In a paper “On some General Theorems relating to Vibrations,” published in the Mathematical Society's Proceedings for 1873 [Art. xxi], I proved a very general reciprocal property of systems capable of vibrating, with or without dissipation, about a position of stable equilibrium. The principle may be shortly, though rather imperfectly, stated thus:—If a periodic force of harmonic type and of given amplitude and period act upon the system at the point P, the resulting displacement at a second point Q will be the same both in amplitude and phase as it would be at the point P were the force to act at Q.

If we suppose the period of the force to be very great, the effects both of dissipation and inertia will ultimately disappear, and the system will be in a condition of what is called moveable equilibrium; that is to say, it will be found at any moment in that configuration in which it would be maintained at rest by the then acting forces, supposed to remain unaltered. The statical theorem to which the general principle then reduces is so extremely simple that it can hardly be supposed to be altogether new; nevertheless it is not to be found in any of the works on mechanics to which I have access, and was not known to the physicists to whom I have mentioned it. In any case, I think, two or three pages may not improperly be devoted to the consideration of it.