506 BELL SYSTEM TECHNICAL JOURNAL 



much less than the order of 10~^^ seconds, since in general either the 

 internal friction or the molecular radius of materials having polar 

 molecules will be greater than those of water, resulting in longer 

 relaxation-times. No long-time limit can be placed on the relaxation- 

 times which dipole polarizations may have, for they are limited only 

 by the values which the internal friction can assume. For materials, 

 such as glycerine, which tend to become very viscous at low tempera- 

 tures the time of relaxation of the dipoles may be a matter of minutes. 

 Studies of the dielectric constant of crystalline solids, to be discussed 

 in a later paper, show also that in some cases polar molecules are able 

 to rotate even in the crystalline state, where the ordinary coefficient 

 of viscosity has no meaning because the materials do not flow. In 

 connection with the dielectric properties we are concerned only with 

 the ability of the polar molecules to undergo rotational motion and 

 it is likely that in these solids, which constitute a special class, the 

 internal frictional force opposing rotation of the molecules is small 

 even though the forces opposing translational motion may be very 

 large. The particular equation for the calculation of the time of 

 relaxation given above obviously does not apply to solids. 



In discussing the three types of polarizations which have been 

 considered thus far, it has been pointed out that the magnitude of 

 the dielectric constant depends upon the polarizability of the material. 

 Each type of polarization makes a contribution to the dielectric 

 constant if the measuring frequency is considerably below its relax- 

 ation-frequency. However, if the frequency of the applied field used 

 for measuring the dielectric constant is too high the presence of 

 polarizations with low rela.xation-frequencies will not be detected. 

 Thus the refractive index of water in the visible spectrum is 1.3 and 

 therefore gives no evidence whatever of the presence of permanent 

 dipoles. This is due to the fact that the H2O molecules do not change 

 their orientations rapidly enough to allow fields which alternate in 

 direction as rapidly as those of light to cause an appreciable deviation 

 from the original random orientation which prevails in the absence of 

 an applied field. 



The band of frequencies in which the dielectric constant decreases 

 with increasing frequency because of inability of the polarization to 

 form completely in the time available during a cycle, is called a region 

 of absorption or of anomalous dispersion. The discussion of this 

 characteristic of dielectric materials forms an important part of 

 dielectric theory. The term anomalous dispersion is no doubt usually 

 thought of in connection with the anomalous dispersion of light: when 

 the refractive index of light decreases with increasing frequency the 



