During the expedition on the Fram , Nansen found 7662 freezing degree-days for the winter of 

 1894-1895, which, according to formula (6), corresponds to 224 cm of ice. Evidently, these values 

 are nearly maximum for the east longitudes of the Arctic Basin. 



LITERATURE: 62, 77, 87, 88, 107, 172, 177. 



Section 84. Ice Accretion as a Function of the Vertical 

 Distribution of Temperature and Salinity 

 Beneath) the Ice 



We have seen that neither Stefan's theoretical formula which reduces to 



^~ 2x86,400 k ' ^^' 



where R is the number of freezing degree-days, A is the heat of crystallization, 6j is the ice den- 

 sity, k is the heat conductivity of the ice and i is the ice thickness in centimeters, nor any of the 

 empirical formulas consider the vertical distribution of temperature and salinity beneath the ice. 

 In other words, in all the formulas it is assumed that all the heat transmitted through the ice to the 

 atmosphere is produced solely by the heat of crystallization. 



Let us assume that we have a fresh-water lake in which there is no movement of water and, 

 consequently, no frictional mixing. In first approximation, let us ignore the molecular processes 

 in the water. Further, let us assume that prior to the initial cooling, the temperature of the lake 

 was somewhat higher than the temperature of the greatest density, i.e., 4° . After the tempera- 

 ture of the lake from the surface to the bottom drops to 4°, all convective phenomena in the lake 

 will cease, and ice formation wiU start after the uppermost, thinnest layer cools to 0°. From this 

 moment on, we can apply Stefan's reasoning to what follows, after augmenting it somewhat, namely: 

 the elementary amount of heat released to the atmosphere in time dT through a unit area of ice of i 

 thickness is 



dg=^dT, (2) 



where 6 is the difference between the temperatures of the upper and lower surfaces of the ice. 



This elementary amount of heat should be equal to the sum of the heat released during the 

 formation of an additional layer of ice and it is 



^h di, (3) 



and of the heat released during the cooling of a column of water dh -high from 4° to 0°, from which 

 an additional column d i-high forms, and it is 



A°cJh=A°c^^di, (4) 



W 



where c^ is the specific heat of water and 6j^ is the density of the water. Thus 



W„ /.,, ... l,\.. (5, 



«.r-(x8+4xi)^'. 



214 



