and f 2 the mole fractions, p the density, and P x and P 2 the polarizability 

 From equation (12) we can derive 



p(e+2) ' 

 therefore, 



6-1 M x f x +M 2 f 2 M 1 f 1 , M 2 / 2 



;+2 7? pi p. 



(14) 



which is an expression for the relation of the resultant dielectric of a 

 mixture to the concentration of two components. This equation is applied 

 below to the two-phase system of air-ice and to the three-phase system 

 of air-ice-water. The latter, of course, predominates on the surface of 

 Grand Banks and North Atlantic Ocean icebergs. The assumptions pro- 

 hibit a precise quantitative determination of the reflection coefficient, 

 and the results of computations based upon equation (14) can be expected 

 to indicate only the magnitudes of the effects of air and water contam- 

 ination of pure ice. The values for the terms in equation (14) are known 

 with some degree of accuracy however. The entrapped air is known to 

 have the same composition as the atmosphere, and is normally under a 

 slight pressure. The sublimation of the ice surrounding an air "particle" 

 would provide the maximum vapor pressure of moisture and at 0°C the 

 density of the entrapped air becomes 0.00132 gms/cc and the "molecular 

 weight" very nearly 30. The density of pure ice is 0.9167 gms/cc and the 

 relative permittivity is 3.05. Based on these quantities and equations 

 (10) and (14), the lower portion of the curve presented in figure 27 was 

 constructed. As the second-right term of equation (14) becomes zero for 

 all practical purposes in the case of air and ice mixture, examination of 

 the curve reveals the relation between ice density and reflection coefficient 

 is very approximately given by 



R = 0.029p (15) 



The measurements of iceberg density by Barnes [15], Smith \J4~\, the 

 writer, and others indicate that a density of 0.86 gms/cc is close to the 

 mean. At this density the reflection coefficient is 0.26 (slightly lower than 

 that for pure ice). This simple relation between reflection coefficient and 

 density seems to fit the observations for snow covered forests, and frozen 

 muskeg and gravel measured from aircraft \_15~\. However, the simple 

 mixture of ice and air is rarely met on an iceberg approaching or in the 

 shipping lanes. As the ice begins to melt the presence of even a small 

 amount of liquid water becomes of considerable importance. The problem 

 of melt water was handled by the same arguments used for the air-ice 

 system. The upper portion of the curve in figure 27 was derived using 

 aerated ice of 0.86 density as one component and pure water as the other 

 in equation (14), and a modulus of 80 for the complex dielectric constant 



65 



