Fig. 27—Bohr-Sommerfeld model of the hydrogen atom with stationary orbits corresponding to principal quantum numbers and auxiliary or azimuthal quantum numbers. The next quantitative success of the Bohr theory came when Epstein,[160] of the California Institute, applied his amazing grasp of orbit theory to the exceedingly difficult problem of computing the perturbations in electron orbits, and hence the change in energy of each, due to exciting hydrogen and helium atoms to radiate in an electrostatic field. He thus predicted the whole complex character of what we call the “Stark effect,” showing just how many new lines [Pg 220] were to be expected and where each one should fall, and then the spectroscope yielded, in practically every detail, precisely the result which the Epstein theory demanded. Another quantitative success of the orbit theory is one which Mr. I. S. Bowen and the author,[161] at the California Institute, have just brought to light. Through creating what we call “hot sparks” in extreme vacuum we have succeeded in stripping in succession, 1, 2, 3, 4, 5, and 6 of the valence, or outer, electrons from the atoms studied. In going from lithium, through beryllium, boron and carbon to nitrogen, we have thus been able to work with stripped atoms of all these substances. Now these stripped atoms constitute structures which are all exactly alike save that the fields in which the single electron is radiating as it returns toward the nucleus increase in the ratios 1, 2, 3, 4, 5, as we go from stripped lithium to stripped nitrogen. We have applied the relativity-doublet formula, which, as indicated above, Sommerfeld had developed for the simple nucleus-electron system found in hydrogen and ionized helium, and have found that it not only predicts everywhere the observed doublet-separation of the doublet-lines produced by all these stripped atoms, but that it enables us to compute how many electrons are in the inmost, or shell, screening the nucleus from the radiating electron. This number comes out just 2, as we know from radioactive and other data that it should. (See inset photograph, Fig. 37, following Fig. 36, opposite p. 260.) Further, when we examine the spectra due to the stripped atoms of the group of elements from sodium to sulphur, one electron having been [Pg 221] knocked off from sodium, two from magnesium, three from aluminum, four from silicon, five from phosphorus, and six from sulphur, we ought to find that the number of screening electrons in the two inmost shells combined is , and it does come out 10, precisely as predicted, and all this through the simple application of the principle of change of mass with speed in elliptical electronic orbits of the type shown in Fig. 27.