But more than that: this notion of effort does not teach us the real nature of force; it reduces itself finally to a remembrance of muscular sensations, and it will hardly be maintained that the sun feels a muscular sensation when it draws the earth.
All that can there be sought is a symbol, less precise and less convenient than the arrows the geometers use, but just as remote from the reality.
Anthropomorphism has played a considerable historic rôle in the genesis of mechanics; perhaps it will still at times furnish a symbol which will appear convenient to some minds; but it can not serve as foundation for anything of a truly scientific or philosophic character.
'The School of the Thread.'—M. Andrade, in his Leçons de mécanique physique, has rejuvenated anthropomorphic mechanics. To the school of mechanics to which Kirchhoff belongs, he opposes that which he bizarrely calls the school of the thread.
This school tries to reduce everything to "the consideration of certain material systems of negligible mass, envisaged in the state of tension and capable of transmitting considerable efforts to distant bodies, systems of which the ideal type is the thread."
A thread which transmits 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.
One may then conceive an experiment such as this. A body A is attached to a thread; at the other extremity of the thread any force acts which varies until the thread takes an elongation α; the acceleration of the body A is noted; A is detached and the body B attached to the same thread; the same force or another force acts anew, and is made to vary until the thread takes again the elongation α; the acceleration of the body B is noted. The experiment is then renewed with both A and B, but so that the thread takes the elongation ßβ. The four observed accelerations should be proportional. We have thus an experimental verification of the law of acceleration above enunciated.
Or still better, a body is submitted to the simultaneous action of several identical threads in equal tension, and by experiment it is sought what must be the orientations of all these threads that the body may remain in equilibrium. We have then an experimental verification of the law of the composition of forces.
But, after all, what have we done? We have defined the force to which the thread is subjected by the deformation undergone by this thread, which is reasonable enough; we have further assumed that if a body is attached to this thread, the effort transmitted to it by the thread is equal to the action this body exercises on this thread; after all, we have therefore used the principle of the equality of action and reaction, in considering it, not as an experimental truth, but as the very definition of force.
This definition is just as conventional as Kirchhoff's, but far less general.