curves of Figure 18 were obtained* Curve 1 shows the observed time re- 

 quired for the accretion of ice. Curve 2 shows the ice accretion computed 

 by evaluating Zubov's formula with the first constant determined so that 

 the initial value of time was equal to the observed value. Curve 3 is the 

 same when the constant is determined to make the final value the same as 

 the final observed value. Curve 4 is found by using an average of the 

 two constants in curves 2 and 3» A second-degree polynomial of the form 

 of Zubov's equation can be determined by a statistical analysis of the 

 observations. An equation of this type will yield a curve with a compara- 

 tively close fit to the observed data. However, in all these cases the 

 value of the constants depends upon the average value of the parameters 

 involved. Thus, this expression of Zubov's as with other empirical re- 

 lations of this form, is valid only for observations obtained under simi- 

 lar conditions to those for which they are derived and is not generally 

 applicable to all locations and all meteorological and oceanographlc condi- 

 tions. 



Another empirical equation of this type is that of Barnes (1928), 

 which is of the forms 



£ 2 +2£ = -^fAT X f , (27) 



where <£ = ice thickness, 



^i = conductivity of ice, 



K*=K + T x (c 2 ^-C, 



k - latent heat of crystallization, 

 T\~ freezing point of sea water, 

 Cj ~ specific heat of ice, 

 C5 ™ specific heat of sea water, 

 /\ - density of ice, 

 ?x ~ density of sea water, 

 ^ T Q s difference in temperature between the top and bottom of the 

 ice, and 

 t m time 



This expression evaluates theoretically the constant which Zubov secures 

 empirically. No account, however, is taken of snow thickness, which is 

 of paramount importance in determining the rate of accretion of ice thick- 

 ness. 



