652 BELL SYSTEM TECHNICAL JOURNAL 



stants in the formula in terms of properties of the material. Another 

 adaptation of optical dispersion theory to the explanation of dispersion 

 in the electrical frequency range was proposed by Decombe ^^ in 1912. 

 He employed the Lorentz electron theory for the dispersion of light as a 

 basis for the consideration that if the environment of some of the 

 electrons in dielectrics is suitable their motions in an applied field could 

 produce anomalous dispersion and dielectric loss in the electric fre- 

 quency range. A similar simple and arbitrary assumption regarding 

 the structure of dielectrics will also be employed here. However, it is 

 not proposed as a theory of dielectric behavior but merely employed as 

 a comparatively simple means of deriving and discussing relationships 

 which can be demonstrated as well on a simple and arbitrary model 

 as on the more complex ones which correspond more closely to the 

 actual structure of dielectrics. The relation of the constants in the 

 dispersion formulae which will be derived here to the actual structure 

 of dielectrics will only be indicated in a general qualitative way for the 

 purpose of illustrating the physical nature of the processes involved; 

 no attempt will be made to provide expressions for the dispersion 

 constants in terms of other observable properties of the material. 



In Fig. 2, let the applied potential be V, where V may vary in general 

 in any way with the time, though in the present discussion it will be 

 considered to vary sinusoidally with the time; the impressed field 

 strength is then given hy E = V/d. As in the more general discussion 

 which preceded this, it will be assumed that the imaginary cells 

 pictured in Fig. 2 contain large numbers of polarizable complexes 

 consisting of positive and negative charges in equal numbers held 

 in position by constitutive forces — the origin of which need not be 

 specified for our present purposes — such that if they are displaced a 

 distance 5 from their initial positions they will experience a force fs, 

 where /is a constant, tending to restore them to their initial positions; 

 and that while these charges are in motion as a result of the action of 

 the impressed field they experience a frictional force rs, where r is a 

 constant and s is the velocity in the direction of the impressed field: 

 and, finally that their motion is also retarded by an inertia reaction 

 nis, proportional to the mass m and the acceleration s of the particles. 



The equation of motion for any typical charge e in a polarizable 

 complex having the above-described specifications is 



ms + rs +/s = eF, (10) 



where F is given by equation (3) in materials to which the Lorentz 

 calculation of the internal field applies, hy F = E in the case of gases 

 1* L. Decombe, Journal de Physique, (5), 3, 315 (1912). 



