As has been said (cf. p. 130), it has been found that in the limiting region (sufficiently low frequencies) where the Bohr theory and the classical electrodynamics are merged in their outward features, a series of frequencies ν₁, ν₂, ν₃ for monochromatic radiation, emitted by different atoms in the single jumps, double jumps, etc., of the electrons, are equal to the frequencies ω, 2ω, 3ω ... which, according to the laws of electrodynamics, are contained in each of these atoms respectively as fundamental and the first, second ... overtones in the motion of the electron. Farther away from this region the two sets of frequencies are no longer equally large, but it is easy to understand, from the foregoing, the meaning of the statement that, for example, the radiation of a triple jump with the frequency ν₃ “corresponds” to the second overtone 3ω in the revolution of the electron. It is this correspondence which Bohr traces back to the regions where there is even a great difference in two successive orbits and where the frequency produced by a transition between these orbits is very different from the frequencies of revolution in the two orbits or their overtones. He expresses himself as follows: “The probability for the occurrence of single, double, triple jumps, etc., is conditioned by the presence in the motion of the atom of the different constituent harmonic vibrations having the frequency of the fundamental, first overtone, second overtone, etc., respectively.” In order to understand how this “correspondence,” apparently so indefinite, can be used to derive important results, we shall give an illustration. Let us assume that the mechanical theory for the revolution of an electron in the hydrogen atom had led to the result that the orbits of the electrons always had to be circles. According to the laws of electrodynamics, the motion of the electron would in this case never give any overtones, and, according to the correspondence principle, there could not appear among the frequencies emitted by hydrogen any which would correspond to the overtones, _i.e._, there would not be any double jumps, triple jumps, etc., produced, but the only transitions would be those between successive stationary orbits. The investigation of the spectrum shows, however, that multiple jumps occur as well as single jumps, and this fact may be taken as evidence that the orbits in the hydrogen atom are not usually circles. Let us next assume that, instead, we had obtained the result that the orbits of the electrons are always ellipses of a certain quite definite eccentricity, corresponding to certain definite ratios in intensity between the overtones and the fundamentals; that, for instance, the intensity of the classical radiation due to the first overtone is in all states of motion always one-half that due to the fundamental, the intensity due to the second overtone always one-third that due to the fundamental, etc.