368 Wisconsin Academy of Sciences , Arts , and Letters. 
indifferent equilibrium at 4° (D =1) to a similar condition at 
a higher temperature and a smaller density. 
This formula* is 
W = (CG) X (RT) X (1 — Dm). (Formula III.) 
In this formula, CG equals the distance from the surface 
of the lake to the plane in which is found the center of gravity 
of the lake. 
RT is in this case the mean depth of the lake. 
1 — Dm is the mean value of 1 — D for the lake at the higher 
temperature conditions that have been developed. 
This formula means that the work involved in the pro¬ 
cess described is that necessary to move a weight equal to 
(1 — D) multiplied by the mean depth of the lake, through a 
distance equal to that of the center of gravity from the sur¬ 
face of the lake. 
The value of 1 — Dm for lake Mendota in the temperature 
conditions used in former examples is 0.001705. 
The value of CG is 835 cm.; of RT 1210 cm., which for a 
column 1 cm. square is equal in weight to the same number of 
grams. 
Therefore W =835x1210x0.001705 = 1722.65 g. cm. per 
sq. cm. of the surface of the lake. 
But it has been already shown (p. 349) that the work nec¬ 
essary to produce the temperature condition here discussed 
is 1209.18 g. cm. The work necessary to complete the dis¬ 
tribution of the heat, according to Schmidt’s method, is 
514.25 g. cm. (p. 367). The sum of these is 1723.41 g. cm., a 
result which checks quite accurately with that given above. 
If therefore one desires to know the stability of a lake for 
which he has computed the work necessary to bring its tem¬ 
perature into a certain condition, the result may be derived 
as above. 
It should be noted that the value of (CG) X (RT) is ap¬ 
proximately equal to the sum of the factors given in table 1, 
col. G for RTxZ. Conversely, the position of CG may be 
derived from the formula 
CG = 2(RTXZ)^ 
*This formula has been given to me by Professor G. S. Slichter, who also 
pointed out the relation here stated between my results and those of 
Schmidt. 
