290 Mr. G. H. Livens ; Influence of Density on Position 



large number of cases. The mean of some of his values give 

 for 



1. Hydrogen D = 10907 



2. Oxygen D= 5360 



3. Nitrogen D= 4870 



These values are calculated for the gases mentioned under 

 standard conditions of temperature and pressure. They were 

 also made on the assumption that the gases are optically 

 simple, that is that their absorption spectra consist of only 

 one or two definite lines. Although for most gases this is 

 not quite true, yet the results obtained will enable us to 

 arrive at the order of magnitude of the quantities required, 

 as the following argument will show. Natanson's experi- 

 ments were made with monochromatic light of different 

 wave-lengths. From the formula 



■&' 



P - 1 - v P__ 



we see that for light of a given frequency the principal terms 

 on the right-hand side are those which arise from the very 

 limited number of groups of electrons (each group corre- 

 sponding to a definite spectrum line) whose free natural 

 periods are approximately equal to n, that of the light used. 



Thus the ( — ) of our formula, which refers to the electrons 

 \ m J 



giving rise to a single line, is of the same order of magnitude 



as that given by Natanson's formulae, and therefore the 



order of magnitude of the shifts can be deduced from these 



results. 



We use a = j, and then we have the displacements in the 



three gases as follows : — 



1. Hydrogen — ^ = 3-6 x 10 ~ 6 approx. 



2. Oxygen -— - = 7 '2 x 10~ 6 approx. 



3. Nitrogen V° = 8 x 10 ~ 6 a PP rox - 



A 



Now what are the facts ? Unfortunately very little infor- 

 mation is available with regard to the shifts of the lines in 

 the spectra of either of the three gases we have just con- 

 sidered. Wilsing once obtained what he considered a 

 reasonable estimate of the displacement of the hydrogen 



