The formula for the energy associated with the quantum numbers , now becomes much more complicated; its great merit is that it accounts for the fine structure of the hydrogen line spectrum. It must be felt that this minuteness of agreement between theory and observation is very remarkable. But it is still the case that the only empirical evidence concerns differences of energy in connection with different quantum numbers, and that the theory of actual orbits, proceeding, during steady motion, according to Newtonian principles, must inevitably remain a hypothesis—a hypothesis which,[Pg 41] as we shall see, has disappeared from the latest form of the quantum theory. The fact of the existence of the quantum is as strange as it is undeniable, unless it should turn out to be deducible from classical principles. It seems to be the case that quantum principles regulate all interchange of energy between matter and the surrounding medium. There are grave difficulties in reconciling the quantum theory with the undulatory theory of light, but we shall not consider these until a later stage. What is much to be wished is some way of formulating the quantum principle which shall be less strange and ad hoc than that due to Wilson and Sommerfeld. For practical purposes, it amounts to something like this: that a periodic process of frequency has an amount of energy which is a multiple of , and, conversely, if a given amount of energy is expended in starting a periodic process, it will start a process with a frequency such that the given amount of energy shall be a multiple of . When a process has a frequency and an energy , the amount of "action" during one period is . But we cannot say: In any periodic process the amount of action in one period is or a multiple of . Nevertheless, some formulation analogous to this might in time turn out to be possible. As has appeared from the theory of relativity, "action" is more fundamental than energy in physical theory; it is therefore perhaps not surprising that action should be found to play an important part. But the whole theory of the interaction of matter and the surrounding medium, at present, rests upon the conservation of energy. Perhaps a theory giving more prominence to action may be possible, and may facilitate a simpler statement of the quantum principle.