Birge—Heat Budgets of American and European Lakes . 173 
is true for the columns of water whose gains are shown, and in 
which the rise of temperature of a 10 m. section of the deep 
water involves as much heat as that of the water near the sur¬ 
face. Since, however, the volume of the lower strata of the lake 
is smaller than that of the upper, the amount of heat necessary 
to warm a given stratum of the deeper water of the lake is less 
than that needed to warm a corresponding stratum of the up¬ 
per water, and when the volumes of the several strata are con¬ 
sidered, the budget of 1910 was less than 11% greater than that 
of 1911, as is shown in Table A. 
Forel’s method, therefore, states the losses and gains of heat 
in a way which, while true for the column in which the temper¬ 
atures were measured, may be obviously impossible when applied 
to the whole lake. Thus he gives for Ladoga (’01, p. 46) be¬ 
tween certain dates a mean daily gain of 101 kg. cal. per sq. dm. 
and in a similar way for lake Enare a gain of 163 kg. cal. pei^ 
day. These sums are equal to 1010 and 1630 gr. cal. per sq. cm., 
respectively. This amount of heat is far greater than can pos¬ 
sibly be furnished to a lake by sun and sky. They are, as Bruck¬ 
ner states “vollkommen unverstandlich. ” The sun would very 
rarely deliver so much as 600 gr. cal. per sq. cm. per day for a 
month on a horizontal surface, and 1000 cal. are impossible. 
Thus it is plain that much of the apparent gain of heat in the 
column of water observed has come from other sources than sun 
and sky. As a matter of fact, it has been contributed by other 
parts of the lake whose column of water is shorter and whose 
gains are correspondingly smaller. If the gains of Ladoga are 
computed on the basis of the mean temperature and mean depth 
of the lake, they amount during the period named to about 160 
gr. cal. per sq. cm. per day, instead of more than 1000 cal. The 
smaller figure is very moderate and wholly intelligible. The 
gains of lake Enare can not be thus computed since the mean 
depth of the lake is not known; but they are probably no greater 
than those of Ladoga and can not equal one-tenth of the amount 
computed by Forel. Obviously, the results of computations 
based on the maximum depth of lakes afford no basis for estab¬ 
lishing laws concerning the relation of heat budget and latitude. 
Any conclusion on such a subject must be based on a knowl¬ 
edge of the heat gains of the average of the lake and not on those 
of a selected column of water. 
