Birge—Heat Budgets of American and European Lakes. 175 
duces the number of calories to a comprehensible sum, but the 
expression is little more than a mathematical result under the 
circumstances to which it is applied. If temperatures had been 
tkken daily, or even weekly, during the warming period of these 
lakes, it might be worth while to compute daily gains. But the 
case is far different. We must depend on a few—perhaps two— 
isolated observations in each year, one for winter and a second 
one for summer. Under such conditions a statement of “mean 
daily gains” has little meaning. There is really no significance 
in a ‘'mean value” for the daily gain between (say) Feb. 5 and 
Sept. 7. The first month of this period may represent a daily 
loss; then may come daily gains increasing in amount and reach¬ 
ing a maximum in April or early May; then a slowing of gain 
leading to an almost stationary condition by late July and Au¬ 
gust, and passing probably into small losses in the later part of 
the period. Under such conditions, a statement of the mean 
daily gain or loss means little or nothing. A good illustration 
may be taken from lago di Como in 1904 (Halbfass, ’10, p. 62). 
The winter temperatures were as follows: Jan. 26, 7.11°; Feb. 
26, 7:00°; Mar. 28, 7.15°. The maximum recorded temperature 
of 8.96° was noted on Aug. 27. If the winter temperature in 
January only had been recorded, the mean daily gain would have 
been stated as about 160 cal. per day; if February had been 
taken, about 200 cal.; if March, about 220 cal. As a matter of 
fact, the temperature was substantially stationary during two 
months of the winter, and the mean daily gains stated for the 
season will vary nearly 40%, according to the winter date se¬ 
lected as the point of departure. The annual heat budget, how¬ 
ever, is much the same whichever winter date is chosen. 
The third method was first proposed, so far as I know, by 
Wojeikoff (’02, pp. 193-199) in a discussion of Forel’s results. 
The same method was suggested by Wedderburn* (’10, p. 134). 
This method could not be applied widely until such a compila¬ 
tion of lake temperatures had been made as Halbfass’ papers 
have furnished, and neither of the authors named has made any 
serious attempt to apply it. 
The Wisconsin Geological and Natural History Survey has 
used this method in all of its work on Wisconsin lakes, which 
* It may be noted that the figures given for lake Geneva by Wedder- 
burn (76,000 gr. cal. per sq. cm.) are certainly much too high. Loch 
Ness is assigned 34,000 cal., which is lower than my computations. 
