[barnes-hayward- EXPANSIVE FORCE OF ICE 35 



mcleod] 



"The results obtained were uniformly less than those obtained 

 by Andrews 1 , varying from eighty-five to ninety per cent of his re- 

 sults. There are two reasons which may account for this difference. 

 1. The ice in our experiment probably adhered to the plank forming 

 the bottom, and free expansion was partly prevented. 2. The cross 

 section of the column was large enough to prevent it assuming the 

 temperature of the air in a short time, the observed lag in the tempera- 

 ture placed in the ice being very noticeable. Then too as the column 

 was protected on the bottom by the plank, the temperature was not 

 uniform throughout its mass, and the temperatures in the ice probably 

 registered a greater variation than actually occurred in the ice as a 

 whole. 



"A study of the curves shows that the coefficient of expansion 

 is a maximum at the freezing point, decreasing rapidly at first, the 

 rate of decrease becoming less as the temperature approaches zero, 

 while below zero the coefficient appears to decrease very slowly. 



"Having demonstrated to our own satisfaction that ice expands 

 or contracts as the temperature rises or falls let us consider the effect 

 of variations of temperature of the ice covering the surface of a lake, 

 assuming the ice to be free from snow. 



If the temperature of the air is ti° F and that of the water t 2 ° F. 

 the temperature of the top surface of the ice will be nearly the same 

 as the air when below the freezing point, while the bottom surface 

 of the ice being in contact with the water will be at a little below the 

 freezing point. As the ice in contact with the water remains at nearly 

 the same temperature, and consequently expands and contracts 

 but little, and as the ice in contact with the air is exposed to the greatest 

 variations in temperature, and consequently the greatest amount of ex- 

 pansion and contraction, the actual expansion of the whole mass 

 will be one-half of the maximum computed expansion of the range 

 of temperature. The average coefficient of expansion of ice between 

 -20°F. and 32° is -0000284, so that the total expansion of a sheet 

 of ice a mile long for a rise in temperature of 50 degrees Fahrenheit 

 would be — 



5-280 X -0000284 X 50° = ? f 



"This corresponds closely with a statement by E. R. Beardsley in 

 his pamphlet on the "Gravity Dam," that ice will expand nine- 

 tenths of an inch per hundred feet for the maximum range in the tem- 



1 The best results we have of the expansion of ice at different temperatures 

 were obtained by T. Andrews in 1885. 



