Birge—Work of Wind in Warming a Lake. 367 
is proportional to the moment of each one-meter stratum of 
the lake. On this diagram are platted the several values of 
1 — D for the temperature condition found. The area to the 
left of the curve A A is proportional to the amount of work 
needed to overthrow the stability. That part which lies 
above C G, the center of gravity, is to be taken as positive 
and that below as negative. The areas may be measured by 
a planimeter and the quantity of energy thus determined. 
This quantity will be expressed in kilogram-meters and if 
the result is divided by the volume of the lake expressed in 
liters the quotient will equal the displacement of the center 
of gravity in meters. In this case the amount of work done 
above the center of gravity is 2867.9 X10 6 kg. m. and that 
below the center of gravity is 837.1 XlO 6 kg. m. Subtracting 
the second result from the first, we have 2030.8XlO 6 kg. m. 
as the amount of work necessary to restore the lake to a 
condition of indifferent equilibrium. 
The volume of the lake is 478000 XlO 6 liters. The measure of 
the stability is therefore S = iG ~ 6 = 0-425 cm, ; * s 
to say, the work of restoring the lake to a condition of in¬ 
different equilibrium at the higher temperature is equal to 
that of raising the weight of the lake through a distance of 
0.425 cm. 
17. COMPARISON OF SCHMIDT’S RESULTS WITH THOSE REACHED 
THE PRECEDING PAPER. 
The above result can be stated in terms similar to those 
which I have employed in this paper, in gram-centimeters 
per square centimeter of the area of the lake, and by so 
doing the relation of Schmidt’s method and mine will be 
made apparent. The mean depth of the lake is 12.1 m. and 
a column of water with this height and a base of 1 sq. cm. 
weighs 1210 g. The work necessary to restore indifferent 
equilibrium would raise all of these columns through a dis¬ 
tance of 0.425 cm., involving work to the amount of 514.25 g. 
cm. on each column (1210x0.425). 
This result may be called the complement of that reached 
by me, as the following considerations will show. A formula 
may be given from which may be computed the amount of 
work necessary to cause a lake to pass from a condition of 
