the Magnetic Influence on Spectra. 507 



period, and a third type which does not involve any rotation 

 with respect to that axis. Now that extraneous axis may 

 have any direction with reference to the molecule. Hence 

 a principal oscillation which is thus magnetically tripled must 

 be capable of being excited with reference to any axis in the 

 molecule : otherwise there would be merely hazy broadening 

 or duplication instead of definite triplication. 



7. A system of electrons or ions of the same sign, confined 

 to a surface over which they are free to move and constituting 

 an electric charge on it, is an artificial vibrator whose periods 

 illustrate these results. The free periods of such a vibrating 

 system in which the forces acting on the electrons work 

 against the inertia of the moving electrons, would be only 

 theoretically different from the free periods of an actual elec- 

 tric charge on a metallic conductor ; although in the latter 

 case the forces acting on the ions work mainly against the 

 ohmic diffusive resistance to their transfer either actual or 

 electrolytic through the crowd of neighbouring molecules, 

 which is far greater than the reaction arising from inertia 

 alone unless it is rapid optical vibrations that are dealt with. 

 In either case the forces acting on the ions are so great com- 

 pared w r ith the possible kinetic reactions to their motion that 

 their distribution is at each instant practically in equilibrium 

 on the surface, so that there is no electric force along it : and 

 either set of conditions simply reduces to the condition that 

 there shall be no electric or magnetic field in the interior. It 

 follows that the oscillations of an electric charge on any con- 

 ductor of the form of a surface of revolution are modified by 

 the introduction of a magnetic field along the direction of the 

 axis of the surface, just as if the angular velocity \ k above 

 given were imparted to the vibrating system. All the free 

 periods except those of zonal oscillations would be duplicated 

 in the manner above explained, the interval measured in dif- 

 ference of frequencies between the components of the doubled 

 vibration being the same for all. In the special case of zonal 

 oscillations on a sphere they would be triplicated, because the 

 period of a zonal vibration along the axis would not be 

 modified : but the middle line would be very weak compared 

 with the flanking ones*. 



8. This analysis gives a hint as to one way in which a 



* The radiation from a continuously distributed electric charge is, 

 however, known to be so great as to make its oscillations dead-beat; 

 hence these conclusions could only be applied if (i.) there are only a 

 limited number of discrete ions moving on the surface, or (ii.) there are 

 material forces other than electric imagined to act between the ions, 

 whose energy could maintain the vibration for a large number of periods. 

 (See § 10.) 



