56 THE ROYAL SOCIETY OF CANADA 



which reduce by the use of Maxwell's equations to the form 



• • • 



— eKH. cos a; —eKH. cos /3 and —eKH. cos y, 



where cos a, cos /3 and cos y are the direction cosines of the field H. 



dH 

 Thus there is a resultant couple —eK~-r producing rotation 



about an axis which lies in the direction of the applied field. The 



e 

 solution of the equation of motion gives the angular velocity —— H. 



It will be noted that the rotation and its velocity are independent of 

 the particular arrangement, subject, of course, to the condition of 

 isotropism imposed on the whole system. 



Now, since it has been shown that with either the dynamic or 

 the static atom model there are electrons in rotation in the atom 

 when the external magnetic field is applied, the theory of diamagnetism 

 can be applied to calculate the magnetic susceptibility in term.s of 

 these electronic orbits. 



IfL is the self-induction and R the resistance of the electronic 

 circuit and E the electromotive force produced by the application of 

 the external magnetic field the instantaneous equation for the circuit is 



dLi 



-57 + ^' = ^- 



But the circuits are resistanceless, i.e., R=o, and the applied 

 electromotive force 



dB d 



for an orbit of radius Vp inclined at an angle 6 to the field H. 

 Integration givesLî = —H tt Vp cos 6. 

 Further, the magnetic energy associated with a circuit of this 



type is~r" and this energy must be equal to the kinetic energy im- 



t- mv- 



£=- — = -- (wr; H cos d) 



parted to the electron, i.e. ~r 



For an electronic orbit i = e.n, where n is the frequency of rotation, 

 and the velocity of rotation is z^ = 2irrp . n where fp is the radius of an 

 orbit of type p. 



Making these substitutions in the above 



H g- cos d 

 The change in magnetic moment of the circuit due to this current is 



