It must be pointed out that the above considerations only hold if the hydrogen atoms, strictly speaking, are undisturbed. Thus, very small external forces, which may be due to the neighbourhood of other atoms, etc., will be sufficient to cause changes in the eccentricity of the stationary orbits. In such a case the above definition of the auxiliary quantum number becomes obviously illusory, and the original character of the fine structure disappears. This is in agreement with the experiments, since the Sommerfeld fine structure can be found only when the conditions in the discharge tube are especially quiet and favourable. Influence of Magnetic and Electric Fields on the Hydrogen Lines. [Illustration: FIG. 28.—The splitting of three hydrogen lines under the influence of a strong electric field.] As previously mentioned (p. 76), the spectral lines are split into three components when the atoms emitting lights are exposed to magnetic forces. The agreement found here between observation and the Lorentz electron theory was considered as strong evidence of the correctness of the latter. According to the Bohr theory, the picture upon which this explanation rested must be abandoned entirely; but fortunately it has been shown that the Bohr theory leads to the same results; and, moreover, Bohr, with the assistance of the correspondence principle, has been able to set forth the more fundamental reason for this agreement. The German scientist, Stark, showed, in 1912, that hydrogen lines are also split by electric fields of force. In Fig. 28 it is shown how very complicated this phenomenon is; here the classical electron theory could not at all explain what happened. This phenomenon could also be accounted for by the extended Bohr theory (with the introduction of more than one quantum number), as it was shown independently by Epstein and by Schwarzschild in 1916; further, the correspondence principle has again shown its superiority, since it makes possible an approximate determination of the different intensities of the different lines. A calculation carried out by H. A. Kramers has shown that the theory gives a remarkably good agreement with the experiments. Not until we think of the extraordinary accuracy of the measurements which are obtained by spectrum analysis, can we thoroughly appreciate the importance of the quantitative agreement between theory and observation in the hydrogen spectrum that has just been mentioned. Moreover, we must remember how completely helpless we previously were in the strange puzzles offered even by the simplest of all spectra, that of hydrogen. CHAPTER VI VARIOUS APPLICATIONS OF THE BOHR THEORY Introduction.