Displacement of Spectral Lines produced by Pressure. 559 



which, for small displacements, are proportional to their dis- 

 placement from the equilibrium configuration, and that the 

 displacement gives rise to an electric doublet of moment 

 proportional to it. Whatever may be urged against these 

 hypotheses, it must be conceded that a theory based on a 

 similar set of assumptions gives a fairly satisfactory account 

 of the phenomena of dispersion. 



We know from the Zeeman effect that the lines of most 

 emission spectra originate with the negative electrons, and it 

 is probable that the value of e/m for the positive electrons is 

 so great compared with the corresponding quantity for the 

 negative, that the positive electricity may be regarded as 

 stationary to a first approximation. Under these conditions 

 the equation of motion for an electron in an isolated atom 

 will take the simple form 



m P = -f^ <» 



where £ is the displacement from the equilibrium configura- 

 tion, m the mass, and e the charge of the electron. The 

 constant Xi depends on the constitution of the atom and the 

 configuration of the electron in it. The time T of a complete 

 vibration of this type for an isolated atom is given by 



T » = 4w»^. ...... (2) 



If the atom were placed in an electric field so that the 

 electric intensity at the electron were equal to X 2 the equation 

 of motion would become 



d 2 £ e 



m w = eXi ~\^ (3) 



Now if the atom containing the vibrating doublet is sur- 

 rounded by other atoms, even if there is no externally 

 impressed electric field, there will be an electric field due to 

 the doublets induced in the surrounding atoms by the vibrating 

 doublet. The effect is similar to the additional force called 

 into play by dielectric polarization. We shall proceed to 

 calculate the magnitude of this force X x on the assumptions, 

 first of all, (1) that the whole field of force of the vibrating 

 doublet is available outside the atom containing it; and 

 (2) that the induced doublets have the same value as if the 

 exciting field were a static one. The way in which these 

 limitations affect the calculation will be considered later. 



We shall suppose that the vibrating electron when in its 



2P2 



