While the Stark-effect has not been studied so extensively as the Zeeman-effect, either in the experiments or in their interpretations, many of the more prominent features have been observed and have received adequate explanation on the quantum theory. Among these may be mentioned the patterns characteristic of the different series in the singlet system of parhelium. The variety of observed patterns in the Stark-effect, as contrasted with the normal Zeeman-effect found for all series of this system, arises from a differential action of the external electric field on the initial and final states, and a breaking down of the usual selection rule for the azimuthal quantum number. Some simplification is brought about, however, by the fact that only the absolute value of the quantum number
m
has any meaning in the interpretation of these photographs, since the action of the field is the same for right or left-handed motion of the outer electron in its orbit. This results in asymmetrical patterns for all the lines. The number of components observed in the patterns of individual lines of parhelium is in accord with the theoretical view that the vector
j
(here equal to
l
) is resolved along the direction of the applied field to give the integral
m
values ranging from -
j
to +
j
, and that the usual selection rule holds for
m
. The displacements and intensities are in excellent agreement with the theoretical calculations based on the perturbation theory of quantum mechanics. The spacing of the sub-levels identified by ±
m
in the initial state is decidedly irregular in the Stark-effect as compared with the normal Zeeman-effect, where the displacements are proportional to
m
. The Zeeman order of the levels is usually reversed, in fact, and the spacing is uneven. Displacements in the final state are theoretically very small, and have not been observed with certainty. In the Stark-effect for orthohelium (triplet system) the same group of patterns was observed. An explanation of these observations, which is slightly less satisfactory than that obtained with parhelium, has been made by similar methods, neglecting the electron spin. Thus the
m
values were again given ranges determined in each case by the
l
of the outer electron, and not by the
j
for the whole atom. Most of the plates failed to reveal any of the fine structure of the normal orthohelium spectrum.
EIGENMODE OF THE DECISION-BY-MAJORITY PROCESS IN COMPLEX NETWORKS
