444 Mr. J. H. Jeans on the 



The solution of equation (32) will be of the form 



P^(n)+Hw$(n), 



where (/) and <3> are the same for the same spectrum-series. 



The separation is therefore directly proportional to the 

 strength of the field ; and we can see reasons for expecting 

 the remaining factor to be intimately dependent upon the 

 spectrum-series to which the line belongs, as well as upon its 

 position in this series. 



§ 31. In considering the polarization of the various lines, 

 we shall neglect the ratio of the radius of the atom to the 

 wave-length. In this case the radiation emitted by the atom 

 may be taken to be the same as the radiation emitted by an 

 u equivalent particle/' this particle moving so that its dis- 

 placement multiplied by its charge is equal to the vector- 

 sum of the displacements of the ions of the atom multiplied 

 by their various charges"*. 



We have seen that the central line of a Zeeman group is 

 emitted by a vibration which is specified by a zonal harmonic, 

 having the direction t of magnetic force as axis. The orbits 

 of the ions are therefore in the meridional planes, and are 

 the same in all such planes. The resultant radiation is there- 

 fore such as would be emitted by a single particle vibrating 

 along the axis. 



The vibrations by which the side lines are emitted may 

 each be regarded as composed of two parts : — 



(a) A vibration parallel to the axis of harmonics. 



(/3) A vibration in which every ion describes an orbit 

 parallel to the equatorial plane. 



The amount of the former will be different in different 

 meridional planes. Since this amount will, for the line m, 



* The radiation emitted by a vibrating system of ions cnn be calculated 

 as follows: — Let the displacement arising from a single vibration be 

 such that £, rj, £ (the components along three rectangular axes) are the 

 real parts of aei p t, (Seipt, yew*, and introduce a complex vector C of 

 which the components are a, /3, y. Then the radiation at an external 

 point can be determined from the single vector P which is the real 

 part of 



e i P t 



fc* fjf R-ie- WfyC dx dy dz, 



where K is the distance of the external point from the element dxdy dz. 

 When we neglect the radius of the atom we may take R— 1 e— WV out- 

 side the integral, and this leads to the rule for the vector composit on of 

 displacements. The radiation is given by the equations 



Cf. Larmor, ^Ether and Matter, §§ 151-156. 



