Polarisability and relative permittivity

To relate polarisability, a, to the relative permittivity, it is necessary to remember that each 

Lorentz, using classical electrostatic theory, showed that the local field in an isotropic insulator such as a gas, a glass or a crystal with cubic symmetry is uniform everywhere and given by  

Using Equations (11.3)-(11.5) it is possible to derive the most widely used relationship between relative permittivity and polarisability, the Clausius-Mossotti relation. Equation (11.6), usually written  

Several alternative forms of the Clausius-Mossotti equation are encountered. Frequently, the term N is replaced by its reciprocal, the volume of one atom or one formula unit of stmcture, Vin = /N and is set out in terms of a, thus  

Quite often, the equation is expressed in terms of the molar polarisability, Pm- This form is obtained 

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