348 Wisconsin Academy of Sciences, Arts, and Letters. 
be in the direction of increasing the discrepancy just pointed 
out, since it would lessen the weight of T in the upper and 
warmer strata. See plates IV and V for an illustration of this 
matter. 
It will be found convenient to compute, once for all, the 
products of RT and Z for the several strata of any lake which 
it is desired to study. I have usually computed them by 
single meters to a depth of 20 m. or 25 m. and by 5 m. or 
10 m. intervals at greater depths. The sums of the several 
factors for single meters of any 5 m. interval may be used in 
case computation by single meters is not desirable or neces¬ 
sary. 
The factor 1 — D is readily taken from a table showing the 
values of 1 — D. Such a table is given herewith, (p. 391.) 
Thus a single multiplication shows the work required for 
warming any given stratum. In multiplying I have ordi¬ 
narily used only three significant figures in the factors and 
have multiplied by the aid of Crelle’s Rechentafeln. A 
certain amount of inaccuracy results from this short method, 
but there is no use in securing an accuracy of computation 
far beyond that of the data on which the computation is 
based. 
5. COMPUTATION OF WORK FOR AN ENTIRE LAKE. 
An illustration is given herewith of the process and results 
for Lake Mendota. The results show, substantially, the 
summer heat-income of the lake for 1910 and the amount 
of work necessary to distribute it through the lake. The 
temperatures are the mean of daily observations, August 
9-15, 1910. 
In practice the results shown in this table would be reached 
with much less trouble than appears. The numbers in the 
column RTxZ would be taken from a table, as would the 
values of 1 — D. The products only would need to be written 
down and added. 
The number of calories in any stratum, as shown in col. 
F, is found from the formula: Cal. =RT (T—4), in which 
RT is the reduced thickness of the stratum in centimeters 
and T is its mean temperature. See Birge and Juday T4, 
p. 559, and numerous tables in that paper. 
