The following formula is derived from the Fourier Law of the distribution with depth of 

 periodic surface-temperature changes of a uniform infinite body, 



= 2,/f, 



(3) 



where s is the depth of the level computed from the surface of the ice, t is the time lag of the max- 

 imum or minimum at a [given] depth, fc is the thermometric conductivity, T is the period of tem- 

 perature change (in our case, 10.4 months is the time it takes for the temperature of the surface 

 layer of the ice to return to the initial temperature) . 



From formula (3) , we obtain 



4^=0.00029^ 



(4) 



where t is expressed in days, s in centimeters and fe in cm^/sec. 



Malmgren computed the dates of minimum temperature at different levels in the ice (table 81) 

 from his observations of ice temperature and from his theoretical sinusoidal curves (figure 80) . I 

 obtained the values of the coefficients of thermometric conductivity of ice, given in table 82, by 

 successive substitution of the following in formula (4): the depths 25, 75, 125 and 200 cm, and the 

 corresponding time intervals 8, 19, 29 and 50 days, taken from the surface minimum (on 26 

 January) . 



--TuT- 



Figure 83 . Diagram of the drop in the 

 level of minimum ice tem- 

 perature in the summer. 



TABLE 81. THE DATES OF MINIMUM ICE TEMPERA- 

 TURES AT DIFFERENT LEVELS, ACCORD- 

 ING TO MALMGREN' S OBSERVATIONS 



cm 26 January 



25 cm 3 February 



75 cm 14 February 



125 cm 24 February 



200 cm 17 February 



237 



