168 Wisconsin Academy of Sciences, Arts, and Letters. 
the same conditions that limit the rise of temperature of a lake 
in summer limit also its fall in winter. Thus the gross heat 
budget may differ widely in lakes whose actual gain of heat per 
unit of surface are closely similar. 
A single example of this may suffice. If the mean summer 
temperature, as given in Table A, of Owasco, Cayuga, and Sen¬ 
eca lakes is multiplied by the respective mean depths of the 
lakes, the products will be 39,800 cal., 50,500 cal., 68,300 cal., re¬ 
spectively—sums which represent the number of gram calories 
per sq. cm. of surface of the lake necessary to raise its water 
from 0° to the summer temperature. These sums differ very 
greatly; but if the mean temperature of the water in winter is 
multiplied by the mean depth the result shows how much heat 
was left in each lake at the winter minimum. These amounts 
are for Owasco lake 2,400 cal., for Cayuga, 12,200 cal., and 
for Seneca, 30,000 cal. When these sums, which are no part 
of any actual heat budget, are subtracted from the gross 
sums, the remainders (which represent the annual heat bud¬ 
get) are closely alike; 37,400 cal., 38,300 cal., and 38,300 cal., 
respectively. These numbers show that the indication of the 
gross heat budget is incorrect, and that each unit of surface of 
these lakes, in spite of wide differences in area and depth (see 
Table A.), is capable of taking up the same amount of heat from 
sun and sky; and this is a fact of no little interest. 
The second conception, that of the annual heat budget, is a 
statement of facts of the first order of importance in the heat 
cycle of a lake. This method, therefore, which was used by 
Halbfass, in his comparisons of lakes, is by far the most funda¬ 
mental of these three conceptions, and should always be used 
where the data are at hand. 
The third conception, that of the wind-distributed heat, or 
summer heat-income, is one which serves much the same purpose 
as the second in cases to which it is applicable. It may be used 
in many cases where winter data are lacking, as is still true for 
many lakes. It applies only to the temperate lakes of ForePs 
classification. It has no significance for polar lakes, which do 
not rise above 4°; and in reference to tropical taxes it has the 
same difficulties that apply to the gross heat budget, as noted 
above. But for temperate lakes, the temperature of 4° con¬ 
stitutes, not a terminal point, but an important turning point 
in their annual temperature cycle, and most such lakes may 
