62G Mr. G-. H. Livens on the Influence of Physical 



3. On the broadening of the lines of a spectrum with increasing 

 density. 



We shall now turn to the last type of effect which is 

 generally concerned with the alteration in the appearance 

 of the lines or bands in a spectrum produced by changing 

 the physical conditions. It is to be noticed that the theory 

 here given will apply equally well to both emission and 

 absorption spectra. 



The theory in its present form does not, however, offer any 

 explanation of a phenomenon of this kind ; but an obvious 

 and fairly plausible extension makes most of the experimental 

 results so obvious that, on these grounds alone, it might be 

 claimed as the effectively correct explanation. The extension 

 is arrived at by a reconsideration of the constant a which 

 occurs in our formulae. It was introduced as the coefficient 

 of the polarization in the expression for the force on unit 

 charge in a small cavity in the polarized medium. This 

 expression represents simply the local part of the total forcive 

 acting on a charge placed there, and arises entirely from the 

 molecmes in the immediate neighbourhood. Such a quantity, 

 of course, is quite indeterminate in any real case, but an ideal 

 estimate gives a = 1/3. In an actual case the constant would 

 approximate more or less accurately to this limiting value. 

 Now in discussing spectrum lines in the above manner, we 

 have to deal separately with the oscillations of each indi- 

 vidual electron, and a value of this constant a has to be used 

 for each one. Now it seems most probable that the constant a 

 is not a constant for each individual electron but varies from one 

 electron to another. It seems in fact that it would be better 

 to take a range of more or less probable values grouped 

 about the ideal value a =1/3. Moreover, the actual facts 

 seem to indicate that the extent of the range should decrease 

 as the condition of the substance approaches the limiting- 

 condition, i. e. the ideal limit of gas theory (practically when 

 the density 8 = 0). Moreover, the range cannot extend 

 beyond the value a = on the one side; but except for the 

 conditions implied in the analytical approximations, there 

 seems to be no reason to exclude indefinite extension on 

 the other side. Without attaching any special significance 

 to the form of the functions given, I shall, for the sake of 

 argument, assume that the range of most probable (not 

 necessarily equally probable) values is bounded by the values 



where C x and c 2 are constants of each line and $ the density. 



