The evidence for the soundness of the conception of non-radiating electronic orbits is to be looked for, then, first, in the success of the constants involved, and, second, in the physical significance, if any, which attaches to the third assumption. If these constants come out right within the limits of experimental error, then the theory of non-radiating electronic orbits has been given the most crucial imaginable of tests, especially if these constants are accurately determinable. [Pg 214] What are the facts? The constant of the Balmer series in hydrogen, that is, the value of in equation (34), is known with the great precision attained in all wave-length determinations and is equal to . From the Bohr theory it is given by the simplest algebra (Appendix G) as As already indicated, in 1917 I redetermined[156] with an estimated accuracy of one part in 1,000 and obtained for it the value . As will be shown in the next chapter, I have also determined photo-electrically[157] with an error, in the case of sodium, of no more than one-half of 1 per cent, the value for sodium, upon which I got the most reliable data, being . The value found by Duane’s X-ray method,[158] which is thought to yield a result correct to one part in 700, is exceedingly close to mine, namely, . Substituting this in (38), we get with the aid of Bucherer’s value of (), which is probably correct to 0.1 per cent, , which agrees within a fourth of 1 per cent with the observed value. This agreement constitutes most extraordinary justification of the theory of non-radiating electronic orbits. It demonstrates that the behavior of the negative electron in the hydrogen atom is at least correctly described by the equation of a circular non-radiating orbit. If this equation can be obtained from some other physical condition than that of an actual [Pg 215] orbit, it is obviously incumbent upon those who so hold to show what that condition is. Until this is done, it is justifiable to suppose that the equation of an orbit means an actual orbit. Again, the radii of the stable orbits for hydrogen are easily found from Bohr’s assumptions to take the mathematical form (Appendix G) In other words, since is a whole number, the radii of these orbits bear the ratios 1, 4, 9, 16, 25. If normal hydrogen is assumed to be that in which the electron is in the inmost possible orbit, namely, that for which , the diameter of the normal hydrogen atom, comes out . The best determination for the diameter of the hydrogen molecule yields in extraordinarily close agreement with the prediction from Bohr’s theory. [Pg 216]