"To provide and make that all the weights of the descending side of a wheel shall be perpetually farther from the center than those of the mounting side, and yet equal in number and heft to the one side as the other. A most incredible thing, if not seen; but tried before the late King (of blessed memory) in the Tower by my directions, two extraordinary ambassadors accompanying his Majesty, and the Duke of Richmond, and Duke of Hamilton, with most of the court attending him. The wheel was fourteen foot over and had forty weights of fifty pounds a piece. Sir William Balfore, then Lieutenant of the Tower, can justify it with several others. They all saw that no sooner these great weights passed the diameter line of the lower side, but they hung a foot farther from the center; nor no sooner passed the diameter line of the upper side, but they hung a foot nearer. Be pleased to judge of the consequence." [Illustration] Now the consequence of this and such like machines, is nothing less than a perpetual motion; and the fallacy is this: The velocity of any weight is not the line which it describes in general, but the height that it rises up to or falls from, with respect to its distance from the center of the earth. So that when the weight (Fig. 3) describes the arc A _a_, its velocity is the line A C, which shows the perpendicular descent (or measures how much it is come nearer to the center of the earth), and likewise the line B C denotes the velocity of the weight B, or the height that it rises to when it ascends in any of the arcs B _b_, instead of the arc B D: so that in this case whether the weight B in its ascent be brought nearer the center or not, it loses no velocity which it ought to do in order to be raised up by the weight A. Nay, the weight in rising nearer the center of a wheel may not only lose of its velocity, but be made to gain velocity in proportion to the velocity of its counterpoising weights that descend in the circumference of the opposite side of the wheel; for if we consider two radii of the wheel, one of which is horizontal, and the other (fastened to and moving with it) inclined under the horizon in an angle of 60 degrees (Fig. 5) and by the descent of the end B of the radius B C, the radius C D by its motion causes the weight at D to rise up the line _p_ P, which is in a plane that stops the said weight from rising in the curve D A, that weight will gain velocity, and in the beginning of its rise it will have twice the velocity of the weight at B; and consequently, instead of being raised, will overpoise, if it be equal to the last mentioned weight. And this velocity will be so much the greater in proportion as the angle A C D is greater, or as the plane P _p_ (along which the weight D must rise) is nearer to the center. Indeed, if the weight at B (Fig. 3) could, by any means, be lifted up to β, and move in the