In its fundamental aspects, practically the whole of modern physics is concerned with the discussion of the relations which exist between the motions of two sets of points in such a way as to establish a sort of one-one correspondence between the things which we do, and the behavior of one set of points on the one hand, and the things which we observe and the behavior of the other set of points on the other hand. We send a beam of electrons through an X-ray tube, and certain dark lines appear on photographic plates elsewhere, or electrons are emitted with certain velocities which we measure indirectly. As regards the electrons which are emitted into our apparatus, we can almost say that we observe them directly. As regards the blackening of the photographic plate, we are content if we can account for certain electronic emissions or motions to which we can attribute it. We do not, however, try to establish a direct relation between the original beam of electrons and the photographic plate or photoelectric cell, because we find that certain other apparatus was necessary for the experiment, a calcite grating and X-ray target, and so forth. These pieces of apparatus are replaced in the mind's eye by other sets of points grouped into atoms and molecules, in a manner characteristic of the substances in such a way that we may hope to be able to establish a relation between the first set of points, those in the target, those in the calcite and those in the final photographic plate or photoelectric cell. The whole problem is to discover how the points must be assigned and what function their mutual motions are of each other in order that the correlation may be satisfactorily made.