where m = quantity of heat absorbed by a unit of water area in a unit of time, 



w = area of water surface between floes, 

 T = time. 



If this heat is expended entirely in melting, then, assuming that during melting a decrease 

 occurs only in ice area and not in thickness, we obtain 



mwdT = hS^lds, (l) 



where h = ice thickness, 



6. = density of ice, 



X = heat of fusion, 



ds = decrease in ice area. 



If we denote , ^ . = , and bear in mind that the decrease in ice area, ds , is equal to the 

 flo-K 



increase in area of open water, dw , we obtain 



aw dT = dw, 



— =adT. 



w 



Considering a as constant for a certain period of time and integrating, we obtain 



lnw = aT + C, 



where C = an arbitrary value, determined by the condition that the initial moment the water 



area w 



Thence it follows that 



In Wi = In jVo + aT. 



Discarding the logarithms, we obtain 



Wi= WqC"''' 



m 



°^ Wf = ivoe"^' , (2) 



where w, = area of water at the instant r . 



From the latter equation it follows that with a change of time in arithmetic progression, the 

 area of water between the floes increases in geometrical progression. 



The areas of water w, and w are most readily expressed in units of tenths of the entire area 

 of the sea section under observation. Actually, if we consider the latter as being equal to 10, we 

 obtain 



n,= \0-w,,\ ^3j 



no= \0 — Wo, 



317 



