The anomalous dispersion of radio frequencies exhibited by polar mole- 

 cules has been discussed by Debye [6»] and others; and it has been shown 

 that the water molecule shows anomalous dispersion in the frequency 

 range 10 3 to 10 6 Mc/s [7]. However for ice, the maximum dispersion is 

 near 6 Kc/s at a temperature of — 2°C. and occurs at even lower fre- 

 quencies as the temperature decreases; and the observations of Errera [#] 

 in the frequency range between about 0.4 Kc/s to 37.5 Kc/s indicate that 

 ice behaves as if it were a polar liquid with very high internal friction. 

 However, by use of the formulae Debye [6~] presented to calculate the 

 generalized dielectric constant (liquid formula) we find that the imaginary 

 part of the complex dielectric constant, e i} becomes nearly zero in the 

 frequency range above 1000 Mc/s. As Saxton [9~\ has summarized, the 

 most recent observations of Lamb \_10~\ together with those of Smyth 

 and Hitchcock [ii] indicate that the dielectric constant of pure ice is 

 3.05, and as no absorption band exists between 30 Mc/s and 30,000 

 Mc/s (the upper limit of observations) this value may be assumed con- 

 stant and equal to 3.05 in the radar bands. It is therefore easily derived 

 from equation (11) that there should be no difference in the behavior of 

 S- and X-band frequencies on ice. By equation (10) the reflection coeffi- 

 cient of pure ice is 0.272. 



However, iceberg ice is far from pure, being composed of up to 15 per- 

 cent co-volume of air and varying amounts of melt water depending on 

 the meteorological conditions. As far as the writer is aware, there are no 

 direct measurements of the dielectric properties of aerated ice, iceberg 

 ice, or snow. It is important to determine the importance of the air 

 and melt water effects on the magnitude of the reflection coefficient 

 in order to assess the most probable theoretical value for icebergs. In 

 order to do this it is necessary to make certain assumptions concern- 

 ing the characteristics of the ice-air-water mixture on the surface of a 

 Grand Banks iceberg. First, it is assumed that the mixture of ice and air 

 is homogeneous and the internal force of the "particles" is zero; the 

 latter is true in the case of a cubic crystal or non-associated liquids \_12~\. 

 Based on the assumption that the internal force is negligible and that 

 Mosotti's computations are correct; i.e., the relation between the di- 

 electric constant and molecular polarizability is given by 



l = Np (12) 



+2 3x 



where A' is Avagadro's number, and a is the molecular polarizability, 

 Debye [6?] derived an expression for the relation of the dielectric constant 

 to the polarization of the components of a binary solution : 



^MiMMih. Plfl+ p tf , (13) 



e + 2 ;; 



where .1/, and .1/,. are the molecular weights of the two components, /i 



64 



