452 SCIENCE PROGRESS 



and by the electromagnetic theory of light 



4ttP = 47r2Ner = (jx 3 - i)E 



/i being the refractive index of the medium for the frequency n. 

 Putting a == J for simplicity, which is very nearly true for a gas, 

 we obtain, by eliminating E and P from the above equations, 

 the relation 



— — =—<■ ttS (K - n + ihn)- 1 



fi J + 2 3 m 



For values of n near the free period n we may for a gas 

 neglect the effect produced by all the electrons other than those 

 with this free period : since n* — n 2 in the denominator of this 

 term is then small, the imaginary part, ihn, now becomes 

 important, signifying absorption. Therefore, near an absorption 

 band, it follows that 



/x 3 - i = 47rNe 2 {m(nf - n 3 ) + ihn}- 1 



where n^ is defined by means of 



nf = n* - 47rNe 2 /3m 



If s is the real refractive index of the gas and k its absorp- 

 tion coefficient, then yx=s — ik, and there results 



sk = 27rNe 2 hn{m s (X 3 - n 2 ) 2 + h 2 n 2 }- x 



The centre of the absorption band, defined as the position of 

 maximum absorption, is evidently give by 



n = n' = n - 2rrNe 2 /3mn J 



(approximately), and so, due to a given change of pressure, the 

 position of the absorption band is shifted by exactly the same 

 amount as the corresponding emission line, in agreement with 

 experimental results. 



Moreover, if the width of the absorption band be defined 

 as the distance between the two places where the absorption 

 has a value which is some definite fraction of the maximum 

 absorption, the width is found to be proportional to h, and 

 since the resistance coefficient will increase with the pressure, 

 a symmetrical broadening of the absorption band is to be 

 expected on this account. That the broadening observed is not 

 always s^ymmetrical is due to other and obscure causes which 

 need not be discussed here. 



This theory is thus seen to give a very satisfactory and 

 complete explanation of the main experimental results, with 



