10 



Indiana University Studies 



for the 'Tinger lakes" of New York and some of the Wisconsin 

 lakes that the ''heat budget" does not change materially during the 

 months of July and 'August, i.e. radiation equals absorption 

 during this period. Since all of our observations were made during 

 these months, they probably form a very accurate picture of the 

 maximum load. It is of course evident that the heat content 

 would vary more in our Indiana lakes because the variable 

 epilimnion forms a larger proportion of their volume than it 

 does in the deeper ''Finger lakes". 



There have been proposed three methods of calculating and 

 expressing the amount of heat contained in lakes. Forel (1895) 

 calculated the amount of heat in a column of water extending 

 from the bottom to the surface in the deepest part of Lake 

 Geneva. This method makes it possible to compare profitably 

 only lakes of similar depth, thus limiting the value of the method. 



Halbfass (1910) calculated the total heat energy in a lake. 

 This makes possible the comparison of the heat budgets in 

 various lakes, but since it takes no account of the area of a lake, 

 it is impossible to infer the rate of cooling, the influence of the lake 

 on climate, liability to freeze, etc. 



Birge (1914) has proposed a method by which the heat of a 

 lake is expressed in gram calories per square centimeters of surface. 

 This is determined by multiplying the average temperature of 

 the lake by the average depth in centimeters. For the purpose 

 of comparison, this method of expressing heat is evidently superior 

 to the methods of Halbfass and Forel. 



The method used by Professor Birge in calculating the average 

 temperature was to take the average temperature of the water 

 between two adjacent contours and multiply this by the volume 

 contained between them; then add the products and divide by the 

 total volume. Percentages of volume were also used, which of course 

 produced the same result. In determining the average tempera- 

 ture of the water between two contours, Birge takes the arith- 

 metical mean of the temperature at the two contours. This is 

 absolutely correct for lakes with vertical sides, but in lakes with 

 gently sloping sides it gives an average below the true one. 

 Professor Birge was perfectly aware of this discrepancy, which 

 is never great in our lakes. 



A closer approximation is obtained by applying the formula 

 for obtaining the average temperature of the frustrum of a cone, 

 whose bases differ in temperature and in which the gradient is a 



