This relation between the sus ceptibility and the concentration does not hold invariably, for in some cases the state of the salt varies with the concentration ow ing to interaction with the solvent.
For water, according to concord ant measurements of P. Seve, A. Piccard, B. Cabrera and others, x w —72 X at 20° C (this is probably correct to within 1%). The susceptibility of diamagnetic salts found from measurements on solutions fre quently agrees fairly closely with that found for the solids directly, but there are many exceptions to this rule.
A salt such as NaC1 exists in solution in the form of Na+ and ions. The ionic character of solid salts is well established also, in many cases, from X-ray crystal analysis. By carrying out measurements on series of salts with the same anion or kation, ionic susceptibility constants may be arrived at in the way indi These values are shown in the graph. Considering the series to there is a steady increase in the ionic susceptibility with increasing number of electrons. From the Langevin theory, for an ion containing n electrons, the mean square radius of the elec tronic orbits is given by For the halide ions this leads to a value for the mean radius of about .6X cm. Regularities are revealed in the study of ionic susceptibilities which are not found when the elements themselves are considered. In the group of ions to Ca++, all have the same number of electrons, but the positive nuclear charge increases from 17 to 2o; this results in a decrease in the size of the elec tronic configuration, as would be anticipated in the basis of the quantum theory of atomic structure, which is reflected in the decrease in the diamagnetic susceptibility.
From the susceptibilities of neighbouring ions, probable values for the atomic susceptibilities of the inert gas atoms may be de duced. These differ considerably from the values obtained in early experiments. A. P. Wills and G. Hector measured directly the susceptibilities of He, Ne and A by the magnetic balance method (Phys. Rev. 1924) taking great precautions to ensure purity of the materials. They found the following values. These agree well with the values deduced indirectly, and afford for — X for the inert gases: He, 1.7; Ne, 6.1; A, 16.5 confirmation of the general correctness of the theoretical treat ment, in which the susceptibility is connected with the area of the orbits swept out by the electrons. The idea of electrons mov
ing in definite orbits in atoms may have to be abandoned, but L. Pauling (Proc. Roy. Soc., A., 1927) has shown that a satis factory treatment of ionic diamagnetic susceptibility may be given along somewhat similar lines, on the basis of a view of the exten sion in space of an atom which is suggested by Schrodinger's wave mechanics.
Gases.—The susceptibilities of a number of gases have been measured by T. Sone (Phil. Mag. 192o) by a Gouy method, by Wills and Hector, and by V. I. Vaidyanathan (Phys. Rev. 1927). The values found for a few of the commoner gases are here shown, together with some results deduced by Pascal from ex periments on liquids.
The rough estimates of the sizes of the molecules which may be made from the susceptibilities are in fair agreement with those deduced from the kinetic theory of gases. The greatest contribu tion to the diamagnetism will come from the electrons moving in the largest orbits, that is the "outer electrons" which are most loosely bound to the nuclei. In this connection it is interesting to note that the molecular susceptibility of N2 is only slightly greater than that of neon. This supports the view rendered probable by consideration of the band spectrum and the chemical properties, that the outer electrons of the two nitrogen atoms are shared, the whole molecule behaving as a "pseudo-atom." Analysis of the diamagnetic susceptibilities of molecules in relation to those of the constituent atoms frequently throws a valuable side-light on the character of chemical combination.
If the molecular susceptibility of a gas is constant, and inde pendent of orientation in the field, and so of collisions between the molecules, it would be expected that the volume susceptibility would vary linearly with the pressure. Some very delicate experi ments by A. Glaser (Ann. der Phys. 1924) seemed to indicate that at low pressures this relation did not hold, and that the molecular susceptibility of the gases investigated N2, CO2, CO) in creased eventually by a factor of three at low pressures and in high fields. This "anomaly" gave rise to considerable discussion, but a repetition of the experiments by G. W. Hammar (Nat. Acad. Sci. Proc. 1926) and an investigation by another method by E. Lehrer (Ann. der Phys. 1926) showed that the apparent anomaly was due to secondary experimental effect inherent in Glaser's method, and that the volume susceptibility of gases was accu rately proportional to the pressure.