(-) 



If the displacement of the electron can no longer be regarded as 

 infinitely small, the value of the potential energy may be expanded 

 according to ascending powers of ,c, y, z. In a perfectly isotropic 

 molecule we may write therefore, only retaining the first correction 

 term 



./) = — kv- -Y — /;>' (3) 



k' being a second constant. 



If the electron now performs vibrations (^, ?;, ?) about the new 

 position of equilibrium, which it shall take under the action of the 

 force A in an electric field parallel to the axis of .Y, then one finds 

 easily with Voigt ^) for the components of the total force (.Y -f- X' , etc.) 



— (k^-zu.r^^)l, -{k\u,v.:-)^^, —{k^u^rr-y;. ... (4) 



The fjictor by which the displacement is to be multiplied in order 

 to find the force, has now another value with a displacement parallel 

 to the lines of force than with a displacement at right angles to the 

 field. The frequencies of vibrations in these principal directions are 

 therefore different. 



Applying these considerations to all the electrons contained in the 

 atoms of a substance such as luminous sodium vapour, Voigt comes 

 to the following remarkable theoretical result. 



If by means of a spectroscope we examine the light that is radiated 

 along the lines of force of the electric field, we shall observe a 

 displacement of the unpolarized spectral line from its original position. 

 At right angles to the field we may expect a transverse electric 

 efifect, the original line being separated into two polarized components. 

 The component vibrating parallel to the field undergoes a displacement 

 three times as large as that of the component vibrating perpen- 

 dicularly to the field. 



It is easily seen that the electric change of frequency must be 

 proportional to the square of the electric force. 



It is remarked by Voigt that, if the negatively charged electrons 

 are embedded in a positively charged sphere with a density deer easing 

 from the centre outward, the expected displacement of the spectral 

 lines must be towards the red. 



In what follows 1 shall, in order to fix the ideas, suppose that 

 the spectral lines are shifted in the sense indicated, but this is not 

 essential. 



') Voigt. Zur Theorie der Einwirkung eines elektrostatischen Feldes auf die 

 optischen Eigenschaften der Körper. Ann. d. Phys. 69 S. 297. 1899, Ueber das 

 electrische Analogon des ZEEMAN-etfektes. LoRENTZ-bandel. Archiv. Neerl. 1900, 

 Magneto- und Elektrooptik. Kapitel IX u. X. 1908. 



1* 



