CONTEMPORARY ADVANCES IN PHYSICS 229 



whatever is the mechanism whereb>' the field ahgns the atoms, it is a 

 mechanism which operates during the impacts and not between them. 

 Partial alignment at the collisions, no change in the situation during 

 the free flights — this amounts pretty nearly to standing the classical 

 theory on its head! 



Nevertheless the mathematics of the classical theory remains en- 

 tirely unchanged. This is because the mathematics merely expresses 

 the assumption that the field has managed to find some way of partially 

 aligning the atoms, and does not concern itself in the least with what 

 that way may be. This sounds rather vague, so let me remind you 

 just what the assumption is. Suppose to begin with that the vectors 

 of the atoms are capable of only two orientations in the applied field: 

 one parallel, the other anti-parallel to the field-direction. To transfer 

 an atom from the one orientation to the other, we must do work against 

 the torque of the field (or receive work from the torque of the field) 

 amounting to 2^H. We have, therefore, two classes of atoms, differing 

 in energy by 2ixH. Let Ni and Nz stand for the numbers in these 

 classes at some particular instant. Now the classical theory, as I have 

 been calling it, is strictly no more than the assumption that the ratio 

 of Ni and N2 is given by Boltzmann's theorem: 



NiINz = exp (- IfxHJkT) (1) 



and the essence of this assumption, I take it, is that the atoms are able 

 to change their orientation so as to pass from either class to the other, 

 and that they employ this facility of free passage to get themselves into 

 thermodynamic equilibrium at the temperature T of the gas. This has 

 been the assumption ever since Langevin founded the theory, and it 

 still is the assumption, even though we may no longer enjoy that 

 pretty picture of the mechanism of the change of orientation which 

 once we accepted, and have no other to replace it. 



I can readily write down the complete theory of this case. We intro- 

 duce the two additional equations, 



iVi + iVo = iV, / = (.Vi - iVo)M, (2, 3) 



of which the first says that all the atoms are in either the parallel or the 

 anti-parallel class, and the second that the magnetization / of the unit 

 volume of gas is the resultant of the vectors of all its atoms. Now we 

 eliminate iVi and N2 between the three equations, and swiftly arrive at 

 the result: 



I = NixtanhifiHlkT), (4) 



which is the equation of a curve starting obliquely off to the right from 



