It follows from formula (5) that for the same ice (the same coefficient of deflection) the 

 maximum point of deflection increases in proportion to the increase in weight, and that the weight 

 of the load creating this maximum point of deflection is inversely proportional to the square of the 

 coefficient of deflection. It is clear that the value of the coefficient of deflection is a function of 

 the physical properties of ice and its thickness and that the smaller the coefficient the better, in- 

 asmuch as in this case, with the same maximum deflection, the ice bends more smoothly. 



If we have simultaneous measurements of the deflections at 2 points located on the same line 

 with the point of application of the load, we can easily compute the coefficient of deflection. 



From 25 corresponding observations on the Volga River which I had at my disposal, I found 

 as an average that h =0.1 reciprocal meters with a maximum of 0. 18 and a minimum of 0. 044. A 

 check of the obtained coefficient of deflection by means of observations conducted in the winter of 

 1941 and 1942 along the railroad crossing across the Kugrechikha River in Archangelsk brought 

 about no changes. 



Formula (5), however, does not take into consideration the area occupied by the load and the 

 latter has a fundamental importance inasmuch as the greater the area over which the load is dis- 

 tributed, the thinner the ice may be. 



Let us suppose that a rectangular load of weight p, the perimeter of which equals r and the 

 area q, is placed on the ice. We can assume that the lines of equal deflections will pass, as shown 

 in figure 67, namely: at the comers of the load, they will be circular arcs but along the straight 

 lines of the contour they will be straight. The greatest deflection, understandably will travel 

 according to the contour of the load. 



Figure 67. Isolines of ice sag around a 

 rectangular load. 



As heretofore, let us further assume that the volume of the depressed part of ice will 

 equalize the weight. In this case the entire depressed volume will equal 





(6) 



where s is the maximum deflection (near the contour of the load), and a and b are the sides of the 

 rectangiilar load. 



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