Birge—Work of Wind in Warming a Lake. 369 
In this formula 2 (RT X Z) is the sum of the products in 
table 1, column G. A is the area of the lake and V its volume. 
The result thus obtained will be only approximately correct 
and will need adjustment if accurate computations are to be 
made by Schmidt’s method. 
The value for the stability thus obtained may readily be 
converted into other units, such as the displacement of the 
center of gravity, or the total amount of work in kg. m. 
Attention is again directed to the point, that in formula 
III the value of 1 — D for the mean temperature of the lake 
can not be used instead of the mean value of 1 ~ D (cf. p. 347). 
It is also apparent that the value of the total work, as 
computed in this paper, may be called the complement of the 
results obtained by Schmidt, and may be derived from his 
results in the same way that his results may be derived from 
mine. The choice of methods is, however, by no means a 
matter of indifference. So far as total results go they reach 
the same conclusions and involve about equally tedious com¬ 
putations. They lend themselves equally well to graphical 
methods. But the case is different when one desires to examine 
the results for single strata of the lake or to compare strata in 
different lakes. In my method the datum plane, from which all 
computations start, is the surface of the lake; in Schmidt’s 
method the datum plane is that of the center of gravity. I 
use the surface to which the energy of the wind is directly 
applied and that from which the distribution of heat starts in 
fact. It is also the surface which is a chief factor in any dis¬ 
cussion that involves other surfaces and volumes of the lake. 
We must start from this surface for instance, in order to 
determine the position of the center of gravity. My method 
therefore seems to be the more simple and direct one. The 
results which Schmidt reaches can readily be obtained by it, 
and others as well which may be used in the discussion of a 
wider range of problems. 
