where n ^ and tiq = quantity of ice in tenths . 



We note further that by use of logarithms in equation (2) we obtain 



Ig Wt ~ Ig Wq SjXA ^ 



\ge 



m 



(4) 



From this equation it may be seen that, other conditions being equal, the time intervals in 

 which percentage of ice of diverse thickness decreases equally are proportional to the thickness of 

 ice and inversely proportional to the quantity of heat absorbed by the water. 



TABLE 89. NUMBER OF DAYS NEEDED FOR REDUCTION IN PERCENTAGE OF ICE 100 CM 

 THICK WITH HEAT ABSORBED BY WATER EQUAL TO 300 G/CAL/CM2 PER DAY 



Table 89 is compiled from equations (2), (3) and (4) above with the assumptions that the ice 

 thickness is equal to 100 cm, density is equal to 0.9 g per cubic cm, heat of fusion equals 80 g-cal 

 per g, and quantity of heat absorbed by water and expended in melting equals 300 g-cal per square 

 cm per day. From the table we find the number of days necessary for the initial ice percentage 

 rig to become the sought- for percentage n^ . 



We may find the value for any thickness of ice by a simple multiplication of the figure from 

 the table by the relation of the given ice thickness to that for which the table was compiled, i. e. , 

 ice thickness equal to 100 cm. Thus, for example, according to table 89, tenths ice 100 cm thick 

 will become five-tenths ice in 22 days. Thence we obtain the fact that eight- tenths ice 200 cm 

 thick will become five-tenths ice in 44 days . 



In similar fashion we may find the figures for any quantity of heat absorbed by the water by 

 simple multiplication of the figure from the table by the relation between 300 g-cal per square cm 

 per day (the value for which the table was compiled) and the given quantity of heat. Thus, e.g., if 

 we consider that only 150 g-cal per square cm per day is absorbed by the water, the table figure 

 must be multiplied by 2 . 



In this manner we may readily obtain from table 89 the values for any quantity of heat 

 absorbed by the water and for any thickness of ice. 



318 



