2. The temperatures of water and ice differ from each other, but the temperature and mass 

 of the water and ice are in such a ratio that the reserve of "heat" in the water is exactly equal to the 

 reserve of "cold" in the ice. Such an interrelation is characterized by formula (3). 



Inasmuch as in the investigated case there is no melting or freezing, then, as in the pre- 

 ceeding case, we have 



^w ^^ "-'^ • 



Thus, in the second case, we have dynamic equilibrium (there is neither melting nor freezing), but 

 there is no thermal equilibrium. Heat exchange between water and ice continues until the temper- 

 ature of the water and the ice become the same and become equal to the temperature of freezing. 



The discussions which have been given and the formulas, permit the solution of many ques- 

 tions connected with the interaction of water and ice. I shall give several examples. 



Let us assume that 0^,= 1.0, c i = 0.5 and A = 80 g-cal. With such assumptions, we find 

 that one (metric) ton of sea water, the salinity of which equals 35.00 o/oo and the temperature 30° 

 at the initial moment, melts 399 kilograms of fresh ice, the temperature of which equals 0°, in 

 which case the sea water is diluted to 25. 02 o/oo by mixii^ with the melted water and is cooled to 

 the temperature of freezing, i.e. , to - 1.35°. 



With the same assumptions, one ton of sea water, the salinity of which equals 35. 00 o/oo at 

 the initial moment but the temperature of which equals 0°, melts 23 kg of fresh ice, the tempera- 

 ture of which is also 0°, in which case the salinity of the water decreases to 34.21 o/oo by mixing 

 with the melted water, and the temperature decreases to - 1.35°. 



On the same assumptions, during interaction of one ton of sea water (S^ = 35. 00 o/oo, 

 t = 0°) and one ton of ice ('5'^= o/oo, t^ = 0°), 35 kg of ice are melted, in which case the salinity of 

 the water decreases to 33. 81 o/oo and the temperature of the water and the remaining 965 kg of ice 

 decreases to - 1. 83°. 



It should be pointed that the first example characterizes the condition which occurs when an 

 iceberg is carried into the warm and salty waters of the Gulf Stream; the second and third examples 

 are conditions existing at high polar latitudes. The difference in the end results of the first and 

 second examples is explained by the difference in the initial temperatures of the water. In the 

 second and third examples, with equal initial temperatures and salinities of water and ice, the final 

 temperatures and salinities are determined exclusively by the ratio of the masses of water and ice 

 which come in contact. The final temperatures are extremely close to each other and actually dif- 

 fer within the limits of exactness of the conducted observations whereas the salinity differs very 

 much. The fact that the surface arctic waters (see Section 146) are outstanding in their very large 

 vertical gradients of salinity and very small vertical gradients of temperature (the temperature 

 throughout is very close to the freezing temperature) is partially explained by this. This same fact 

 is convincing proof that the surface arctic waters are finally formed not as a result of vertical 

 winter circulation and not as a result of mixing with other waters, but as a result of melting. Ac- 

 tually, when there is vertical winter circulation, we always find complete homogeneity of the upper 

 layers both in temperature (equal to the temperature of freezing under ice formation condition) and 

 in salinity. When water and ice coexist, we always meet with temperatures close to the tempera- 

 tures of freezing, but the salinities of the upper layers can differ sharply. 



Let us imagine a cylindrical iceberg consisting of horizontal layers, and having a vertical 

 axis; the salinity of the layers is the same and the temperature decreases with height. After the 



157 



