468 



SCIENCE 



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



and the up and down velocities of tlie mole- 

 cules will exceed the horizontal velocities, 

 until after a short time involving many 

 collisions, a redistribution, as required by the 

 principle of equipartition, will have occurred, 

 in which the component squared velocities are 

 equalized and the whole mass of gas has a 

 temperature greater than before. If D^ de- 

 notes the density of the gas at the bottom of 

 the enclosure, I) the density at any height 

 X, m the mass of one molecule, r the gas con- 

 stant for one molecule, T the absolute tem- 

 perature and g the acceleration of gravity, 

 we have the relation 



D/Do = e - 



rT' 



(8) 



in which iv = mgx is the work necessary to 

 raise one molecule through the distance x 

 against gravity. 



Now suppose each molecule to have a mag- 

 netic moment fj. and imagine a vertical raag- 

 netic field applied throughout the enclosure 

 instead of the gi-avitational field. The mole- 

 cules will be driven to set themselves with 

 their magnetic axes parallel to the magnetic 

 intensity just as before the molecules were 

 driven downward, and rotational velocities 

 about lines normal to the field intensity will 

 be favored, but thermal agitation will redis- 

 tribute them as before until the law of equi- 

 partition is satisfied. If now d denotes the 

 angle made by the axis of any molecular 

 magnet with the (vertical) magnetic inten- 

 sity H, p the number of molecules per unit 

 volume with their axes between and + dO, 

 and pf, the number between and dO, we have, 

 by strict analogy with the gravitational case, 

 mH (1 — cos 8) 



p/po 



rT 



(9) 



Starting from this formula we can readily 

 calculate the total change produced in the 

 magnetic moment of the gas (0 before the 

 application of the field) and thus the inten- 

 sity of magnetization I. If a is written for 



mH 



rT 

 we get the expression 



(10) 



(12) 



(13) 



where N = the number of molecules per unit 

 voluma 



When a is small, as it is except for very 

 intense fields and very low temperatures, this 

 equation becomes, with negligible error, 



which gives for the susceptibility 

 K - Tiff - ^"^ 



The susceptibility is thus independent of B., 

 and inversely proportional to T. So far as 

 temperature is concerned it expresses the law 

 of Curie, which holds for the paramagnetic 

 gas oxygen over a great range of tempera- 

 tures, and which holds over a great range in 

 many other cases in which the molecular 

 magnets are so far apart as not to act appre- 

 ciably on one another. 



Inasmuch as r is known, and as "N is known 

 for any value of T at known pressure, we can 

 calculate fi. from the observed value of K. We 

 thus obtain for oxygen, reckoning from 0° C 

 and 760 mm. pressure. 



2.5 X 10- 



(14) 





(11) 



Langevin's theory of paramagnetism is not 

 an electron theory, as it has been developed 

 without regard to the permanent electrical 

 rotations assumed on this theory to account 

 for the permanent magnetic moment of the 

 elementary magnet. Nevertheless, it has 

 rendered great services and has important 

 relations to the electron theory. 



Investigation of the behavior of free 

 electron orbits, as distinguished from the 

 fixed orbits of Weber, in a magnetic field, 

 have been made by Voigt^ and J. J. Thomson,^ 

 who independently, in 1902 and 1903, reached 

 the conclusion that the existence, without 

 damping, of such orbits in a substance would 

 give it neither diamagnetic nor paramagnetic 

 properties. The diamagnetic effects arising 

 from change of velocities produced by the 

 magnetic intensity are just balanced by the 

 paramagnetic effects due to the change of 

 orbital orientation. With suitable dissipation 



sPTiiL Mag. (6), 6, 1903, p. 673. 



