152 Wisconsin Academy of Sciences, Arts, and Letters, 



of 49° F. in the temperature. This amount is so small that it 

 will not need further consideration. 



The tensile stresses in the horizontal directions accumulate 

 until one or the other overcomes the strength of the ice and 

 cracks form. As stated before, the tensile stresses are greatest 

 at the surface and rupture will begin when these stresses over- 

 come the strength of the ice at this place. When once started, 

 the cracks will continue either part way or entirely through the 

 thickness of the ice. 



The linear contraction of a field of ice four miles wide, pro- 

 vided movement took place with perfect freedom, would be 0.586 

 feet for each degree F. In a case similar to the one under dis- 

 cussion, where the temperature of the surface layer is hypothet- 

 icallv lowered 49^ F., the contraction of this layer would be 

 28.714 feet. On the other hand the layer next to the water hav- 

 ing a temperature of 32° F. Avould suffer no contraction. 



Cracks that are once formed often open again and again, but 

 each time they reach the under surface of the ice they fill with 

 water. Tlie water rises about nine-tenths of the way to the sur- 

 face and there solidifies. (See Plate XVII.) As the ice in- 

 creases in thickness it is buoyed up higher and higher, on ac- 

 count of which the water in the cracks rises successively to a 

 point which is further from the surface. Each time the cracks 

 fill, the water is at a lower level. When it freezes, steps like 

 terraces are formed from the center to the margin of the vein. 



During the entire period of lowering temperature, the ice 

 sheet increases in thickness by the solidification of the water at 

 the lower surface. It also increases in density through contrac- 

 tion. The amount of horizontal contraction is about equivalent 

 to the volume of new ice which fills the cracks that show at the 

 surface. As the ice sheet increases in volume it is buoyed up 

 by the water, increasing its general level. This increase in vol- 

 ume comes at a time when contraction is at a maximum and may 

 affect more or less the results. 



The water which fills the cracks expands when it freezes, 

 resulting in inducing compressive stresses which neutralize in 

 part the subsequent contraction. 



When the temperature has reached the lowest point the ice 

 sheet is a solid mass filling the entire lake basin. When the 



