They take it for granted that if a weight descending in a wheel at a determined distance from the center, does, in its ascent, approach nearer to it; such a weight in its descent will always preponderate and cause a weight equal to it to rise, provided it comes nearer the center in its rise; and accordingly as itself, rises, will be overbalanced by another weight equal to it; and, therefore, they endeavour by various contrivances to produce that effect as if the consequence of it would be a perpetual motion. But I shall show that they mistake one particular case of a general theorem, or rather a corollary of it, for the theorem itself. The theorem is as follows: THEOR.--If one weight in its descent does, by means of any contrivance, cause another weight to ascend with a less momentum or quantity of motion than itself, it will preponderate and raise the other weight. COR. 1.--Therefore, if the weights be equal, the descending weight must have more velocity than the ascending weight, because the momentum is made up of the weight multiplied into the quantity of matter. COR. 2.--Therefore, if a leaver or balance have equal weights fastened or hanging at its ends, and the brachia be ever so little unequal that weight will preponderate which is farthest from the center. SCHOLIUM.--This second corollary causes the mistake; because those who think the velocity of the weight is the line it describes, expect that that weight shall be overpoised, which describes the shortest line, and, therefore, contrive machines to cause the ascending weight to describe a shorter line than the descending weight. As for example, in the circle A D B _a_ (Fig. 3) the weights A and B being supposed equal, they imagine that if (by any contrivance whatever) whilst the weight A describes the arc A _a_, the weight B is carried in any arc, as B _b_, so as to come nearer the center in its rising than if it went up the arc B D; the said weight shall be overpoised, and consequently, by a number of such weights a perpetual motion will be produced. This is attempted by several contrivances, which all depend upon this false principle; but I shall only mention one which is represented by Fig. 4, where a wheel having two parallel circumferences, has the space between them divided into cells, which being curved, will (when the wheel goes round) cause weights placed loose in the said cells to descend on the side A at the outer circumference of the wheel, and on the side D to ascend in the line B _b b b_, which comes nearer the center and touches the inner circumference of the wheel. In a machine of this kind the weights will indeed move in such a manner if the wheel be turned round, but will never be the cause of the wheel's going round. Such a machine is mentioned by the Marquis of Worcester in his "Century of Inventions," in the following words, No. 56: [Illustration]