Stefan also recommended that this expression be used for practical purposes. 



I computed table 68, setting \ = 80 g-cal/g and 6 = 0.9 in formula (4). 



TABLE 68. NUMBER OF FREEZING DEGREE-DAYS REQUIRED TO FORM ICE i CM THICK, 

 WITH DIFFERENT HEAT CONDUCTIVITY VALUES 



As is known from observations, the temperature of the ice surface differs little from the air 

 temperature, while the temperature of the lower ice surface is equal to the temperature of the 

 water in which the ice forms. Thus, we can consider the value R, which enters into formula (4), 

 as the sum of the negative air temperatures, or, actually, the number of degree-days. 



As Stefan himself admitted, his formula is not entirely accurate. It presupposes that the 

 vertical temperature gradient in the ice is constant, whereas the temperature changes considerably 

 faster with depth in the upper layers of the ice than in the lower layers. Further, at the beginning 

 of spring, the air temperature, remaining negative, can be higher than the temperature of the 

 middle layers of the ice. In such a case, the heat of crystallization of the ice layers accreting 

 from below will be expended on warming the middle layers of the ice and will not be transferred to 

 the atmosphere. Taking this into consideration, Stefan gave a second theoretical formula, namely: 



^-f(' + f)' 



(5) 



where c is the specific heat of ice and 0' is the temperature of the ice surface at the end of time T. 



This formula is also approximate, inasmuch as the expression in parentheses gives only the 

 first two terms of the series expansion. However, Stefan recommended that this formula be used 

 for spring, although he notes that the specific heat of ice is low compared with the heat of crystal- 

 lization and, consequently, the second term of the expression in parentheses is small compared 

 with the first. Stefan's first and simpler formula can be used to draw general conclusions if we 

 keep in mind that many of the conditions accompanying ice formation at sea cannot be calculated. 



Furthermore, it should be kept in mind that the rate of ice accretion in nature is a function 

 not only of negative air temperature, but also of other conditions, such as solar radiation, atmos- 

 pheric humidity, wind, amount of snow on the ice surface, the magnitude of oceanographic gradients 

 beneath the lower surface of the ice, the presence or absence of sea currents, etc. Consequently, 

 many authors have followed the course indicated by Weyprecht; namely, the establishment of 

 empirical relationships. The empirical formulas of Baker, Barnes, Bydin and others are examples 

 of this. 



206 



