The following chief processes may be distinguished in hummocking: 



1. The firmness of ice, which results in the destruction of the spaces between the ice blocks 

 ("beams"). 



2. Ice packing, which results from squeezing air and brine bubbles from the ice. 



3. Fracture and break-up of ice into the largest or the smallest fragments. 



4. Formation of hummocks, which consists of the moving of ice fragments to the upper sur- 

 face of the ice and the packing of fragments under the ice. 



Let us assume that we have two ice fields, moving in one direction with different velocities. 

 After collision, the united field will move with a common velocity where m is the mass of the ice 

 field. 



miVi + m.v^ 



The kinetic energy, according to formula (1), of the united ice fields after the collision will be 



mv^ _ Wi -f- ffla ( miVi+m ^v^V 

 2 2 [ m,+m, ) ' ^'^ 



Before the collision, the energy of the first field was Ei = — ^— !■ 



2 

 rri. I • 



while that of the second was fo = 





Consequently, the energy of the two fields was 



E, + E,= ^ivi + m,v| ^ (3) 



Subtracting (2) from (3) , we obtain the kinetic energy lost in the deformation of the collided ice 

 fields; namely 



A,£_ ^1^2 (^1— V2)' 



mi + ^2 2 ■ (4) 



It is evident that if the second field is not mobile, then 



^g^ milTl^ ^? El 



mi 4-/772 2 , , m 

 m 



where E^is the energy of the first field. 



l+P (5) 



If the mass of the second field is immeasurably great, compared to that of the first field, 

 then from formula (5), we see that the total energy of the first field is expended in the deformation. 



Let us now assume that a rectangular ice field was pushed up on a straight vertical shore 

 (figure 90) with one of its sides perpendicular to the shoreline. 



Its energy, before coming to rest at the shore, was equal to 



£ = ^=/.Z,S,^, (6) 



255 



