It is possible to assume that the loss of energy in jamming of ice is insignificant, as com- 

 pared with other losses. The energy expended in the complete break-up of ice hummocks is greater 

 the thicker and firmer the ice. The energy expended in ice-humm^ock formation is more according 

 to the size of the ice hummock; in other words, the greater the decrease of the length and the 

 greater the thickness of the ice field, the more energy is expended. 



The durability of the ice depends to the greatest degree on its temperature. From that, it 

 follows that significantly less energy is expended in the break-up of warm ice than in the break-up 

 of cold ice of the same volume. 



As regards to the dimensions of the formation of ice hummocks, we have seen that 



bhAl = V,+V=-^{H,a, + H,a,), (lO) 



where F^ is the volume of the part of the ice hummock over the ice, V^ is the volimie of part of 

 the ice heap under the ice, Ai is the decrease In length of the ice field, ff^ is the height of the 

 above-water part of the ice hummock over the top surface of the ice field, a j^ is the range of the 

 above-water part of the ice hummock from the shore, H^is the depth of the underwater part of the 

 ice hummock under the lower surface of the ice field, Qg is the extent of the underwater part of the 

 ice hummock from the shore . 



But if the ice hummock is isostatically coimterbalanced, (see Section 103), then 



ai=a2=a, 



where 5^ is the ice density, 6jy is the water density. 



From formula (10), we derive 



f'^^=i^^n^^- (n) 



According to the observations, the angle of the slope of above-ice part of hummocks is about 

 30°; in such a case, it is approximately 



a = 2H^, 



2 S (12) 



K — s,- 



Let us assume that a rectangular ice field, with width b and length i , was hooked by its side 

 to the shore. It is clear that if the vnnds blow perpendicular to the shore, the force of the pressure 

 of the ice field on the shore will be equal to 



F= kblw^, (13) 



where w is the wind velocity, k is the coefficient of proportionality, depending on the unevenness of 

 the upper and lower surfaces of the ice, and also on other circumstances. It is natural that at a 

 distance x from the outer border of the field, the forces being caused by the movement of the left 

 side of the field compress the given field and will be equal to 



F^=-kbxw\ 



258 



