504 Mr. J. Larmor on the Theory of 



latter will he approximately p = a + fc 2 /Sa±^K, or with suffi- 

 cient accuracy p = a + ^k. Each vibration period will 

 therefore be tripled : and the striking feature is that the 

 modification thus produced is the same whatever be the 

 orientation of the orbit with respect to the magnetic field. 



An inquiry into the cause of this feature enables us to 

 generalize the result. Suppose that the original orbit is 

 referred to a system of axes (#, y, z) that are themselves 

 revolving with angular velocity to round an axis of which 

 the direction is (I, m, n). The component velocities (u, v, w) 

 referred to this moving space are ic— yam + zoom, ... , . .., 

 and the component accelerations are u — vam + ica>m } ........ 



Thus the component acceleration parallel to x is 



x — 2w(iiy — mz) — (o 2 x + co 2 l(lx + my -f- nz). 



If, then, we take w equal to ^k, and so can neglect co 2 , the 

 equations of the original orbit referred to this revolving 

 space are identical with those of that orbit as modified b}- 

 the magnetic field. In other words, the oscillation thus 

 modified will be brought back to its original aspect if the 

 observer is attached to a frame which revolves with angular 

 velocity \k or eH/2Mc 2 round the axis of the magnetic field. 

 In a circular orbit described one way round this axis the 

 apparent rotation will in fact be retarded, in one described 

 the other way round it will be accelerated, in a linear oscil- 

 lation along the axis there will be no alteration : hence the 

 three periods found above. 



2. Now the argument above given still applies, whatever 

 be the number of revolving ions in the molecule, and however 

 they attract each other or are attracted to fixed centres on 

 the axis, provided k has the same value for them all. In 

 any such case the actual oscillation in the magnetic field is 

 identical with the unmodified oscillation as seen from a 

 revolving frame ; or, more simply, the modification may be 

 represented by imparting an opposite angular velocity \k to 

 the vibrating system. Thus the period of a principal oscil- 

 lation of the system will be affected by the magnetic field 

 in the opposite way to that of its optical image in a plane 

 parallel to the field ; and these two oscillations, previously 

 identical as regards period, will be separated on account of 

 their right-handed and left-handed qualities. An oscillation 

 which does not involve rotation round an axis parallel to the 

 field will, however, present the same aspect to the field as 

 its image, and will not be affected at all. This latter type of 

 oscillation, in a compound system, will be a very special one ; 

 and when a crowd of vibrators indifferently orientated are 



