270 Mr. Gr. H. Livens : Influence of Density on Position 



index of refraction fi of a simple gaseous substance with its 

 density p, viz. 



i 2 , on = const. 



Physically the function of the new term seems to be ex- 

 pressed by saying that the presence of neighbouring electrons 

 causes an increase in the effective inertia of the typical 

 oscillating electron more particularly considered. In the 

 words of Prof. Larmor*: "Each molecule individually, 

 through the agency of its plastic held of force or aether 

 strain, provides a yielding region in the aether in which the 

 effective stiffness is diminished. The elastic energy which 

 maintains the free vibrations of a radiator is located in the 

 field of force in the adjacent aether, and by dynamical prin- 

 ciples any loosening of the constraint in that field, such as 

 an adjacent molecule would produce, which would itself be 

 somewhat intensified by equality of period, must in general 

 tend towards increasing the free period, involving displace- 

 ment of the radiation towards longer wave-length." 



The paper is divided into three sections : the first deals 

 with absorption effects ; the second with a theory of the 

 emission effects ; and the third contains a quantitative com- 

 parison of the theoretical and experimental results. The 

 results obtained in the first section showed such a remarkable 

 similarity with the experimental results obtained for the 

 emission spectra that I was induced to construct the theory 

 presented in the second section. 



Throughout the work I have followed, with Lorentz, the 

 Hertz-Heaviside choice of mixed units. The unit of elec- 

 tricity adopted is therefore $/ \rrr times smaller than the 

 usual electrostatic unit. 



I might here also express my indebtedness to the various 

 works and papers of the following authors : Lorentz, Voigt, 

 Drude, Larmor, and Campbell. Verbal quotations have often 

 been adopted from them. 



1. General Theory for the Absorption Spectrum. 



§ 1. The fundamental basis. — The whole theory of electro- 

 and magneto-optics is based on the fundamental laws of 

 electrodynamics. These are 



1. Ampkre's Circuital Relation. 

 The line integral of magnetic force round any circuit is 

 * Astrophysical Journal, 1907. 



