If the nucleus and the electron were held apart by some sort of elastic force, and if the frequencies were given by the ordinary laws of simple harmonic motion, we should have the same fractions entering, but under a radical sign. So the corrections would be only half as large. In Langmuir's theory, the “quantum force," introduced to replace Bohr's centrifuThis is one pos

gal force, is modified arbitrarily by the factor

sible solution. Another would be to say that when the electron drops from one position to another, with the center of gravity of the atom fixed, the frequency of the radiation is determined by the work done on the electron alone, and not on the electron and nucleus together. Either assumption is rather arbitrary. But it may be that there is some more reasonable way to obtain this factor. At least it is not utterly impossible to obtain it without orbital motion.

Thus there is much left to be done. But one point at least is fairly certain, namely, the value of Bohr's assumption that the energy to be released as a quantum is determined by some sort of a drop of the electron from one position in the atom to another, and that the frequency of the vibration is determined by the energy released, and not by the position when it vibrates, This hypothesis is confirmed by a considerable mass of data on the excitation of light and of X-rays by the impacts of electrons on atoms. For in such experiments, the energy of the electron making the impact is related to the frequency, sometimes by the quantum law E=hv, and sometimes by modifications of it, due to the fact that the impacting electron may have to knock a second electron out of the atom, and then the radiation may be emitted by still a third electron falling into the position where the second one was. In all cases where data are available, both in light and X-rays, the quantum law is confirmed, either in the original or modified form, although in most of them the Bohr orbits have never been worked out satisfactorily, if at all.

This makes it desirable for many purposes to use the Bohr energy hypothesis by application to a set of empirical positions for electrons, that we may call "energy levels," the use of the word "level" being suggested by the analogy between a drop of the electron toward the nucleus, under electrostatic force, and of a drop of a stone toward the earth, under gravity. Figure 1 gives such a set of energy levels for the internal electrons of a platinum atom, that are concerned in X-ray emission. The energies here are expressed as voltages needed to give those energies to single electrons. In this figure, the top of the diagram represents the highest potential energy, i.e., that of an electron on the outside of the atom, and the lowest line represents the potential energy of an electron at the lowest point it can reach, called the K position, from its close con

Fig. 1.-Lower energy levels in platinum atom, as obtained from X-ray data. This figure shows only the most important levels, omitting some of the minor ones too near these to be resolved from them on this scale. These are typical of all elements.

nection with the K series of X-rays. The positions used in light emission are all crowded so close together at the top that they can not be drawn on the scale of this diagram. The next diagram, Figure 2, shows on a more enlarged scale the outer positions of electrons in a sodium atom, i.e., the ones concerned in the emission of light; and Figure 3 shows the corresponding positions in the more complex atom of mercury. In all these cases, and many others, a drop from one of these positions to another makes the electron radiate a frequency that depends only on the energy released in the drop, and not on the environment in which the electron

finds itself when it lands. For the question of what these positions are, they may be something like Bohr's orbits, or they may be positions of static equilibrium of the electrons, such as the corners of the cubes in the Lewis-Langmuir atom. The chemical evidence would seem to make the a tter the more probable.x

Fig. 2.-Upper energy levels in sodium atom, as obtained from data on light. This type of energy level system is found in all the alkali metals, the P levels all being double.

THE DYNAMICS OF THE ELECTRON

Whatever the energy levels are, the fact that the frequency is determined by the energy released, rather than by the environment, suggests strongly the idea that the electron is not a simple charged sphere, but that, like the nucleus, the electron has a structure and a dynamics of its Or, specifically, that it carries in itself a mechanism for maintaining continuous vibrations as long as they are needed to emit the released energy, with a constant frequency, given only by the amount of energy released. And this mechanism must be independent of the environment. It is, for example, just as if the electron was a thin ring, such as Parson assumed, with the charge free to flow on it just as it is on a wireless antenna. In this case, we can readily imagine continuous electrical oscillations on the ring, and we can see how an outside static charge would merely produce a static displacement of the electron's charge, but would not in any way influence its frequency of vibration. The new element in the dynamics of this situation is the law that the frequency is given by the energy released.

However this may happen, this idea of the electron's carrying its own vibratory mechanism fits remarkably well with the available data, not only on the line spectra, but also on the continuous part of the X-ray spectrum, or the "general radiation" as Bragg has called it. For the distribution of this general radiation around the target is most peculiar, and it can be shown to be explained most readily on the assumption that if a cathode ray electron collides with an atom, and releases only a part of its energy for radiation, it may keep the rest as kinetic energy and emit continuous waves while it is traveling along through several atoms. This can be done only if it carries its own mechanism of vibration with it as it moves.1

So much for the dynamics of the emission of radiation. The absorption of radiation also brings up some interesting problems. For the frequency that an electron can absorb is often determined by a curious inversion of Bohr's reversed Planck hypothesis, namely, that it will absorb a frequency that will give it a quantum large enough to raise it to some energy level where there is an unoccupied position for it to land in.

Now a man on a crowded stairway can see when a space is open on a step above him, and gather energy enough to step up to it. But if he expends the energy when the space is not open, he not only fails to get there, but also makes trouble for himself in the attempt. The electron apparently has more discretion, and does not try it unless the space is open. Not only that, but if the position is unoccupied but the frequency of the light is wrong, either too large or too small, it again refuses to take a

D. L. Webster, Bull. Nat. Research Council, 1, 427, 1920.