158 WILLIAM H. HOBBS 



quickly frozen in the prevailing low temperature so as to form 

 intercalated "planks" of younger ice. The lake cover is thus 

 again completed at a low temperature, so that a "warm wave," 

 if it can quickly communicate its temperature to the ice, causes an 

 expansion which according to Tyrrell amounts to one to three 

 inches per mile per degree Fahrenheit. Thus expanded the ice 

 cover is too large, and a push is exerted against the shore if the 

 cover is a structure competent to transmit the stresses induced in it. 

 The range of action of this push, and the consequent size of the 

 ridge raised upon the shore will depend upon the number of times the 

 process is repeated; for each alternation of "cold" and "warm" 

 wave introduces a new series of wedges into the ice cover and 

 correspondingly extends its margins. 



To recapitulate: (1) there must be a wide and probably also a 

 relatively sudden alternation of lower and higher air tempera- 

 tures over the lake: (2) these temperature changes must be 

 promptly communicated to the ice; (3) the ice cover regarded as 

 a girder must be competent to transmit the stresses to the shore; 

 and (4) for large effects the alternations of temperature must be 

 several times repeated. Obviously, also, the shores of the lake 

 must be of such form and materials as to be subject to movement 

 under stresses below the crushing strength of the ice itself. 



The first and last conditions are meteorological and can be 

 determined for any given district. Not only is a severe winter 

 climate essential, but there must be an alternating occurrence of 

 cold and warm waves. 



The second and third conditions are crucial. In Buckley's 

 studies of ice ramparts at Madison, Wisconsin, the most thorough 

 that have been made, 1 it was found that ramparts seldom formed 

 during seasons when the lakes were snow covered. The probable 

 explanation of this is that snow blankets the ice and prevents a 

 quick communication to it of the air temperatures above the snow 

 surface. We have here emphasized the element of time, for the 

 reason that studies in Greenland show that air temperatures are 

 slowly communicated downward through snow blankets to very 



*E. R. Buckley, "Ice Ramparts," Trans. Wis. Acad. (1901), XIII, 141-62; pis. 

 1-18 (discussion by C. R. Van Hise). 



