[young] calculation OF ATOiMIC DIAMETERS 55 



Rutherford and others have provided a plausible origin of these 

 atomic or molecular currents. In fact, Bohr's theory of atomic 

 structure, in supposing the electrons to rotate about a common centre, 

 the nucleus, actually provides the resistanceless electric circuits which 

 were assumed by Weber. Langevin was then able to apply this 

 electron theory to give a fairly reasonable theory of diamagnetic and 

 paramagnetic phenomena and a later extension by Weiss explained in 

 a qualitative way at least the properties of ferromagnetism. 



The theory can be applied at once to Bohr's model of the atom 

 since in it the electrons are rotating. But in the case of the Langmuir 

 atom model, which is of the static type, it is necessary to make use 

 of a theorem due to Lorentz^ by which it can be shown that electrons 

 at rest in the atom will be set in motion by the superposition of an 

 external magnetic field and then the theory of magnetism applies. 



Let there be a system of electrons at rest such that their dis- 

 tribution is isotropic with respect to three rectangular axes of reference, 

 which may have any orientation about the origin 0. Then this iso- 

 tropism of the system may be expressed by 



The moment of inertia of the electrons about any axis through 

 the system will be 



Q = 2mK 



where K = 2x'-' = 2/ = Zz^ 

 and I,xy I,yz = Sxs = 0, 

 due to the isotropism of the system. 



If the components of the electric field created by external causes 

 are designated by Ex, Ey, E^, and the assumption can be made 

 that the system of electrons is small in dimensions, i.e., the electrons 

 are closely clustered around the centre, 0, just as atomic theories 

 picture them about a nucleus, then the electric force will depend on 

 the position of the point, i.e., E = F(x, y, z). On making a few simple 

 substitutions, the components of the couple acting on an electron 

 become 



eK , 



dy 



eK 



\ dy dz / 



\ dz dx / 



/^ „ ^A 

 \ dx dy y 



*Lorentz, Theory of Electrons, p. 124. 



