12 IOWA STUDIES IN NATURAL HISTORY 



We may state therefore that the mid-summer tempera- 

 ture of Okoboji lake in 1919 was close to 21° C. 



Quantity of Heat. From the data thus stated it is pos- 

 sible to compute the quantity of heat represented by this 

 rise of temperature to 21°. If this gain is to be stated there 

 must be a starting point from which the gain may be com- 

 puted. This obviously is not zero, as no lake has so low a 

 temperature. As stated in another paper (Birge '15, p. 

 170), there are two methods of stating the gains of heat. 

 One is the anniuil heat budget, which takes as its starting- 

 point the mean temperature of the water immediately after 

 the time of freezing, or, less accurately, at any time during 

 the ice-period. The other is the summer heat-income, which 

 starts from the temperature of 4°C. — that of the maximum 

 density of water. For reasons stated in the paper referred 

 to, the conclusions to be drawn from either of these methods 

 are much the same. In all cases the gains between the win- 

 ter temperature and 4° must be discussed apart from those 

 above 4°. In the case of Okoboji lake we are limited to the 

 summer heat-income, since the winter temperatures are still 

 unknown. The gains of heat are stated in gram calories 

 per square centimeter of the surface of the lake. A rise of 

 1° in a stratum 100 cm. thick represents a gain of 100 cal. 

 per sq. cm. of surface. 



The formula for computing the summer heat-income is 

 (T-4) • RT; in which T is the mean temperature of any 

 stratum and RT the reduced thickness of the stratum stated 

 in centimeters. If the lake is considered as a unit, RT is 

 the mean depth. In this case the mean temperature is 21.0° 

 and the mean depth 12.3 m., or more exactly 1227 cm. The 

 summer heat-income is therefore (21-4) • 1227=20849 cal., 

 or approximately 21,000 cal. per square centimeter of the 

 surface. 



The value of the summer heat-income will vary slightly 

 with the stratum used in the computation. If the computa- 

 tion is made by 5 m. strata the result is the same as that 

 from the mean temperature, as the following table shows: 



