Birge—Work of Wind in Warming a Lake . 
347 
4. ILLUSTRATION OF USE OF FORMULA I. 
As an illustration of the use of formula I, let the stratum 
between 20 m. and 21 m., in a given lake, be warmed from 
4° to 8°. How much work is involved in this rise of tem¬ 
perature? 
In this case let RT = 56 cm. or 56 g. for a column 1 sq. 
cm. in area. 
Z = 2050 cm. 
The density of water at 8° is 0.999876. Hence 1 — D 8 = - 
0.000124. 
Hence, W =56X2050X0.000124 = 14.235 g. cm. 
It thus appears that work amounting to 14.235 gram- 
centimeters per square centimeter of the surface of the 
lake is needed to raise the temperature of the stratum in 
question from 4° to 8°. 
To the 20 m.-21 m. stratum there have been delivered' 
224 g. cal. (56 X [8-4]) per square centimeter of the area 
of the surface of the lake. It is therefore fair to say that 
the transport of 224 cal. from the surface to a mean depth of 
20.5 m. has cost 14.235 g. cm. of work. 
In a similar way the work required to warm each stratum 
of the lake may be computed. The sum of the several 
products will equal the work expended in warming the lake. 
It must be noted that the work cannot be correctly com¬ 
puted for the lake as a whole by using for RT the mean 
depth of the lake, and for D the density of water at the 
mean temperature. This is because the density does not 
vary directly as the temperature, but decreases more rapidly 
than the temperature rises. As a result the value of 1 — D in 
the warm strata has greater weight in determining the 
mean density than has the value of T in the same strata in 
determining the mean temperature. The mean value of 1 — D 
for the several strata of the lake is therefore higher than the 
value of 1—D for the mean temperature of the same strata. 
Compare on this matter plates IV and V. 
It is also true that in order to secure great exactness in 
determining the mean temperature the density of the several 
strata should be considered. If this were done, however, 
the results would be but little altered, and any change would 
