The Relative Intensities of Nebular Lines

It is proved rigorously for multipole radiation that the transition $j=0\mathrm{}\to j=0\mathrm{}$ cannot occur. The relative intensities of the lines of the multiplet ${}_{}{}^2{}_{}{}^{}P\to {}_{}{}^2{}_{}{}^{}D$ are calculated. They are in the ratio $\frac{3}{2}\to \frac{5}{2}:\frac{1}{2}\to \frac{3}{2}:\frac{3}{2}\to \frac{3}{2}:\frac{1}{2}\to \frac{5}{2}=10:5:2:1\mathrm{}$, approximately. This is not in agreement with experiment in that the weaker lines are not observed. The relative intensities of the intercombination lines comprising the multiplet ${}_{}{}^1{}_{}{}^{}D\to {}_{}{}^3{}_{}{}^{}P$ are calculated, using in part the Darwin-Pauli theory of the spinning election as applied by Houston to the study of intercombination lines. The line ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ always is strongest according to the calculations, and the experiments confirm this. The line ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ is about half as strong, which also checks experiment. The intensity of ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ varies, however, from zero to a value of the same order of magnitude as that of ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$. This is in disagreement with experiment in that the line is not observed. This is the same sort of disagreement as for the multiplet ${}_{}{}^2{}_{}{}^{}P\to {}_{}{}^2{}_{}{}^{}D$. It is concluded that Bowen's hypothesis, attributing the emission of the "forbidden" nebular lines to quadrupole radiation, is substantiated to some extent, but not fully. The discrepancies between theory and experiment may arise from the simplifying assumptions introduced.