, we find out how much energy the above loses in the different transitions from orbit to orbit that are possible. The terms in the spectrum are proportional to the energies in the different possible orbits, and the frequencies of the lines are proportional to the loss of energy in passing from one orbit to another. We can calculate what the different possible orbits should be from the fact that their energies must differ by an amount
, where
is the frequency of some line in the hydrogen spectrum. We can also calculate the possible orbits from the fact that the mass of the electron multiplied by the circumference of an orbit multiplied by the velocity in that orbit must be an exact multiple of
. These two methods lead to the same result, and thus confirm our theory.
There are, however, certain minutiæ of the hydrogen spectrum which cannot be explained by Bohr’s theory in its original form. All these, down to the smallest particular, are explained by the generalized form of the theory which is due in the main to Sommerfeld. We shall explain this generalized theory in the next chapter.
The quantity