Now 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 centre of the earth. So that when the weight describes the arc A _a_, its velocity is the line A C, which shows the perpendicular descent, 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 centre or not, it loses no velocity, which it ought to do, in order to be raised up by the weight A. Indeed, if the weight at B, could by any means spring as it were, or be lifted up to _x_, and move in the arc _x b_, the end would be answered, because then the velocity would be diminished, and become _x_C. FIGURE 2. In "The Life, Times, and Scientific Labours of the Marquis of Worcester," 1865, page 454, will be found a full account of the present diagram, which is intended to illustrate as far as possible, an approach to the probable construction of the wheel by the Marquis in the 56th article of his memorable "Century of Inventions." If any likely-looking method, could, more than another, render hopelessness more hopeless, surely this mechanical demonstration must prove most efficient for that purpose. For here, we actually produce a wheel agreeing to the terms with which Desaguliers closes his demonstration, when he suggests the only likely method to effect the end proposed, namely, perpetual motion. We find the fallen weight is absolutely "lifted up" as he desires, and "moves in the arc" he describes, and yet although he declares that then "the end would be answered"--it absolutely is _not_ answered in this instance. It is not requisite to calculate throughout the effect of the Marquis's entire number of 40 weights; four will suffice, taking the vertical and horizontal spokes _a a a a_, showing two rings _a_ and _b_; one, _b_, 12 inches within the other, so that the wheel being, as the Marquis says, 14 feet diameter, the inner ring will be 12 feet diameter. Now let each weight D be attached in the centre of a cord or chain _a_´, D, b´, 2 feet long, and then secure one end, as _a_´, so the extreme end of each spoke _a_´, and the other end of the cord, as b´, to place on one lesser ring, as at _b_, or 12 inches from each spoke. We shall then find by admeasurement that the upper weight on the vertical spoke is 7 feet from the centre, and the lower weight 6 feet; while at the same time there appears to be a preponderance due to the superior length of the horizontal arm A´; but against this latter we have the rising weight _b_´D, 1 foot from the centre, which, added to the 6 feet on the horizontal spoke, neutralizes the hoped-for effect, and the wheel remains in _statu quo_. THE END. * * * * * [Illustration: Plate 1.