A LIMNOLOGICAL RECONNAISSANCE 25 



in four months, or about as much as may reach the surface 

 in twenty minutes at noon. 



It is obvious that this computation is not based on average 

 conditions, since on the one hand the reading was made near 

 noon, when the sun was at a high altitude, and on the other 

 hand it was far from the zenith and the path of its rays 

 through each meter of depth would be more than 100 cm. 

 It is quite possible to determine the energy present at 100 

 cm. and the rate of transmission if the sun were vertical ; 

 and it is also possible from this new curve to determine the 

 same data for the mean conditions during the warming 

 period. The computation has been made with the follow- 

 ing result: 



Energy at 100 cm. Transmission 

 Observed, July 29 15.3% 53%— 54% 



Vertical sun 16.0% 56%— 57% 



Mean sun, (Apl. 15-Aug. 15) 14.2% 50%— 51% 



It would be possible to use the computed mean sun in the 

 following work instead of the observed data. But the dif- 

 ference is not great, and the result is at best only a rough 

 approximation. The value of the mean sun is based on five 

 years of observation at Madison, Wis., in the same latitude 

 as Okoboji. 



Effect of Direct Insolation. We may now go on to com- 

 pute the direct effect of the sun on the distribution of heat. 

 We have as data (1) the downward movement of heat 

 amounting to 20,933 cal. cm.- at the surface (table 11).; 

 (2) the amount of work needed to distribute this heat 

 (table 13, G) ; (3) the heat directly contributed by the sun 

 to various depths (table 15). The following table gives the 

 result : 



