somewhat lower than the temperature of freezing, even a slight change in temperature causes con- 

 siderable changes in the amount of pure ice per unit of volume. 



In his investigations, Malmgren supposed that sea ice consists of pure ice into which are em- 

 bedded more or less equally isolated cells of brine. The brine in these cells follows the eutectic 

 law: a certain amount of ice melts from the walls of the salt cells with each rise in the brine tem- 

 perature; conversely, with each decrease in temperature, a certain additional amount of ice pre- 

 cipitates on the walls of the cells. 



Further, Malmgren indicated that with each change of ice temperature, a number of proc- 

 esses occur which affect the properties of sea ice in one way or another. 



Thus, with a decrease in temperature: 



1. Volume of ice increases and its temperature falls; 



2. A certain additional amount of ice separates from the brine cell which is accompanied by 

 a great release of heat and a great increase in the volume; 



3. The temperature of the brine decreases and its volume changes; 



4. All sorts of thermo- chemical processes occur in the brine itself which are related to the 

 change in the volume and temperature. 



In deriving his theoretical formulas, Malmgren assumed that the effect of the thermic and 

 volumetric changes in the brine of sea ice (inasmuch as there is little brine in ice), is so insignif- 

 icant in comparison with the effect of the same changes in pure ice, that it could be neglected. 



Proceeding from the same suppositions as Malmgren, let us derive the necessary formulas 

 by a method which in my opinion, is simpler. 



Specific heat is based on 1 g of matter and 1° of temperature. Remembering that 1 g of sea 



Si Si 



ice has (1 --5-' ) grams of pure ice and 5— grams of brine and neglecting the effect of thermal chem- 



leal processes, we may write: 



where c ^ is the specific heat of sea ice, 



c j is the specific heat of pure ice, 



Cg is the specific heat of brine, 



iSj is the salinity of sea ice, 



St is the salinity of brine at a temperature t, 



Ax is the heat of fusion at a temperature r (the meaning of this amount will be explained 

 below) , 



d Ci- ~ Si/S^ )/(!■,■ =S^/S J X dS^/dT is the change in the amount of pure ice in 1 g of sea ice 

 during a change of 1° in its temperature. 



151 



