The potential energy of a system has a particular significance with respect to this point of view. In an ordinary mechanical system, the potential energy simply measures the work done by the applied forces in being displaced from the initial to the final positions; that is, the potential energy is a measure of the deviation from the initial position, and so measures a certain feature of the history of the system. In the more general system, in which we may not have differential equations, we may look for something analogous to the potential energy which shall measure the displacement of the system from its initial configuration. Such a measure is always possible as long as the past can be reconstructed from the present (or the present from the future). We recall a remark of Poincaré's[20] to the effect that we of necessity must always have conservation, because if we have a system in which conservation apparently fails, we merely have to invent a new form of potential energy. This remark is obviously not of entire generality, but applies only to such systems as those considered here, in which the past may be reconstructed from the present. [Footnote 20: Henri Poincaré, Wissenschaft und Hypothese, translated into German by F. and L. Lindemann, Teubner, Leipzig, 1906, Chap. VIII.] Of late there has been much discussion of the advisability, on the basis of certain quantum phenomena, of giving up conservation as a principle applied to the details of the emission and absorption of light, retaining it only in a statistical sense. It seems to me that the question here in the minds of physicists was always merely one of convenience, and that few, if any, doubted the ultimate applicability of the principle of Poincaré, or thought that we were here concerned with a system of such great generality that the past could not be reconstructed from the present. The question was merely whether those variables in terms of which the potential energy is defined make close enough connection with other things of immediate experimental significance, or whether on the whole the retention of a potential energy is not more trouble than is justified by its convenience, making a treatment from the statistical point of view preferable. However, this is all now a matter of more or less past history, because with the recent extension of the experiments of Compton,[21] we seem to have experimental evidence for the validity of the conservation law in detail for elementary quantum processes, with a corresponding simple potential energy. [Footnote 21: W. Bothe and H. Geiger, 2S. f. Phys. 32, 639-663, 1925. A. H. Compton, Proc. Nat. Acad. Soc., II, 303-306, 1925.]