From figure 100 it follows 



hi-=ho+k—Afl, (7) 



2l = Zo — fc + Az, (8) 



where Ah = the change of the above-water height of the ice as a consequence of evaporation, of 

 deposition, and of melting away, flowing of water under the ice, during the time between the ob- 

 servation, 



A 3 = the change of the underwater emersion of the ice with freezing and the melting of ice 

 from below, 



k = the change in the position of the level of the sea with regard to the ice. It is clear that 

 all individual particles within the ice are shifted to this same value with regard to the level of the 

 sea. 



Substituting formulas (7) and (8) in formula (5) we derive 



(fto+/c-A/z)S,+(Zo-/c+Az)8, = (z„-fc + Az)S^. o) 



Subtracting formula (3) from formula (9) and transposing the members, we derive 



k(8,-B^+K)-U\-{-^z (8,-SJ =0. (10) 



Furthermore, from formulas (7) and (8) we get 



where AH = the overall change of the ice thickness. 



During the winter, when ice thawing does not occur, the value A if is determined by the dif- 

 ference between the quantity of the fall in precipitation and evaporation, the deposition and the 

 evaporation in the central arctic are not great in the winter, and we may disregard in the first 

 approximation this difference and reckon 



Ah =0. 



Furthermore, the difference of the densities of the above- and under-water parts of ice which 

 is significant in summer, is small In winter. From this we may derive for winter 



^h =^3' 

 In such a case, from formula (10) we shall derive 



Az. (12) 



Siv — Sj 



s.. 



280 



