Mechanism of Radiation. 443 



2 2 ' 2D ^ E , />HW • n ndft , . 9Z) SE\ 



<rpVsm 2 0t0= -— -f " — f sm (9 cos 6~^ +r sin 2 #-«>- ). 



Equate coefficients of e im ®, multiply by /m/sin 2 0, add to 

 (30) and we obtain, after some simplification, 



<*P Sr nK } 



We can now equate coefficients and obtain 



- <rpV(/3- + tmTj) = jn(n + 1) + ^!i] J- + ^^ ^. (31) 



It appears, therefore, that under the influence of a mag- 

 netic field, the normal coordinates will fall into the same two 

 classes as before. The frequency of the lines of the visible 

 spectrum is, however, no longer given by equation (18) but 

 by an equation of the form 



/O 2 , 7i) + HpmF(p' 2 ,n)=0 (32) 



§ 29. We see from this that the effect of the magnetic 

 field is to separate the (2?i + l) lines, which, in the absence 

 of a magnetic field, coincide in the nth line of a spectrum- 

 series, in such a way that the line m = () remains in its original 

 position and forms the central one of a group of (2/1+1) 

 equidistant lines. Thus the line n = will be unaffected by 

 a magnetic field, the line n = l separated into a symmetrical 

 triplet, the line n = 2 into an evenly-spaced quintet, and 

 so on. 



§ 30. The lines of the spectrum of the actual atom must 

 be influenced by a magnetic field in a manner approximately 

 the same as that found for the ideal atom. It may, however, 

 happen that some of the side lines w r ill be too faint for 

 observation. It may also happen that the (2n-fl) lines did 

 not originally form a single coincident line, but a doublet or 

 even more complex structure. It may thus happen that the 

 number of equal periods represented by any single line is an 

 even number. In this case it is known that the lines must 

 spread symmetrically * so that there will be no middle line left, 

 and the separated line will consist of a doublet, quartet, &c. 



* Lorentz, Astrophys. Journal, ix. p. 37. 



