in the Magnetic Field, 171 



assigns a dynamical cause for this precession in the action of 

 the magnetic field on the ionic charge moving through it. 



But up to this point the electromagnetic solution deals 

 with a perturbation which is really not the full equivalent 

 of a precessional movement of the orbit, and therefore the 

 investigation given by Dr. Larmor applies, as he himself 

 states, to a single simple case. For the equations of motion 

 of a particle describing under a central force an elliptic orbit 

 which precesses with angular velocity co round a line whose 

 direction-cosines are (/, m, n) are 



x=—Q / 2 x + 2(o(ny — mz) + co^x — (o' 2 l(l% + my + nz), . (1) 



with two similar equations for y and z, whereas the equations 

 of motion of the ionic charge moving under a central force in 

 a magnetic field are, as given by Dr. Larmor, 



x=—£l 2 %-\-k(ny—mz), .... (2) 



with two similar expressions for y and z. The latter equation 

 coincides with the former if we neglect co 2 and take 2a>=#, 

 that is, when the precessional motion is relatively small. 



The motion imposed on the ion by the electromagnetic 

 theory is therefore merely a simple type of precessional pertur- 

 bation of the orbit, and, as other perturbations may occur, 

 and indeed ought to be expected to occur, it is clear that the 

 simple triplet is not the only form which we should expect to 

 meet with when the matter is investigated experimentally. 

 Thus, if the orbit besides having a precessional motion has in 

 addition an apsidal motion, that is a motion of revolution in 

 its own plane, then each member of the triplet arising from 

 precession will be doubled, and we are presented with a 

 sextet as in the case of the D 2 line of sodium. Similarly, if 

 the inclination of the plane of the orbit to the line round 

 which precession takes place be subject to periodic variations, 

 then each member of the precessional triplet will itself become 

 a triplet, and so on for other types of perturbation. 



It is quite unnecessary to enter into these matters in any 

 detail here, for the whole explanation was fully given and 

 published in 1891 by Dr. G. J. Stoney *, that is, six years 

 before the effects requiring explanation had been observed. 



Dr. Stoney's aim was to explain the occurrence of doublets 

 and equidistant satellites in the spectra of gases, that is in 

 the normal spectra unaffected by the magnetic field — for at 



* This most important paper of Dr. Stoney's was published in the 

 Scientific Transactions of the Royal Dublin Societ}^ vol. iv. p. 563 

 (1891), " On the Cause of Double Lines and of Equidistant Satellites in 

 the Spectra of Gases." 



