174 Wisconsin Academy of Sciences, Arts, and Letters. 
Bruckner (’09, p. 305) thinks that in spite of the objections 
of Wojeikoff and Halbfass, Forel’s units are the best for the 
study of the physics of lakes, since they give exactly the facts 
of temperature for that part of the lake which covers the cen¬ 
tral plain (“der sogenannte Sehweb”). We do not know ex¬ 
actly the temperature of the shallow parts of the lake, nor do we 
know exactly its volume, so that we cannot apply the needed cor¬ 
rections to this temperature. These considerations have a cer¬ 
tain value, but, as already indicated, they are not of very much 
weight. The statement that Forel’s units give a better idea of 
the physics of the lake may hold perhaps against Halbfass ’ meth¬ 
od, but not against that of Wojeikoff, or that used in this paper. 
Indeed, as has already been indicated, if the student desires to 
correlate the heat cycle of the lake with that of the season, units 
of surface, depth, and temperature must be employed which will 
state the facts for the entire lake and not merely for a part of 
it. 
The second method was introduced by Halbfass and was first 
applied by him in the papers to which reference has already 
been made. It has the fundamental advantage over Forel’s 
method of basing itself on the mean temperature of the entire 
water of the lake and not upon that of part of it. But the use 
of the entire volume of the lake as a factor for computing total 
gains and losses of heat destroys for comparative purposes a 
large part of the advantage gained from the use of the mean 
depth in ascertaining the mean temperature of the water. This 
method employs a factor which varies with the individual lake, 
and thus restores in the result a difficulty similar to that which 
Forel’s method suffers from his use of the maximum depth in¬ 
stead of the mean depth. A method by which the daily gains of 
loch Garry amount to 7 cal.; of loch Ness to 140; lake Geneva, 
1430; and Wettern, 3400 cal. can give no really comparable re¬ 
sults. Halbfass finds that in comparing lakes, he must select 
those of the same volume, and these he can roughly compare. 
This is true also under Forel’s method if confined to lakes whose 
maximum depth is similar and in which the ratio JI m . is nearly 
Dmx 
the same. But in both these methods the opportunity for com¬ 
parison is greatly restricted. 
Halbfass states gains and losses of heat in calories per day 
during the interval between the observations. This method re- 
