Birge—Work of Wind in Warming a Lake . 
363 
It will help to bring, if not a solution, at least a partial un¬ 
derstanding of the difficult questions of the effect of the depth 
and volume of the lower water on its temperature, and so on 
the heat budget of the lakes. 
15. THERMAL RESISTANCE. 
In 1910 (Birge ’10, pp. 989-1004) I discussed the matter 
of thermal resistance. The paper gave a formula for de¬ 
termining the work done in mixing a column of water with 
unit base and height, and a uniform temperature gradient. 
This is 
AT 2 
W (ergs) =—j 2 ~(D 2 —D i) (Formula II.) 
In this A is the area and C the height of the column. D i 
is the density of the water at the upper surface of the col¬ 
umn and D 2 that at the lower surface. 
If A and C are assumed as constants—for instance, 1 
sq. cm. and 100 cm.—then the thermal resistance will vary 
according to the value of D 2 ~ D i, or (to state it in terms of 
(1 — D), according to the value of (1 — D i) — (1 — D 2 ). 
For the purposes of limnology it is convenient to assume 
the values of A as 1 sq. cm. and of C as 100 cm., to take as the 
standard temperature gradient 1° per meter, and as the stand¬ 
ard unit, the amount of work required to mix such a column 
of water whose temperature is 5° at the top and 4° at the 
bottom. In this case W = 0.0067 ergs and this value can be 
taken as the unit of work done in mixing. But since com¬ 
parative values rather than absolute quantities are needed, 
it is just as well to avoid this computation and take as the 
unit of thermal resistance D 4 — D 5 , which equals .000008. 
Then in any column of water 1 sq. cm. in area and 100 cm. 
high with a uniform temperature gradient, the number of 
units of thermal resistance is equal to ^~ - P n ; m and n be- 
o 
ing the temperatures of the water at the ends of the column. 
These relative values for differences of 1° are given in the 
paper referred to (p. 991 column IV) and are also shown 
graphically in pi. LXV (p. 1005). 
If this method is applied to the temperature series from 
lake Mendota discussed in this paper we have the following 
result. Operations are performed with 1 — D, instead of D. 
