and the average normal tension 



rk='ii-'- <^^> 



It is clear that the average tension will increase along the direction from the windward sal- 

 vage of the field toward the shore, and at a certain distance may appear equal or even greater than 

 the boundary of plasticity of the jammed ice field of the given thickness. In the last case, at such 

 a distance, breaking open the ice field, its fracturing and subsequent hummocking are inevitable. 



As direct observations show, ice hummocking, which is caused among the spacious ice fields 

 by wind, is distinguished according to its character from ice hummocking which is caused by push- 

 ing up of ice fields on the shore or on fast ice. In the latter case, ice hummocking is concentrated 

 at the shore and at the salvages; in the first case, ice hummocking is distributed more or less 

 proportionally on the whole area of the region covered by ice hummocking. It follows from that 

 that the thickness of the ice which is hummocked by the wind is approximately equal in the entire 

 region of the ice hummocking. 



Let us note further that the capability to cause ice hummocking with every wind is limited 

 entirely by the specified thickness of the ice. After the attainment by the ice of this limited thick- 

 ness, a wind with the same force blowing even during the course of lengthy periods of time cannot 

 cause any new ice hummocking. 



Taking into consideration the circumstances of ice hummocking, I consider we accept that 



M = a-L{w-w^YT, (15) 



where Ai is the decrease in length of the ice field in the direction of the wind, 



i is the length of the ice field in the direction of the wind, 



h is the ice thickness, 



w is the wind velocity at a given moment, 



w^ is the wind velocity at which the ice of a given thickness is hummocked, or the velocity 

 of the ice hummocking wind, 



T is the time, 



a is the coefficient of proportionality. 



It is natural that formula (15) is applicable only in that case when the velocity of the affecting 

 wind is more than the wind velocity which hummocks ice of a given thickness (with the same 

 durability). 



In formula (15) variables appear: the length of the ice field (gradually decreasing), the 

 average thickness of the ice (correspondently increasing), the velocity of the ice-hummocking 

 wind (proportional to the ice thickness, also gradually increasing), and finally the gradually in- 

 creasing time. 



259 



