Wejrprecht took the numbers in his table from an averaged curve obtained from observations 

 at three points and extrapolated for higher values. Weyprecht's data, recomputed from the 

 Reaumur to the centrigrade scale, are given in table 67. 



TABLE 67. ICE THICKNESS VS. THE NUMBER OF FREEZING DEGREE-DAYS 

 (ACCORDING TO WEYPRECHT) 



Freezing degree days 500 1000 2000 3000 4000 5000 6000 7000 8000 



Ice thickness in cm 51 80 115 145 170 189 208 222 237 



The question of ice formation due to heat conductivity was later developed theoretically by 

 Stefan. 



The elementary amount of heat released by the water to the air per unit area of ice in time 

 dT, will be ,„ 



-dT, 



where i is the ice thickness, k is the heat conductivity of ice, and 9 is the temperature difference 

 between the lower and the upper surfaces of the ice. 



This elementary amount of heat is expended on the formation of an additional ice layer d i 



thick. Thus 



/eft 

 -ydr = XSrfi, (1) 



where X is the heat of crystallization, and 6 is the ice density. Integrating, we get 



T i 











r 



XS/2 



(2) 







If we assume that the temperature difference between the upper and the lower surfaces of the 

 ice remains constant for the time interval T, formula (2) assumes the form 



XS;2 



er 



2k • (3) 



All the values in this formula are given in the CGS system . It is more convenient to compute 

 the time in days, as Weyprecht did. For this, we get 



^ 2-86,400 k' ^"^^ 



where 86,400 is the number of seconds in 24 hours. 



If we set h = 0. 005 in formula (4), we obtain 



205 



