Science and Hypothesis by Henri Poincaré David J. Stump Mélanie Frappier

Author:Henri Poincaré,David J. Stump,Mélanie Frappier
Language: eng
Format: epub
ISBN: 9781350026766
Publisher: Bloomsbury UK
Published: 2017-08-31T04:00:00+00:00

The “School of the Thread”

In his Leçons de mécanique physique, Andrade has revived anthropomorphic mechanics. To the school of physicists to which Kirchhoff belongs, he opposes what he calls rather oddly the “School of the Thread.” This school tries to bring everything back to “the study of certain physical systems of negligible mass, pictured in a state of tension and capable of transmitting considerable strain on distant bodies, systems whose ideal type is the thread.”5 A thread transmitting any force is slightly elongated under the action of this force. The direction of the thread tells us the direction of the force, whose magnitude is measured by the elongation of the thread.

We may then imagine an experiment like the following: A body A is attached to a thread, at the other end of which we apply a force that we vary until the thread has grown by a length α, and we record the acceleration of body A. We detach A and attach body B to the same thread and we reapply the force or another force, varying it until the thread grows again by a length α, and we record the acceleration of body B. We repeat the experiment both with body A and body B, but in such a way that the thread grows by a length β. The four observed accelerations should be proportional. We thus have an experimental verification of the law of acceleration stated above. Or else we could subject a body to the simultaneous action of many identical threads, all equally stretched, and try to determine experimentally what the orientation of all these threads must be for the body to remain in equilibrium. We then have an experimental verification of the rule of composition of forces.

What did we really do, anyway? We defined the force to which the thread is subjected by the deformation it undergoes, which is reasonable enough. We further assumed that if a body is attached to this thread, the strain the thread transmits to this body is equal to the action this body exerts on this thread. In the end, we used the principle of the equality of action and reaction, not as an experimental truth but as the very definition of force.

This definition is quite as conventional as Kirchhoff’s, but far less general. Not all forces are transmitted by threads (besides, to be able to compare them, they would all have to be transmitted by identical threads). Even if we were to admit that the earth is attached to the sun by some invisible thread, we would agree at the very least that we have no means of measuring its elongation. Therefore, nine times out of ten, our definition would fail to deliver. We would find it meaningless and we would have to fall back on Kirchhoff’s definition.

Why then take this detour? You accept a certain definition of force that has a meaning only in certain particular cases. In these cases, you experimentally verify that it leads to the law of acceleration.

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