692 X. ON THE STRUCTURE OF 'MATTER' 

differ from each other in the number of electrons and protons. In Fig. 8 is shown lithiums, with 6 protons and 3 electrons in the nucleus, and 3 revolving electrons. In Fig. 9 is shown lithium?, with 7 protons and 4 electrons in the nucleus and 3 revolving electrons.^{2}
In general terms, Bohr tried to account for all other atoms on the base of the structure of the hydrogen atom. The next important generalization and extension of the Bohr theory was accomplished by Sommerfeld about 1915. The achievement of Sommerfeld can be compared with the advance which Kepler made over the copernican theory of planetary motions. Copernicus considered the planetary orbits as circular. Kepler* considered them as elliptical, and thus introduced a tremendous structural advance in astronomy. Sommerfeld replaced the circular orbits of Bohr by elliptical ones. The theory became much more complicated, because a circle is given by one magnitude; namely, its radius, while an ellipse needs two data, its major and minor axes, and so two quantum numbers for the specification of an orbit. Sommerfeld also introduced some of the results of the Einstein theory; for example, that the mass of a body also depends on its velocity Since the velocity of the negative electrons in the atom is supposedly very large it was quite probable that the relativity considerations should be appreciable. According to the Einstein
theory, the faster a body is moving the greater is its mass. In an elliptical orbit the electron should have a larger mass at the perihelion than at the aphelion, and so the orbit would not be exactly an ellipse but the perihelion would advance slightly at every revolution.
Fig. 10 gives us the relativistic Kepler orbit as introduced by Sommerfeld. 0 is the fixed focus in which the nucleus is situated and P is the initial position of the perihelion. The motion of the perihelion occurs in one sense with that of the orbit.^{3}
The last analogy in the structure of the atom taken over from astronomy was introduced in 1925, when Goudsmit and Uhlenbeck proposed their theory of the spinning electron. The electron was supposed to be spinning about its axis like a planet or a top. A similar notion was used by Compton in 1921, in connection with the magneton, but the notion of using the spinning electron for


♦Kepler's first law states: 'The planet moves in an ellipse, at one focus of which the sun is situated. Perihelion is that point of a planet's orbit at which it is nearest the sun. Aphelion is that point of a planet's orbit at which it is farthest from the sun.' 
