91 



components will be placed symmetrically with respect to the position of the original 

 components and their intensities will be approximately equal, but when the per- 

 turbing influence of the magnetic forces on the motion of the electron becomes of 

 the same order of magnitude as that of the external electric forces, the components 

 in question will in general be placed unsymmetrically with respect to their original 

 position, and their intensities may differ considerably. 



An especially simple example of a magnetic field which possesses axial sym- 

 metry is afforded by the case ofa homogeneous magnetic field, discussed in the 

 beginning of this section. In this case we have that the total magnetic flux of force 

 through the orbit of the electron is equal to the product of the intensity H of the 

 magnetic field and the area of the projection of the orbit on a plane perpendicular 

 to this field. Since this area is equal to «3/2 m w, we get consequently from (84) 



fu^^H. (86) 



From the equations (46) it follows therefore that the effect of a homogeneous mag- 

 netic field, which acts upon a hydrogen atom which at the same time is exposed 

 to an external electric field possessing axial symmetry round an axis through the 

 nucleus parallel to the magnetic force, will consist in a superposition of a uniform 

 rotation of the orbit round the axis with a frequency equal to 



_ J_ ^ _ _?_ u 



on the secular perturbations which would take place In the absence of the magnetic 

 field. This result follows also directly from Larmor's theorem, on which the simple 

 considerations about the effect of a homogeneous magnetic field in the beginning 

 of this section were based. Since a superposed rotation as that in question will 

 not influence the shape of the orbit of the electron or its position relative to the 

 axis, it follows from (61) that the value of ¥e in the stationary states of the atom 

 will not be affected by the presence of the magnetic field, and that consequently the 

 effect of this field on the additional energy of the system will simply consist in the 

 addition of a term given by 



This result was also to be expected from a simple consideration of the mechanical 

 effect produced on the motion by a slow and uniform establishment of the mag- 

 netic field (compare page 81). With reference to the above considerations as regards 

 the probability of transition between stationary states, it will be seen to follow from 

 (87), that the presence of the homogeneous magnetic field will leave the components 

 polarised parallel to the axis unaltered, but will cause every component, which in 

 the absence of the field was polarised perpendicular to the axis, to split up in a 



