0. 92 is the mass in grams of 1 cubic cm of pure ice (density), 



y is the increase in volume when 1 g of pure water freezes, 



9 (1 - 5 j /St ) /dTis the additional amount of pure ice separated from 1 g of sea ice when it 

 is cooled by 1°. 



But 



dA sj-si 



Si \ Si dS-, 



Assuming that |3: 0.92 = 0.000169 and 7 = 0,091, Malmgren concludes 



Si dS. 



Ur = 0.000169 — 0.091 



S'r ^^' 



(2) 



where the coefficient of expansion is not related to the unit of volume as is ordinarily done but to 

 the unit of mass. 



The first member of the right-hand side of formula (2) is the coefficient of expansion of pure 

 ice, the second member is the correction for salinity. 



Table 41 is computed according to Malmgren's formula (2). 



TABLE 41. THE COEFFICIENT OF VOLUMETRIC EXPANSION OF 1 G OF SEA ICE OF 

 VARIOUS TEMPERATURES AND SALINITIES. THE COEFFICIENT IS 

 MULTIPLIED BY 10* 



As yet, one more fundamental difference between sea and fresh ice is apparent from formula 

 (2) which had been checked empirically by Malmgren: fresh ice expands with a rise in temperature; 

 sea ice, when it has low temperatures and slight salinities and at the same time the correction of 

 the coefficient of expansion for salinity is not great, also expands with a rise in temperature, but 

 expansion is less than fresh ice. At high temperatures and great salinities, the amount of the cor- 

 rection for salinity increases so much that the coefficient of volumetric expansion becomes nega- 

 tive, i.e. , the volume of the ice increases with a drop in temperature. Table 42 shows the change 

 (in m) of the length of 1 km of ice of different temperatures and salinities with a 1° rise in 

 temperature. 



159 



