Birge—Work of Wind in Warming a Lake. 361 
distance below the surface. Thus the distance is reduced 
through which this part of the heat must be carried, and the 
work is correspondingly reduced. 
In certain directions we have some quantitative knowledge 
of the effect of insolation. The amount of heat delivered at 
the surface of the lake and that received at a distance below 
the surface can be measured. In lake Mendota the average 
quantities thus received have been found to be as follows: 
At 0.5 m. the sun’s rays have about 24% of the intensity 
which they have in the air; at 1 m., 13%; 2 m., 6.5%; 3 m., 
2 %; 4 m., 1 %. These are average results in the middle of the 
day in summer, and are subject to variation according as the 
lake contains more or less plankton. The corresponding 
figures for other lakes may be higher or lower. In Marl lake 
as much as 20% of the energy present in the air may be 
found at a depth of one meter. In Turtle lake, which has 
very highly colored water, less than 2.5% is found at the 
same depth. These numbers are plainly too high if applied 
to the whole day and to the entire time of warming. Smaller 
percentages would be found in the early and later parts of 
the day, and also in cloudy weather, when a larger percentage 
of incident energy is reflected. 
If we assume that the percentages of penetration indicated 
above are constant, it will be possible to compute roughly the 
amount of aid that the sun renders. For this computation 
we need to know the distribution of heat, computed as shown 
in table 5, col. H, and also the amount of heat delivered by the 
sun during the period under consideration. In this way the 
quantity of heat delivered directly at various depths may be 
computed and compared with the number of calories that 
passed through the corresponding levels. These results can 
be platted as work on the curve of distributed work (pi. VII) 
and the area thus deducted from the work-curve will repre¬ 
sent the aid given by the sun. 
If this method is applied to the mean temperature curve 
of lake Mendota, the result will show that about 16% of the 
work involved in the distribution of the heat may be con¬ 
tributed directly by the sun. The amount thus contributed 
will vary greatly in different parts of the warming season, 
being least in April, when the heat is being carried rapidly 
to considerable depths, and greatest in June, when the 
