176 Wisconsin Academy of Sciences, Arts, and Letters. 
has been going on since 1898. It is the only method applicable 
under our circumstances, which involve a comparison between 
the heat budgets of lakes differing widely in form and area, but 
similarly situated as regards topographic and climatic condi¬ 
tions. It allows us to determine the influence of such factors 
as the area and depth of lakes on the amount of heat taken in 
by them. This unit, therefore, is employed throughout this 
paper. 
If the heat budgets of lakes are to be widely studied, units 
must be selected, both for temperature and area, such that lakes 
may be compared in spite of great differences in area and depth. 
We have, therefore, computed the mean temperature of a lake 
on the basis of its mean depth. We derive the number of gram 
calories per square centimeter above zero, represented in this 
temperature, by multiplying it by the mean depth expressed in 
centimeters. We employ the gram calorie as the unit of heat 
and the square centimeter as the unit of area, because these units 
are employed by the meteorologist in stating the amount of heat 
received by the earth’s surface from the sun. 
C. The third preliminary question concerning the character of 
the observations from which our conclusions regarding lake tem¬ 
peratures are derived. The results shown in Table A are based 
on series of temperatures taken at the deepest part of the lake 
concerned. There is no difficulty in ascertaining with sufficient 
accuracy the mean temperature of the column of water in which 
such observations were taken. Nor is it difficult to compute 
from such observations the mean temperature oi the water of 
the lake, provided a hydrographic survey of the lake has been 
made. But does such an expression give a correct idea of the 
mean temperature of the water? On this matter Wedderburn 
states (’07, p. 408) : “It is in a far greater degree impossible 
to deduce the average temperature of a large loch from observa¬ 
tions made in any one place.” Halbfass also speaks (’13, p. 471) 
of “die Bedeutingslosigkeit einer Beobachtungsserie in verti- 
kaler Richtung in einem vereinzeltem Punkt eines Sees”. 
If these statements are correct, then plainly such a paper as 
this, or those of Halbfass, are of no value, since they are based 
on just such observations as Wedderburn calls “futile” in the 
paper quoted, and which Halbfass thinks are “bedeutungslos” 
These are practically the only kind of observations now published 
for any lake. So far^as I am aware, there is no lake whose tern- 
