An Application of Pauli's Method of Coordination to Atoms Having Four Magnetic Parts

It is shown that the origin of spectral terms of an arc spectrum obtained by adding a highly excited electron to a certain term of the spark may be understood in terms of an application of the principle of mechanical transformability made by Pauli. According to this application it is sufficient to know (a) the strong and weak field magnetic quantum numbers of a level (b) which of the two vectors $r$ or $k$ is the faster in a magnetic field (c) whether the term is inverted or not in order to tell the value of $j$ belonging to that level. The derivation of Pauli's results is based on sufficiently general principles to enable one to apply it to the Pauli-Hund method of tracing spectral terms. The possible groupings of the $j_a\text{'}\mathrm{s}$ or the $j_s\text{'}\mathrm{s}$ are discussed and it is shown that Pauli's principle is valid here also.