Birge—Work of Wind in Warming a Lake. 345 
of cooler and warmer water have been pushed down by mixing 
the several strata there, then work has been done which has 
left a record and this part of the work can be measured. The 
warming of this stratum of the deeper water can be expressed 
in terms of the mechanical work done in pushing the lighter 
and warmer surface water into the heavier and cooler water. 
Here again our knowledge of the process is very small and 
we can ascertain only the net results, not the exact process 
itself. The work thus done in mixing any limited stratum is 
proportional to the temperature gradient of that stratum and 
this gradient is ordinarily unknown exactly, and certainly 
varies enormously from stratum to stratum of depth and 
from place to place of area, and from hour to hour. These 
processes cannot be followed in detail since we have no con¬ 
tinuous record of the temperature changes in the lake. But 
it is possible to compare the temperature of a lake on different 
dates; to determine the amount of heat received and dis¬ 
tributed during the period; and to compute the amount of 
work corresponding to this distribution. In general I shall 
consider in this paper, the amount of work involved in warm¬ 
ing a lake from 4° to the summer maximum—the amount 
necessary for the production of the summer heat-income. 
This may be stated for the lake as a whole or for its several 
strata. 
3. FORMULA FOR COMPUTING THE WORK OF THE WIND. 
In this discussion the following symbols are used: 
A = area of lake; A 0 , or A with no sign, area at the surface; 
A 6 etc., area at the depth of 5 m., etc. 
V = total volume of the lake: V 5 - i o, volume between 5 m. 
and 10 m. 
RT = reduced thickness, i. e., the thickness of any given 
stratum if its area is made equal to that of the lake and 
its sides are vertical. It is computed from the formula 
— ~ m , in which n and m represent any two levels of the 
A o 
lake. The reduced thickness is stated in centimeters. 
T = temperature. T m . mean temperature of the lake as a 
whole; T 20 - 2 i> mean temperature of the 20 m.-21 m. 
stratum. 
