GASEOUS REFRACTIVE INDICES 295 



more available for setting them in motion, and the consequent 

 loss of energy and velocity is greater. 



The best-known theory on the subject is that due to Lorentz, 

 which states that, on the assumption that all the electrons 

 involved in the atom are of the same sort, i.e. have the same 

 period of vibration, the refractivity is directly proportional to 

 the number of electrons, and, inversely, to the difference between 

 the squares of the frequency of the light in question and the free 

 period of the electrons. If there are several classes of electrons, 

 with different free periods, then the total retardation is the sum 

 of the retardations imposed by all. Such a theory, even in the 

 simple form here stated, is discouraging to the experimentalist. 

 For aught we can tell every atom may contain a thousand or a 

 million electrons, no two of which have the same natural period 

 of vibration, and the task of evaluating their total effect on light 

 and comparing it with experimental results would be impossible. 

 All that we can do is to hope that the truth is simpler than this, 

 and that by measuring the dispersion of different elements and 

 comparing those of the same chemical group, we may obtain 

 valuable information with regard to the relative number of 

 electrons they contain. 



At present the results of experiments are not sufficiently 

 numerous to enable us to draw any conclusions of value, and 

 more work is greatly to be desired. 



Such figures as exist are shown in Table II. 1 



The dispersion of hydrogen, nitrogen, oxygen has been 

 measured more than once, but does not appear to exhibit any 

 simple relation. Indeed, it is not to be expected that such a 

 relation should be found at present, for the discrepancies between 

 the results of different observers are so large that the figures are 

 practically worthless. Thus, Mascart himself points out that 



It will be noticed that the dispersions are expressed in terms of Cauchy's 

 formula : 



,-.=a( i+ £) 



which is, strictly speaking, irreconcilable with that of Lorentz : 



fi — I = 2 



p — w l 



where p is the free frequency of the electron and w that of the light ; but since 

 the free period is certainly very remote from the visible spectrum the discrepancy 

 is unimportant, and the constant B expresses the existing experimental results for 

 dispersive power with sufficient accuracy. 



