426 Sir J. J. Thomson on the Origin of 



Principal Series. 



If the magnetic boundary is constant and fixed by the 

 parameter m, and the different lines are due to the vibration 

 of electrons in the positions of equilibrium inside the magnetic 

 boundary, the series will be expressed by 



H(m + S') 2 (" + S) 2 ) ? ' * ' ' (1) 



ay here m is constant and n has successive integral values. 

 When the boundary is that corresponding to the majority 

 of the normal atoms and the number of electrons is the full 

 number proper to the atom, this will be the principal series; 

 as the atoms are in the normal state, the atoms of the cold 

 vapour will contain electrons able to vibrate in these periods, 

 so that the vapour will be able to giA-e this series of lines 

 as an absorption spectrum. 



If the atoms Avere ionized so that ihe number of electrons 

 inside were diminished, this would alter the positions of 

 equilibrium and therefore 8, so that the series of lines given 

 out bv the atoms would be represented by 



^km+sy'^+Wf)' • • • • ( 2 > 



a series with the same limiting frequency as the preceding. 



Inasmuch as these lines proceed from ionized atoms, their 

 frequencies do not correspond to the Adorations of electrons 

 in a normal atom, and so this series would not appear as an 

 absorption spectrum of the cold vapour ; it would not then 

 be a principal series, as the reversibility of the lines is the 

 characteristic of this type of series. 



Let us now take the case when the magnetic boundary is 

 not the same as in the last case, but now corresponds to the 

 parameter m' instead of m. The series of lines will now be 

 given by 



Vh-Si) s "(«+&?)' ■ • • • (3) 



where n has the successive integral A^alues and m 1 is a con- 

 stant integer. This series has a different limit from the 

 preceding. If the neAv magnetic boundary, Avhich by hypo- 

 thesis is a position of equilibrium for electrons, were to be 

 the position of equilibrium next nearer the centre than the 

 one for the atoms giving the series (1), then the electron in 

 the gravest mode of vibration of the atoms in (1) would be 



C 



