366 Wisconsin Academy of Sciences , Arts and Letters. 
amount of work needed to complete the distribution of heat 
through the lake and so to bring the lake again to a condition 
of uniform temperature and indifferent equilibrium. The 
amount of this work may be expressed in kilogram-meters 
for the total volume of the lake or in the amount of the dis¬ 
placement of the center of gravity of the lake, which this 
amount of work would effect. Problems relating to the tem¬ 
perature seiche, and others as well, may be discussed in the 
light thrown on them by the stability thus ascertained. 
Schmidt’s point of view is very different from mine. He 
starts with a certain condition of heat (and therefore of 
density) and desires to follow out the further effects of this 
condition. I ask how much work was required to bring about 
that condition of temperature. He determines the stability 
and sees in this an important factor in advancing our knowl¬ 
edge of movements of the water such as the temperature 
seiche. I attempt to determine the work done in distribut¬ 
ing heat; and I hope, by solving this problem, to get more 
light on the relation of the area, depth, and form of lakes to 
their heat budget. 
Schmidt’s problem begins where the problem ends which is 
discussed in the present paper. He considers not the amount 
of work needed to produce the stability (and this is another 
way of stating my problem) but the amount necessary to 
continue the distribution of heat until an indifferent equili¬ 
brium again results. 
It is not necessary here to discuss Schmidt’s methods in 
detail. Their mathematical theory is very skilfully worked 
out and rests on the calculus. Practically the problems are 
solved graphically and the methods of constructing the dia¬ 
grams are given. These are also excellent, and I will apply 
them to the case of lake Mendota which has already been 
discussed, in order to show more clearly the relation of the 
methods and of the results obtained. 
Since the result is to be stated in terms of the effect on the 
center of gravity, the position of the level is determined in 
which this lies, and the moment of each stratum above this 
plane and below it is computed. The horizontal lines of fig. 
9 show the result for lake Mendota, computed by 1 m. in¬ 
tervals. The center of gravity (CG) lies at 8.35 m. The ver¬ 
tical distance between the several meter lines of the diagram 
