466 



SCIENCE 



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



the magnetic moment of the mass of iron is 

 the sum of the moments of the elementary 

 molecular magnets. Ampere undoubtedly con- 

 sidered that in a neutral mass of iron the 

 molecular magnets are turned indiscrimi- 

 nately in all directions, but he did not enter 

 into any discussion of the process by which 

 their axes are made parallel by the field 

 during magnetization, nor did he consider the 

 nature of the electrical whirls themselves. 



Ampere was the grandfather of the electron 

 theory of magnetism. Wilhelm Weber was 

 its father. In 1852 Weber^ published a paper 

 in which he developed a theory which, slightly 

 modified by Langevra,^ is still perhaps the 

 most widely accepted theory of diamagnetism, 

 together vnth a theory of ferromagnetism 

 which formed the starting point for the well- 

 known theory of Ewing. Weber adopted the 

 molecular whirls of Ampere, but assumed in 

 addition that these whirls, always present in 

 the molecules of magnetic substances, are also 

 present in the molecules of diamagnetic sub- 

 stances when placed in a magnetic field. 

 Further, he took the very important step of 

 attributing mass or inertia to the electricity 

 in the whirls, and he assumed that the elec- 

 tricity moves as if in fixed circular grooves 

 in the molecule, so that each whirl main- 

 tains its diameter and its orientation with 

 respect to the rest of the molecule as if rigidly 

 constrained. According to Weber's concep- 

 tion, a substance is paramagnetic or ferro- 

 magnetic when the molecule, or magnetic 

 element, contains a permanent whirl, with a 

 definite magnetic moment, and so tends to set 

 with its axis in the direction of any magnetic 

 field in which it is placed; and a substance 

 is diamagnetic when the molecule contains one 

 or more frictionless grooves, with the mobile 

 electricity at rest before the creation of the 

 magnetic field. Langevin merely substitutes 

 electrons moving in fiLxed orbits for Weber's 

 electricity in grooves; and assumes that in a 

 diamagnetic substance more than one orbit 

 exists in the molecule and that tlie orbits are 

 80 constituted and grouped that the magnetic 



2 W. Weber 's Werke, III., p. 555. 

 8 Ann. chim. phys. (8), 5, 1905, p. 70. 



moment of the whole molecule is zero in a 

 neutral field. 



In this case, which we shall consider in 

 some detail, the complete molecule will suffer 

 no change of orientation when introduced into 

 a magnetic field, but the si>eed of the elec- 

 tricity in each orbit or groove wiU change on 

 account of the electromotive force around the 

 orbit or groove due to the alteration of the 

 extraneous magnetic flux through it. Its 

 magnetic moment ft, will thus increase (alge- 

 braically) by an amount Aj«,, which can readily 

 be calculated. If e denotes the charge of 

 electricity circulating in an orbit (whether as 

 a single electron, or a ring of electrons, or a 

 continuous ring), m the mass associated with 

 the moving charge, r the radius of the orbit, 

 H the intensity of the extraneous magnetic 

 field, and the angle between the axis of the 

 orbit and the direction of the field, 

 eVH 



A/i = — 



4m 



■ cos 9. 



(1) 



If we assume that there are N orbits per 

 unit volume, all alike; and if we furthermore 

 assume that all the orbits are perpendicular to 

 the direction of the field (as they would be in 

 the case of a saturated ferromagnetic sub- 

 stance) we get for the magnetic moment of 

 unit volume, or the intensity of magnetiza- 

 tion: 



eVNH 



4to 



(2) 



and for the susceptibility 

 K = I/H=- 



eVN 

 4m 



(3) 



If the orbits are not all i)erpendicular to the 

 field intensity, but are uniformly distributed 

 between all values of from to w, as in an 

 isotropic diamagnetic substance, we get in- 

 stead of (3) the expression 



K= - 



12m 



(4) 



If in this equation we substitute the value 

 of e/m known for electrons in slow motion, 

 and assume for a given substance such as 

 bismuth values of N and r which appear to be 

 reasonable from other physical evidence, we 

 obtain from (4) values of K of the same order 

 of magnitude as those found by experiment. 



