5. The form and size of the breakthrough duplicated the form and size of the load almost 

 exactly. 



Vereshchagin said in his letter that the careful measurements of ice deflection under a load 

 conducted by him on 14 January 1944 on the ice of Lake Baikal confirmed the hsrpothesis stated by 

 me. 



Even by the time the present book was being printed, I became acquainted with certain results 

 of measurements of ice deflection under a load conducted by Vatalin, in February- March, 1943 in 

 the Amurskic Liman Bay. Vatalin attempted to correlate the points of deflection he obtained, with 

 a theoretical curve of the deflection of an elastic plate, on an elastic foundation, but this proved to 

 be impossible. However, when Vatalin's measurements were averaged for each distance from the 

 center of the load, surprisingly good agreement was obtained between these points and the logarith- 

 mic curve. At the same time, I was able to acquaint myself with the investigations of ice deflec- 

 tions along railroad and truck crossings along Severmaya Dvina conducted by Shishov at the start of 

 1943. 



The ice deflections observed during these investigations, according to my computations, also 

 agree well with logarithmic curves. Furthermore, it is apparent from the Vatalin and Shishov 

 investigations that the coefficient of deflection decreases with an increase in the thickness of the 

 ice. 



Finally, it should be added that at my request, Zvolinskii rechecked the theoretic basis of 

 ice deflection under a load and it was found that if both the elasticity and plasticity of ice are taken 

 into consideration under known conditions of the moduli of elasticity and shear, the curve of deflec- 

 tion resembles a logarithm. 



Thus, on the basis of available data, it is considered that the theory of deflection of an 

 elastic plate on an elastic foundation is not applicable to the case of ice bending under a load, and 

 that it is necessary to proceed from other premises in order to obtain a theoretical basis on this 

 question. 



In agreement with the third assumption, the maximum point of deflection is determined by 

 the volume of the body formed by rotation around an axis OZ of a certain area: one side of the area 

 is the axis OX , and the other is a logarithmic curve starting at the point of application of the load 

 and leading into infinity which gradually approaches the axis OX. 



The area included between the logarithmic curve and the OX and OZ axes equals 



oo 

 Q= \zdx = h_. (3) 



k 



The volume of the rotating body (around the OZ axis), formed on one side by the OX axis, and 

 on the other, by the logarithmic curves of deflection, is equal to 



V=4°x'dz = ^. (4) 



Kr 



Accepting that the density of water equals unity, and remembering that the volume of the 

 displaced water should equalize the load, we obtain 



''=-^- (5) 



198 



