OF NATURAL PHILOSOPHY. OK arid OL, describe a circle, meeting the cord MA in D : and drawing OD, make AC paral- "^ lei and DC perpendicular thereto. Now, it being indifferent whether the points K, L, D, of the cords be lixed to the plane of the wheel or not, the weights will have the same effect whether they are suspended from the points K and L, or from D and L. Let the whole force of the weight A be represented by the line AD, and let it be resolved into the forces AC and CD ; of which the force AC, drawing the radius OD directly from the centre, will have no effect to move the wheel : but the other force DC, drawing the radius DO perpendicularly, will have the same effect as if it drew perpendicularly the radius OL equal to OD ; that is, it w ill have the same effect as the weight P, if that weight is to the weight A as the force DC is to the force DA ; that is (because of the sim ilar triangles ADC, DOK), as OK to OD or OL. Therefore the weights A and P, which are reciprocally as the radii OK and OL that lie in the same right line, will be equipollent, and so remain in equilibrio ; which is the well known property of the balance, the lever, and the wheel. If either weight is greater than in this ratio, its force to move the wheel will be so much greater. If the weight p, equal to the weight P, is partly suspended by the cord NJO, partly sustained by the oblique plane pG ; draw p}i, NH, the former perpendicular to the horizon, the latter to the plane pG ; and if the force of the weight p tending downwards is represented by the line /?H, it may be resolved into the forces joN, HN. If there was any plane /?Q, perpendicular to the cord y?N, cutting the other plane pG in a line parallel to the horizon, and the weight p was supported only by those planes pQ, pG, it would press those planes perpendicularly with the forces pN, HN; to wit, the plane joQ, with the force joN, and the plane pG with the force HN. And therefore if the plane pQ was taken away, so thnt the weight might stretch the cord, because the cord, now sustaining the weight, supplies the place of the plane that was removed, it will be strained by the same force joN which pressed upon the plane before. Therefore, the tension of this oblique cord joN will be to that of the other perpendic ular cord PN as jt?N to joH. And therefore if the weight p is to the weight A in a ratio compounded of the reciprocal ratio of the least distances of the cords PN, AM, from the centre of the wheel, and of the direct ratio of pH tojoN, the weights will have the same effect towards moving the wheel, and will therefore sustain each other : as any one may find by experiment. But the weight p pressing upon those two oblique planes, may be con sidered as a wedge between the two internal surfaces of a body split by it; and hence tlif ft IV.P* of th^ v, ^dge and the mallet may be determined; foi