It was no doubt the barefaced fallacy of most of the plans for perpetual motion that led the majority of scientific men to con clude at a very early date that the "perpetuum mobile" was an impossibility. We find the Paris Academy of Sciences refusing, as early as 1775, to receive schemes for the perpetual motion, which they class with solutions of the duplication of the cube, the trisection of an angle and the quadrature of the circle. Stevinus and Leibnitz seem to have regarded its impossibility as axiomatic; and Newton at the beginning of his Principia states a principle which virtually amounts to the same thing.
The famous proof of P. de la Hire simply refers to some of the more common gravitational perpetual motions. The truth is that, if proof is to be given, or considered necessary, it must pro ceed by induction from all physical phenomena.
By far the most numerous class of perpetual motions is that which seeks to utilize the action of gravity upon rigid solids. We have not read of any actual proposal of the kind, but the most obvious thing to imagine in this way would be to procure some substance which intercepts gravitational attraction. If this could be had, then, by introducing a plate of it underneath a body while it was raised, we could elevate the body without doing work; then, removing the plate, we could allow the body to fall and do work; eccentrics or other imposing device being added to move the gravitation intercepter, behold a perpetual motion complete! The great difficulty is that no one has found the proper material for an intercepter.
Fig. 1 represents one of the most ancient and oftenest-repeated of gravitational perpetual motions. The idea is that the balls rolling in the compartments between the felloe and the rim of the wheel will, on the whole, so comport themselves that the moment about the centre of those on the descending side exceeds the moment of those on the ascending side. Endless devices, such as curved spokes, levers with elbow-joints, eccentrics, etc., have been proposed for effecting this impossibility. The student of dynamics at once convinces himself that no machinery can effect any such result; because if we give the wheel a complete turn, so that each ball returns to its original position, the whole work done by the ball will, at the most, equal that done on it. We
know that if the laws of motion be true, in each step the kinetic energy given to the whole system of wheel and balls is equal to that taken from the potential energy of the balls less what is dis sipated in the form of heat by frictional forces, or vice versa, if the wheel and balls be losing kinetic energy—save that the friction in both cases leads to dissipation. So that, whatever the system may lose, it can, after it is left to itself, never gain energy during its motion.
The two most famous per petual motions of history, viz., the wheels of the marquis of Worcester (d. 1667) and of Councillor Orffyreus, were prob ably of this type. The marquis of Worcester alludes to the mar vellous performance of his machine in his Century of Inventions (1663) : the wheel was 14 feet in diameter and bore 4o weights of so pounds apiece! Orffyreus (whose real name was Johann Ernst Elias Bessler) appears to have constructed more than one wheel: his last one was 12 ft. in diameter and 1 ft. 2 in. broad; it con sisted of a light framework of wood, covered in with oilcloth so that the interior was concealed, and was mounted on an axle which had no visible connection with any external mover. It was examined and approved of by the landgrave of Hesse-Cassel, in whose castle at Weissenstein it is said to have gone for eight weeks in a sealed room. The most remarkable thing about this machine is that it evidently imposed upon the mathematician W. T. 'sGravesande, who wrote a letter to Newton giving an ac count of his examination of Orffyreus's wheel undertaken at the request of the landgrave, wherein he professes himself dissatis fied with the proofs theretofore given of the impossibility of per petual motion, and indicates his opinion that the invention of Orffyreus is wo4hy of investigation. He himself, however, was not allowed to examine the interior of the wheel. The inventor seems to have destroyed it himself. One story is that he did so on account of difficulties with the landgrave's government as to a licence for it ; another that he was annoyed at the examination by 'sGravesande, and wrote on the wall of the room containing the fragments of his model that he had destroyed it because of the impertinent curiosity of 'sGravesande.