Take the hollow-rimmed wheel A B; let it be air-tight and half filled with water. Let C be the axle; at B place a hollow ball loaded to near sinking. Such a wheel, however fine its axle may be, or however well lubricated, will not make a single revolution, though the weight B occupies that part at which every deluded perpetual-motionist is desirous it should be placed; concluding that, by such an arrangement, the production of another Orffyrean wheel must be inevitable. Discussion by P. Gregorio Fontana P. Gregorio Fontana was professor of higher mathematics at the Royal University of Pavia, in the Province of Lombardy, Italy. In 1786 he published what he designated "Examination of a New Argument in Favor of Perpetual Motion." In part he says: 1. A vertical wheel (Fig. 2) divided in two halves by a vertical plane which passes through its diameter F O, has the half F P O immersed in water under the level M N, and the other half wholly out of the water, being cut off in F O by a peculiar mechanism from all communication with the reservoir, the exterior half of the wheel being F Q O; this turns freely round on an axle passing through the centre C. Now the wheel being specifically lighter than the water, the immersed part F P O comes with a continual rotation to the top with a force equal to the excess of the weight of a volume of water corresponding to the immersed portion, over the weight of the immersed portion; which rotation passing through the centre of gravity of the exterior part, and consequently out of the centre C, obliges the wheel to turn around C. Such being the case, the question to be asked is whether the wheel has itself a perpetual motion, as may be judged at first sight. [Illustration] 2. To reply adequately, it is at first necessary to know what effect is produced on the wheel by the horizontal pressure which the water exercises on the semi-circumference F L O. Having taken for this purpose, a part P _p_, and having drawn to the diameter the ordinate P. R, _p r_, and marked the radius P C, and from it P G perpendicular to the radius C L, which determines the quadrant O L, the distance of the lowest point O from the level of the water will be = _b_, the semi-diameter of the wheel = _a_, C R = _x_, and the specific gravity of the water = 1; the perpendicular pressure against the part P _p_ = P _p_ . R D, which resolved in two, one horizontal P R, the other vertical P G, gives the proportion PG : PR :: P_p_ . RD : (P_p_ . PR . RD) / (PG).