and their Magneto-optic Properties. 271 



Notwithstanding this we shall not use it any further, but 

 shall avail ourselves of the form (1), as split into the 

 equations (3) for each line separately. The two procedures 

 are equivalent to one another. The coefficients c 1? c 2 , etc., 

 are complex, say, c^—p^ 01 , etc. ; but since we are not con- 

 cerned with the phase-difference between the higher and 

 the fundamental line, we can imagine 0{ thrown on e xn{ , by 

 shifting the origin of t for each i separately. 



Thus, our further developments will be based on the simple 

 equations 



an + kxi -f- Wxi = Cie m i\ l=0 , l, 2, ..., 



where a are real constants. For the sake of simplicity we 

 shall henceforth drop the suffix » and write, for each line of 

 the spectrum separately, 



x + kx + Wx = c.e ini , .... (11) 



with similar equations for y, z, keeping in mind that h = N, 

 ni=pN, and so on. At first sight it would seem that these 

 simple equations can hardly yield anything new or important ; 

 but the following sections will prove the reverse. 



3. Emission of Resonance Spectra in a Magnetic Field. 

 Let the fluorescent vapour be placed in a uniform magnetic 

 field of intensity H. Let us take the --axis along the lines 

 of the field, and the x and y axes equally inclined to the 

 electric force of the exciting light, which is supposed to be 

 rectilinearly polarized. Then, for each line of the spectrum, 

 the coefficients c in (11) will be the same for the x- and the 

 ^/-equation. Rigorously speaking, the values of the c's them- 

 selves will be slightly changed by the magnetic field * ; but, 

 for the present at least, these modifications can be disregarded. 

 Thus, the presence of the magnetic field will give only the 



familiar supplementary terms ^M + -^-Hi? for the 



i r j my my 



right sides of the x- and the ^/-equations respectively. The 

 equation for z will remain unaltered. It will be enough 

 to consider the case of exciting electric oscillations perpen- 

 dicular to the magnetic field. Then we can write, simply, 

 £ = 0, and we have, for each line of the spectrum taken 

 separately, the two equations 



x + Wx + kx — Zy = ce int ,\ q 2 ) 



y + Wy + ky + Zx = ce ini , -* 



where Z=-^H. Remember that n stands here for the 



m V 



* Especially if we would look on (11) as the equivalent of a non- 

 Hookean system. 



