found by Langmuir[43] by measuring the heat conduction through the gas from an incandescent wire in hydrogen. On account of the indirect method employed it seems difficult to estimate the accuracy to be ascribed to the latter value. In order to bring the theoretical value in agreement with Langmuir’s value, the magnitude of the angular momentum of the electrons should be only ⅔ of that adopted; this seems, however, difficult to reconcile with the agreement obtained on other points.
From (6) we get
. For the frequency of vibration of the whole ring in the direction parallel to the axis of the system we get
We have assumed in [Part I.] and [Part II.] that the frequency of radiation absorbed by the system and corresponding to vibrations of the electrons in the plane of the ring cannot be calculated from the ordinary mechanics, but is determined by the relation
, where
is Planck’s constant, and