Mat 20, 1921] 



SCIENCE 



467 



but the agreement is in general far from 

 close. The equation requires that K should 

 be independent of the temi)erature, unless 

 e, m, r and N depend upon it. As is well 

 known, the susceptibilities of many diamag- 

 netic substances are independent of the tem- 

 perature over wide ranges, while in other 

 cases there is a marked dei)endence. 



According to this theory also, effects of the 

 same kind must exist in bodies which are 

 ferromagnetic or paramagnetic superposed on 

 effects of opposite sign, the resultant sus- 

 ceptibility being, as Larmor long ago pointed 

 •out, the sum of the two. The paramagnetic 

 term may account for the variation of the 

 resultant susceptibility with temperature in 

 many diamagnetic bodies. From Weber's 

 equation it may be shovm that when 6^0 



where T is the period of the orbit. If we as- 

 sume that this period is that of sodium light, 

 about 2X10"^^ and that 3" = 10= (in excess 

 of any intensity hitherto produced) (5) gives 

 Am 



= - 0.3 X 10-^ 



(6) 



so that tihe maximum diamagnetic effect is a 

 Tery small part of the saturation effect in 

 ferromagnetic substances. The fact that the 

 intensity of magnetization of iron at satura- 

 tion does not decrease appreciably even for 

 great increases of intensity shows that n = 1/T 

 is very great. 



From Weber's equations we may also calcu- 

 late the change in frequency n of an orbit due 

 to the magnetic field, and we find, after 

 Langevin, but more generally, 



eH cos 6 



Am = -: . (7) 



This may correspond in a way to the Zeeman 

 effect in light, but gives a broad band instead 

 of the sharp lines actually found, inasmuch as 

 cos 6 has all values between — 1 and + 1. 



It is unnecessary, however, to have recourse 

 ix> electrons moving in orbits (or initially at 

 rest and constrained to grooves) or to rotating 

 electrified bodies, to explain the occurrence of 

 diamagnetism, as has been shown by J. J. 



Thomson,* Voigt,^ Lorentz,' and others, in- 

 cluding very recently H. A. Wilson.' If a 

 substance contains electrons either at rest or 

 in plain rectilinear motion due to thermal 

 agitation, and a magnetic field is created, an 

 electrical intensity will evidently be developed 

 with a curl equal to the negative rate of in- 

 crease of the fiux density, which will cause 

 the electrons to move in paths curved in such 

 a way as to produce a magnetic moment op- 

 posed to the direction of the applied field; 

 and as the field becomes steady curvature will 

 be maintained by the action of the field on 

 the moving electrons normal to their veloci- 

 ties. Calculation on this hypothesis gives 

 susceptibilities of the same order of magni- 

 tude as those given by the Weber-Langevin 

 theory. This form of theory has the advan- 

 tages over the other of greater freedom from 

 assumptions and of giving, when applied to 

 the optical case, a Zeeman effect with sharp 

 lines. Weber does not attempt to justify his 

 assumption that in a molecule the diameters 

 of his orbital grooves remain constant, and 

 that in a diamagnetic substance the grooves 

 maintain their orientations independent of the 

 applied magnetic intensity. With respect to 

 the diameters, however, Langevin has shown 

 that the magnetic field will produce no alter- 

 ation provided the law of force is not pre- 

 cisely that of the inverse cube, which is quite 

 improbable. 



We shall return to the subject of diamag- 

 netism later. 



The first detailed theory of paramagnetism 

 was given for perfect gases by Langevin in 

 1905.^ Following Langevin, I shall begin 

 with a gravitational analogue. Let us con- 

 sider an enclosure containing a gas at uni- 

 form temperature and let us suppose the 

 gravitational field anulled. The density of 

 the gas will then be uniform throughout the 

 enclosure. If now the uniform gravitational 

 field is brought into action every particle of 

 gas will receive an acceleration downward, 



4 Int. cong. phys., 1900, vol. 3, p. 138. 

 s Ann. der Phys. (4), 9, 1902, p. 130. 



6 ' ' The Theory of Electrons, ' ' p. 124. 



7 Boy. Sec. Proc. A, 97, 1920, p. 321. 



