In figure 90, the above- and below-water parts of hummocks, the belt of completely broken- 

 up ice, the belt of jammed ice, and also the motion for the time of the hummocking of the border of 

 ice field in the direction toward the shore are shown. 



From the assumption, the volume of the ice is not changed with hummocking; it clearly fol- 

 lows that the volimie of the over-ice (F^) and under-ice (V^) parts of the ice hummock are exactly 

 equal to the volume, to which the ice field was reduced during hummocking; that is 



V^ + V, = haM. (8) 



It is natural that in the examined case the hummock reaches the greatest height and depth at 

 shore. The seaward height of the ice hummock decreases in such a way that natural slopes are 

 formed over and under water, which are characteristic for fragments of ice of a given size. 



If the ice field pushes up on a shallow shore rather than a vertical shore, depending on local 

 conditions of ice hummocking in the full sense of the work, that also cannot occur. All kinetic 

 energy in such a case can be expended in jamming, break-up, friction of the lower surface of the 

 ice field against the shore, and in movement of the edge of the ice field on to the shore. 



If the ice field is pushed up onto fast ice, the process proceeds in accordance with the same 

 principle, in the case of movement of ice on to shore, with the difference that jamming, break-up, 

 and ice-hummock formation extend also to the seaward ledge of the grounded ice. It follows from 

 that, that with other similar conditions (other conditions being equal) the directions of the ice heap, 

 which is formed with a collision of the ice field and fast ice, are greater in area and less in height 

 than with the movement of the ice field on to a steep shore. 



With flat ice fields, thin and yet plastic enough, ice hummocking can be discharged in some 

 packing of them, and movement of the edges of the ice fields on to one another without preliminary 

 break-up. 



Returning to the case of an ice field which is pushed up on a steep shore, we see that the loss 

 of energy is equal to all the kinetic energy of the ice field, or 



777V2 



AE=- 



2 * 

 From the formula, it follows that with one and the same durability, one and the same effect can be 



attained either by an increase of velocity or an increase of mass of the ice field. The greatest 

 velocity of drift is observed at that time when the ice fields , twisted and strained from shore by 

 suitable winds, are driven along clear water to the shore with an inverse change of the wind di- 

 rection. But the masses of ice fields are of such size that even with the very smallest velocities 

 of the ice fields huge hummock formation takes place. 



As we have seen, the dimensions of ice hummocking are determined by the loss of kinetic 

 energy. 



Having distinguished three basic processes of ice hummocking, we get 



A£=A£i-|-A£2-l-A£3, (^^ 



where i^E-^ is the loss of energy in jamming, Ai?2 is the loss of energy in break-up, A^3 is the 

 loss of energy in formation of ice hummocks. 



257 



