Naturally, Bohr himself clearly recognized the formal nature of the agreement between the Balmer-Ritz formula and his postulates. But Bohr was the first to see that the quantum theory afforded the possibility of bringing about such an agreement, and he saw, moreover, that the agreement was not merely fortuitous, but contained within it something really fundamental, on which one could build further. That atomic processes on his theory took on an unreasonable character (compared with the classical theory) was nothing to worry about, for Bohr had come to the clear recognition that it was completely impossible to understand from known laws the Planck-Einstein “quantum radiation,” or to deduce the properties of the spectrum from the Rutherford atom alone. He therefore saw that his theory was really not introducing new improbabilities, but was only causing the fundamental nature of the contradictions which had previously hindered development in this field to appear in a clearer light. But in addition to this the choice of the dimensions of the stationary states was by no means so arbitrary as might appear in the foregoing. In his first presentation of the theory of the hydrogen spectrum, Bohr had derived his results from certain considerations connected with the quantum theory—considerations of a purely formal nature, indeed, just as those developed in the preceding, but leading to agreement with the spectral formulæ. He, moreover, called attention to the fact that the values obtained for the orbital dimensions were of the same order of magnitude as those which could be expected on wholly different grounds. The diameter of the innermost orbit, _i.e._, that which defines the outer limit of the atom in the normal state, was found to be, as has been noted above, about 10⁻⁸ cm., _i.e._, of the same order of magnitude as the values obtained for the diameters of molecules on the kinetic theory of gases (see p. 27). The stationary states corresponding to very high quantum numbers one could expect to meet only when hydrogen was very attenuated, for otherwise there could be no room for the large orbits. We note that the 32nd orbit must have a diameter 32² (or over 1000 times) as great as the innermost orbit. Since, now, lines with high number in a hydrogen series correspond on the Bohr theory to transitions from orbits of high number to an inner orbit, it became understandable why only comparatively few lines of the Balmer series are ordinarily observed in the discharge tube, while many more lines are observed in the spectra of certain stars. For in such stars the possibility is left open for hydrogen to exist in a very attenuated state, and yet in such large masses that the lines in question can become strong enough for observation. In fact, one must assume that in a great mass of hydrogen a very large number of atoms send out simultaneously light of the wave-length corresponding to one line. For the ionizing work, _i.e._, the work necessary to