Adding all the heat losses and subtracting the heat gain, the net 

 loss under the first set of meteorological conditions, i.e., air temper- 

 ature -10°C, vapor pressure 3.5 mb., wind velocity meters/second, 

 cloudiness 0$, sun altitude 5°, and water temperature 0°C, will be 

 14.7 cal/cm?/hr. In the second set of meteorological conditions, i.e. 

 air temperature -10°C, vapor pressure 3.5 mb., wind velocity 5 meters/ 

 seconds, cloudiness 100$ (overcast), sun altitude 5° and water temperature 

 0*C, the net loss will be 23.1 cal/cm?/hr. These figures are equivalent 

 to the production per hour of a sheet of ice of thickness 2.0 and 3.2 mm. 

 respectively. 



The above briefly outlined analysis forms the basis for the calcu- 

 lation of the actual growth of an sheet ice under conditions existing in 

 nature. The method could be applied, directly if the surface of the ice 

 retained the temperature of 0°C. and had the same physical properties as 

 water with regard to heat exchange. The first condition is not true, how- 

 ever, as the surface temperature of the ice will be lower when the ice is 

 thicker, if the air temperature is low. 



The flow of heat through the sheet ice takes place in accordance with 

 Fourier's heat conduction equation (l), and the heat budget equations out- 

 lined above must be solved in accordance with this equation. 



C. KOLESNIKOV «S EQUATION AND ITS EVALUATION 



Kolesnikov has recently (1946) derived an expression for the thick- 

 ness of ice as a function of time which involves all of the meteorological 

 factors. This was accomplished by setting up heat budget equations in- 

 volving these parameters and solving in connection with Fourier's heat 

 conduction equation. 



The form of Kolesnikov' s equation for salt water is 

 ^ + I ~P^~ ^ + T?5 X V aS56 + 5. 23XkF^~S" + 2 ^ J A £ 



= 9.73 f h TX -e (22) 



A 



where £ x ~ initial ice thickness in cm., 



A£ = increase in ice thickness in cm., 



S^ = salt content of the ice, 



Sj = salinity of salt water solution at temperature of freezing, 



P x ■ density of ice, . 



