170 Wisconsin Academy of Sciences, Arts, and Letters . 
the annual heat budget, which has little, or nothing, to do with 
the capacity of the lake for absorbing heat. This capacity may 
often be more exactly shown by the wind-distributed heat than 
by the annual heat budget. 
The fact that winter losses and summer gains are measurably 
(although not wholly) independent of each other may also be 
seen in the budgets of tropical lakes, like Como and Geneva. 
Both lakes show greater variations in the winter than in the 
summer temperatures, and the annual heat budgets of both lakes 
are more variable than is common in lakes which regularly 
freeze during the winter. 
B. The heat budget in any of its forms may be expressed in 
various ways, as follows: 
1. The number of calories necessary to warm a column of 
water of unit base in the deepest part of the lake from the se¬ 
lected minimum (0°, 4°, winter minimum) to the summer tem¬ 
perature. This is the method followed by Forel. 
2. The total sum of the calories necessary to warm in a simi¬ 
lar way the whole mass of the water of the lake from the selected 
minimum to the summer temperature. This is the method em¬ 
ployed by Halbfass in his paper of 1910. 
3. The total number of calories necessary to warm in a sim¬ 
ilar way a column of water of unit base and a height equal to 
the mean depth of the lake. This method is used in this paper. 
The first method was that employed by Forel (’95, p. 400, and 
’01, p. 41). It is well suited to very deep and very large 
bodies of water in which the annual temperature changes are 
confined to the surface strata, and whose area is so great that 
we may, without appreciable error, neglect the difference be¬ 
tween the volume of the upper part and the lower part of the 
stratum in which these temperature changes take place. Such 
bodies of water are oceans and seas, and possibly also the very 
largest fresh water lakes. In the ordinary inland lake, how¬ 
ever, neither of these conditions is met, and the method of stat¬ 
ing the heat budget is correspondingly defective. It is also 
true, as stated by Forel, that it is not possible by this method 
to compare the heat budget of different lakes. 
Forel at first took as his data the temperature found at the 
surface and at the successive 10 m. levels of'the lake and added 
them. Since a column of water 1 cm. square and 10 m. high 
