In order to obtain the ice thickness prior to the start of melting, i. e. , the critical maximum 

 ice thickness, we should add the amount of summer melting. 



^max= /i + A/, (5) 



or 



/max = -^ + -2- — 25. (6) 



to the value Ii obtained from formula (3). 



From formula (6) , one can see that the maximum ice thickness tends toward infinity as the 

 amount of summer melting decreases and approaches zero. I shall return to this question later. 



The graph which has already been given in figure 72 can be used to compute maximum ice 

 thickness. Actually, we have seen that when the maximum ice thickness is reached, winter ice 

 accretion is in exact equilibrium with summer melting. Hence, if we consider the isolines of ice 

 growth on this graph to be isolines of melting, their intersection with the vertical lines corre- 

 sponding to freezing degree-days, will give us the minimum ice thickness in a given region. By 

 adding summer melting to this value , we will find the maximum thickness . 



As has already been pointed out, Nansen observed 7662 freezing degree-days during the 

 winter of 1894-1895. Using the graph, we find that when fl = 7662 and io = cm, year-old ac- 

 cretion ice win be 224 cm thick. On the other hand, Nansen noted that the ice melted 100 cm 

 during the summer in the region of the drift of the Fraui. Beginning on the graph at fl = 7662 

 and AI = 100 cm, we find the minimum ice thickness Iy = 231 cm and the maximum ice thickness 

 •^max = 331cm. 



The corrections explained in figure 79 should be entered in Weyprecht's diagram. In this 

 figure, ice thickness is plotted along the Y-axis and the freezing degree-days along the X-axis. 

 The curve ON is plotted according to formula (1). 



If a certain number of freezing degree-days R is characteristic of a given region at the end 

 of the first year , we will find the ice thickness by the end of the first winter , i . e . , i ^^ at the inter- 

 section (point a ) of the vertical line corresponding to the value of R and the plotted curve . 



The ice thickness will change during the summer due mainly to the following processes: 



1. The thickness will increase somewhat from below due to the low temperatures main- 

 tained in the ice itself at the start of melting. This increased ice thickness is expressed by seg- 

 ment ail in figure 79. 



2. The ice thickness will decrease from above by the amount ac due to summer melting. 

 Thus by the end of the summer, the ice thickness will be 



I'l -\-ab — ac = ii -{- i' — i". 



3. The internal temperature of the ice will increase, due in part to the absorption of radiant 

 energy and atmospheric heat by the upper ice layers, and in part due to the absorption, through 



227 



