22 IOWA STUDIES IN NATURAL HISTORY 



that the loss of density per degree is much less at lower 

 temperatures than at higher ones. A full statement of this 

 fact and its results may be found in Birge '10, pp. 989-1004. 



Table 13, Col. E shows the work done m behalf of each 

 stratum or the work needed to carry the warmed water 

 down from the surface and put it in place. Most of the work 

 therefore is done outside of the stratum which is to be 

 warmed. In the case of the 5 m.-lO m. stratum two-thirds 

 of the 629 g. cm. would be needed to bring the warmed, 

 water to the top of the stratum and one-third to distribute 

 it through the stratum. In a similar way each upper stra- 

 tum has its share of the work for all of those below it. It 

 is possible, by a somewhat tedious computation to ascertain 

 the amount of work done in each stratum. The method and 

 details of this computation are shown in Birge '16, p. 354. 

 The results for Okoboji lake are given in table 13, columns 

 G and H, and show the distributed ivork. 



It appears that 971 g. cm., or nearly two-thirds of the 

 whole work are done in the upper 5 m. This amount of work 

 is needed to carry to a depth of 5 m. the heat which goes 

 to the strata below 5 m., and to distribute through the m.- 

 5 m. stratum the heat which remains there. Similarly, 442 

 g. cm. of work are done in the 5 m.-lO m. stratum. 



The Role of the Sun. In this discussion of the distribution 

 of heat it has been assumed that all warming below the 

 surface is done by mixture ; that the warmed water is taken 

 from the surface and distributed by the wind. This assump- 

 tion is, of course, incorrect as it implies that the water is 

 opaque to the sun's radiation. It is necessary therefore to 

 ascertain what aid the sun may give in the distribution of 

 heat. 



From data so small in quantity as those available for lake 

 Okoboji this question can be answered very imperfectly. In- 

 deed, the data can tell us only the possible maximum con- 

 tribution of the sun to the work of distributing heat. 



Observations were made on July 29 with the pyrlimni- 

 meter, an instrument for measuring the penetration of solar 

 radiation into the water of the lake and its absorption by 

 the water. It consists essentially of 20 small thermal 



