470 



SCIENCE 



[N. S. Vol. LIII. No. 1377 



execute true rotations,^" such as Langevia 

 assumed, except as very special cases of pre- 

 cession, Gans^^ has recently developed a gen- 

 eral theory of diamagnetism and paramag- 

 netism, proceeding in accordance with the 

 methods of statistical mechanics. He assumes 

 as his magneton a body rigidly built of nega- 

 tive electrons and placed inside a uniformly 

 and jKJsitively charged sphere whose center 

 is coincident with the center of mass of the 

 electrons, and whose charge is equal in magni- 

 tude to that of the magneton, so that elec- 

 trical actions do not have to be considered. 

 The energy is assumed to be entirely electro- 

 magnetic. 



For simplicity it is assumed that two of 

 the principal (electromagnetic) moments of 

 inertia are equal, but it is not assumed in 

 general that the magneton is a body of 

 revolution; thus the cross-section normal to 

 the unique axis might be a square, and rota- 

 tion about it subject to the effects of thermal 

 collisions, instead of a circle, with rotation 

 independent of such collisions. 



The method of statistical mechanics is then 

 applied to the two cases to be considered: 

 first, that in which the magneton is not a 

 body of revolution so that the rotations about 

 the three axes must all be treated as statistical 

 coordinates; and second, that in which the 

 magneton is a body of revolution so that 

 rotation about the axis of figure is not affected 

 by collisions and can not be treated as a 

 statistical coordinate. 



In the first case it is found that the sus- 

 ceptibility is always negative, or the sub- 

 stance diamagnetic. 



When the three principal moments of in- 

 ertia are equal, the susceptibility is independ- 

 ent of the temperature and of the intensity 

 of the magnetic field, which is the case with 

 many diamagnetic substances. 



When but two of the moments are equal, 

 however, the susceptibility depends on both 

 the temperature and the intensity in somewhat 

 complicated ways. Fig. 1 shows the general 



10 See also P. EJrueger, Ann. der Phys. (4), 50, 

 1916, p. 364. 



11 Ann. der Phys. (4), 49, 1916, p. 149. 



relation between the susceptibility and the 

 intensity according to Gans's theory, while 

 Fig. 2 shows the type of curve found experi- 

 mentally by Honda in many cases. The im- 

 portance of carrying the measurements down 



Fig. 1. 



Fig. 2. 



into weaker fields is manifest; and this has 

 recently been done for bismuth and antimony 

 by Isnardi and Gans,^^ who, working with 

 pure materials, find no dependence on the 

 field strength. As Honda suggests, the de- 

 pendence on intensity suggested by his curves 

 is probably due to the presence of iron, whose 

 positive susceptibility, opposing that of the 

 diamagnetic substances, decreases with in- 

 creasing magnetic intensity. Curves obtained 

 by Honda and Owen, and by Isnardi and 

 Gans, are shown in Fig. 3. 



Fig. 4 shows the way in which, according 

 to the theory, the susceptibility X depends 

 upon the absolute temperature Q, while the 

 type of curve found in Honda's experiments 

 is shown in Fig. 5. Little weight can be 

 given the lower part of the theoretical curve, 

 inasmuch as equipartition of energy and also 

 absence of inter-molecular action were both 

 assumed in its derivation, and it is improbable 



12 Ann. der Phys. (4), 61, 1920, p. 585. 



