472 



SCIENCE 



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



planation, has been observed by Weber and 

 Overbeck^^ in tbe case of copper-zinc alloys, 

 and by Honda in the case of indium. Weber 

 and Overbeck, who have taken great precau- 

 tions and believe their alloys free from iron, 

 have called the phenomenon metamagnetism. 

 The downward trend of paramagnetic sus- 

 ceptibility with increase of field strength is 

 apparent in some of the curves obtained by 

 Honda. 



For weak fields at low temperatures, but 

 with H/T finite, Gans's formula approaches 

 that of Langevin as a limit. Here the para- 

 magnetic rotations are prominent in compari- 

 son with diamagnetic thermal rotations about 

 the other axes. As the field intensity ap- 

 proaches zero with finite values of the tem- 

 perature the susceptibility approaches a limit 

 which is the sum of two terms, a paramagnetic 

 term identical with that of Langevin and a 

 diamagnetic term independent of the tem- 

 perature like that of Weber. 



The theory of Gans thus covers a wide 

 range of cases, but so far has been applied in 

 detail to but few. By taking account of the 

 molecular field, and by applying the quantum 

 theory, although not in the most thorough 

 way, he has more recently extended his theory 

 to cover more accurately the jiaramagnetism 

 exhibited by dense bodies and at low tempera- 

 tures.^* In a similar way the quantum theory 

 has been set into the theory of Langevin by 

 Oesterhuis^^ and Keesom^"; and it has been 

 thoroughly applied, for the case of rotation 

 with one degree of freedom, by Weyssenhoff,^'' 

 and for the case of rotation with two degrees 

 of freedom by Eeiche^^ and by Eotzajn,i» to 

 the system of elementary magnets, without 

 permanent angular momentum, assumed by 

 Langevin. These theories are thus not elec- 

 tron theories, like that of Gans. They reduce 

 to the theory of Langevin at high tempera- 

 is ^7171. der Phys. (4) , 46, 1915, p. 677. 

 i-iA7in. der Phys. (4), 50, 1916, p. 163. 

 15 Phys. Zeit., 14, I5l3, p. 862 



18 Phys. Zeit., 15, 1914, p. 8. 



n Ann. der Phys. (4), 51, 1916, p. 285. 

 IS Ann. der Phys. (4), 54, 1917, p. 401. 



19 Ann. der Phys. (4), 57, 1918, p. 81. 



tures when equipartition exists, and the rigor- 

 ous theories agree well with experimental re- 

 sults obtained at low temperatures, where 

 Langevin's theory completely fails. The next 

 step should be the rigorous application of the 

 quantum theory to the case in which the 

 magneton has a permanent angular momen- 

 tum, with gyroscopic properties, as required 

 by the electron theory. 



According to experiment hydrogen and 

 helium are diamagnetic although according to 

 Bohr's models their molecules have strong 

 magnetic moments. This is apparently con- 

 sistent with the theory of Gans, but incon- 

 sistent with the theory of Weber and Lange- 

 vin. Honda and Okubo,2° in a part of a paper 

 dealing more generally with the kinetic theory 

 of magnetism, have proposed the following ex- 

 planation of this diamagnetic efitect. Suppose 

 the magnetic axis to be rotating about one of 

 the other axes in a plane parallel to the mag- 

 netic intensity. On account of the presence 

 of the field, the velocity of rotation, which 

 would be uniform without the field, is now 

 variable, the motion being more rapid when 

 the moment points in the direction of the field 

 than when it points the other way. Hence 

 the time mean of its directions is opposite to 

 that of the field and the mean effect is dia- 

 magnetic. If the magnetic axis is rotating in 

 a plane not parallel to the direction of the 

 field, we must resolve the effect in the di- 

 rection of the field. Doing this for aU the 

 elementary magnets, originally pointing uni- 

 formly in all directions, we get a resultant 

 diamagnetic effect This, however, is only a 

 part of the total effect found in Langevin's 

 theory to be paramagnetic, though it is only 

 implicit in his treatment, unless we assume 

 permanent rotations, indejiendent of the tem- 

 perature, about an axis normal to the mag- 

 netic axis. This assumption they have made. 



From what we have seen there seems to be 

 no way to account satisfactorily for para- 

 magnetism and ferromagnetism except on the 

 assumption of an elementary magnet which 

 is a permanent electrical whirl, as Ampere 

 assumed; which has also mass, as Weber as- 



20 Phys. Sev., 13, 1919, p. 6. 



