172 ! Wisconsin Academy of Sciences, Arts, and Letters. 
In these tables I have stated the results in small calories pel* 
sq. cm. of surface, in order to make them comparable with those 
given elsewhere in this paper. To agree with Forel’s notation 
they should be divided by 10. 
The figures are much higher for the deeper lakes than are 
those given by the other methods. They are correct so far 
as they go, but they may easily deceive. It is doubtless true-— 
as the defenders of Forel’s method replied to Halbfass—that 
these figures state correctly the amount of heat necessary to 
warm the given column of water in accordance with the observa¬ 
tion. They do not show, however, how much of this heat came 
direct from sun and sky, and how much came in laterally from 
columns of water in the lake which are shorter, and therefore 
contain less heat. In other words, if the result for the column 
is carried over to the lake, the successive levels of the lake are 
treated as if each contained the same volume, and as a result 
the figures given in Table 1 show a much greater gain of heat 
than could possibly come directly from sun and sky, or from any 
other source outside of the lake. It is not probable that more 
than 70,000 gr. cal. per sq. cm. could be thus received by the 
surface of a lake during the five months, April to August, in¬ 
clusive. It is quite beyond possibility that so many as 62,000 of 
these could be stored up in a lake. Thus, while a record of this 
sort may have a certain value for comparing results within a 
single lake at different times or in different years, it has little 
value for such a purpose as that for which it was used by Forel, 
viz., for comparing the relative gains of heat in lakes which lie 
in different latitudes. 
In Table 2 the gains shown for the shallower lakes, Canadice 
and Otisco, are much lower, relatively to the deeper lakes, than 
would be shown by a comparison based on mean depth rather 
than maximum (see Birge and Juday ’14). This is merely an¬ 
other illustration of the fact that different lakes can not be com¬ 
pared by this method. It deals with columns of water, not 
with lakes, and results reached by it can not be applied to lakes. 
Not only may this method make the results larger than can 
be true for the lake, but the amounts of heat shown for the 
same lake in different years may differ more widely than they 
should do. In Seneca lake, for instance, the budget for 1910, 
as shown in Table 1, is nearly 24% greater than in 1911. This 
