Birge—Heat Budgets of American and European Lakes. 167 
Forel and Halbfass in their discussion as to the effect of latitude 
on the heat budget. The mean temperatures employed are 
chiefly taken from two papers by Halbfass (Halbfass ’05, TO). 
Without these compilations of numerous temperature observa¬ 
tions from many authorities, gathered and computed with great 
care and labor, this paper could not have been written. In some 
cases I have checked Halbfass’ results and usually have found 
that my computations closely agree with his. In some other 
cases, I have computed for myself the mean temperature ot 
European lakes and such results are marked by a star in 
Table A. 
No doubt more complete study will show that the heat bud¬ 
gets of the several lakes are influenced by elevation, surround¬ 
ings, size of affluents and effluent, climate, cloudiness, latitude, 
and other conditions as well, but at present a direct and unmis¬ 
takable effect of any one of these conditions can be pointed out 
in very few cases and it is best to consider the budgets in gross 
and without too much attention to particular circumstances. 
Certain preliminary questions must be discussed before pro¬ 
ceeding to the comparison of American and European lakes. 
These are: (A.) The definition of the heat budget. (B.) The 
unit which should be employed in stating it. (C.) The value of 
temperature observations, such as those from which the budgets 
have been computed. 
A. Three things may be understood by the heat budget of a 
lake: 
1. The amount of heat necessary to raise its water from 0° C. 
to the maximum temperature found in summer. This may be 
called the gross or crude heat budget. 
2. The amount of heat necessary to raise its water from the 
minimum temperature of winter to the maximum summer tem¬ 
perature. This may be called the annual heat budget. 
3. The amount of heat necessary to raise its water from 4°C. 
to the maximum summer temperature. This may be called, for 
reasons explained in the report on the Finger lakes, the wind- 
distributed heat or the summer heat-income. (See Birge and 
Juday, T4, p. 562.) 
Of these three conceptions, the first is of least value, since 
it does not correspond to any facts in nature. No lake falls to 
0° in winter, so that this temperature is not a starting point 
for any actual gains or a terminal point for losses. Still further; 
