K-Series of characteristic X-rays; theory assuming orbital motion of the radiating electron.—By combining the equation for orbital motion of an electron about a central positive charge and the Einstein photoelectric equation with the following equation for the nuclear charge, $q=2e(N-3.6\mathrm{})\mathrm{}$, the author gets an equation of the form of Moseley's equation, which gives values of $\lambda$ for the elements from bromine (35) to cerium (58) which agree closely with the observed wave-lengths of the K-radiation. In this calculation, however, $\frac{h^3}{m}$ is assumed constant. Now since the mass of the electron $m$ varies with the speed, if $h$ is constant the ratio $\frac{h^3}{m}$ is not constant and the measured wave-lengths can no longer be computed from the above equation. Deduction. The author presents this as evidence that the quantum constant $h$ varies with the frequency.

Relation between the $\beta$-and $\gamma$-rays of RaB; theory.—Assuming the speed of the $\beta$-rays is their orbital speed before emission and that the Einstein photoelectric equation gives the relation between the energy of a $\beta$-ray and the frequency of the corresponding $\gamma$-radiation, the author computes the wave-lengths of the $\gamma$-rays corresponding to the various $\beta$-rays of RaB. The values differ according to whether $h$ or $\frac{h}{m}$ is assumed to be constant. The agreement between calculated and observed wave-lengths is not striking in either case, but is better if $\frac{h}{m}$ is constant. Deduction. This suggests that the quantum constant h varies with the frequency. The author does not discuss the discrepancy between the conclusions derived respectively from X-ray and $\gamma$-ray data, though it is obvious that $\frac{h^3}{m}$ and $\frac{h}{m}$ cannot both be constant.

• Received 25 June 1919

DOI:https://doi.org/10.1103/PhysRev.15.67