that in this Respect small Wheels have the Advan-tage of large ones. But this Cafe seldom happens.

14. The principal Advantage of small Wheels is, PJ.XIII.that in them the Line of Traction is not parallel to the jrjg^ I2>Horizon as C K, but inclined thereto in a certain

Angle, as C M, making with the Horizon the AngleMCKj now if C M be parallel to the Tangent O K,the whole Force will be employed to draw the Wheelover the Obstacle E F ; whereas, if the Line of Trac-tion were parallel to the Horizon, the Line C K mightthen express the Force, which being resolved into thetwo Forces C E and K E, thews that the Part C E drawsthe Wheel directly upon the Obstacle, and is thereforelost by its Re-action ; and only the Part K E remainsto draw the Wheel over the said Obstacle ; and con-sequently the horizontal Direction is not the best, un-less upon a smooth and even Plane, where no Obstaclesand Ascents are to be surmounted.

15. From what we have said, it is evident that asmall Wheel, whose Radius is K E, and the Line ofTraction parallel to O K, is equivalent to a largeWheel whose Radius is C K, and the Line of Tractionparallel to the Horizon N D ; but E K : C K : : H B :

OB:: C I : C E ; that is, the Radius of the smallerWheel is to that of the larger, as the Co-sine of theAngle E C G to Radius,

16. Though the Force employed be never whollyspent in drawing, but when the Direction is C N, pa-rallel to the Plane on which the Carriage moves ; yet if Fig. 13.it be applied in that oblique Direction C M, where the

Breast of the Horse is higher than the Axle of theWheel C, in which Cafe only the Part B M is em-ployed in drawing, the other Part C B is not howeverwholly lost, but is acting contrary to the Gravity ofthe Carriage, and by that Means leflens somewhat of

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