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23. Perpetual Motion

A demonstration by Dr. Desaguliers in 1719, in regard to the balance of weights at unequal distances from the center of oscillation, showing that the weight P balances the weight W at any position on the cross arm H, I, on the vertical arm B, E, when pivoted to the double-scale beam A, B, and D, E, in which the resolution of forces is made apparent in a practical form so often over-looked by the inventors of perpetual-motion machines.

The cut representing Desaguliers' balance, with his explanation, goes to show how persistently inventors have ignored the geometrical bearing of this problem for nearly two centuries.

Desaguliers' Demonstration.- A, C, B, E, K, D is a balance in the form of a parallelogram passing through a slit in the upright piece, N, O, standing on the pedestal, M, so as to be movable upon the center pins C and K. To the upright pieces, A, D and B, E, of this balance, are fixed at right angles the horizontal pieces F, G and H, I. That the equal weights, P, W, must keep each other in equilibrium is evident; but it does not at first appear so plainly, that if W be removed to V, being suuspended at 6, yet it shall still keep P in equilibrium, though the experiment shows it. Nay, if W be successively moved to any of the points, 1, 2,3, E, 4, 5, or 6, the equilibrium will be continued; or if, W hanging at any of those points, P be successively moved to D, or any of the points of suspension on the crosspiece, F, G, P will at any of those places make an equilibrium with W. Now, when the weights are at P and V, if the least weight that is capable to overcome the friction at the points of suspension C and K be added to V, as w, the weight V will overpower, and that as much at V as if it was at W.

As the lines A, C and K, D, C, B and K, E, always continue of the same length in any position of the machine, the pieces A, D and B, E will always continue parallel to one another and perpendicular to the horizon. However, the whole machine turns upon the points C and K, as appears by bringing the balance to any other position, as a, b, e, d, and, therefore, as the weights applied to any part of the pieces F, G and H, I can only bring down the pieces A, D and B, E perpendicularly, in the same manner as if they were applied to the hooks D and E, or to X and Y, the centers of gravity of A, D and B, E, the force of the weights (if their quantity of matter is equal) will be equal, because their velocities will be their perpendicular ascent or descent, which will always be as the equal lines 4l and 4L, whatever part of the pieces F, G and H, I the weights are applied to. But if to the weight at V be added the little weight, w, those two weights will overpower, because in this case the momentum is made up of the sum of V and w multiplied by the common velocity 4L.

Hence it follows, that it is not the distance, C6, multiplied into the weight, V, which makes its momentum, but its perpendicular velocity, L4, multiplied into its mass.

This is still further evident by taking out the pin at K; for then the weight, P, will overbalance the other weight at V, because then their perpendicular ascent and descent will not be equal.

This "paradox" is illustrated in No. 10, first volume of Mechanical Movements, inviting inquiry by students, a model of which has been exhibited to many doubting amateurs by the author.

(Subsection 914, from p.364-5)

From: Gardner D. Hiscox, M.E., Mechanical Appliances and Novelties of Construction (1927), Norman W. Henley Publ. Co.

Nature bears long with those who wrong her. She is patient under abuse. But when abuse has gone too far, when the time of reckoning finally comes, she is equally slow to be appeased and to turn away her wrath. (1882) -- Nathaniel Egleston, who was writing then about deforestation, but speaks equally well about the danger of climate change today.
Carl Sagan: In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) ...(more by Sagan)

Albert Einstein: I used to wonder how it comes about that the electron is negative. Negative-positivethese are perfectly symmetric in physics. There is no reason whatever to prefer one to the other. Then why is the electron negative? I thought about this for a long time and at last all I could think was It won the fight! ...(more by Einstein)

Richard Feynman: It is the facts that matter, not the proofs. Physics can progress without the proofs, but we can't go on without the facts ... if the facts are right, then the proofs are a matter of playing around with the algebra correctly. ...(more by Feynman)

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by Ian Ellis