354 Wisconsin Academy of Sciences , Arts , and Letters . 
measure the areas. This will be discussed later. There is 
no saving in time and little, if any, gain in accuracy if one 
desires to know the quantity of work done for the single 
strata. 
10. THE CURVE OF DISTRIBUTED WORK. 
The results thus /far reached show the amount of work 
done in warming a single stratum or an entire lake. They 
show that 14.235 g. cm., for instance, are needed to warm a 
given stratum but they do not show where this work is 
done or how it is distributed. The same is true of the state¬ 
ment for the lake as a whole. The several products com¬ 
bined in the general result of table 1 show the amount of 
work done in behalf of each stratum, but not where this 
work was done. If this is to be determined a second compu¬ 
tation is necessary. In the case of the 20 rn.-21 m. stratum 
the warmer and lighter water was carried from the surface 
to a mean depth of 20.5 m. Equal work was done in each 
unit of this distance. If the whole work is divided into 41 
parts, two parts, or 4.88% of the whole, were expended in 
each meter above 20 m. and one part, or 2.44%, in the 20 
m.-21 m. stratum. Thus in order to warm the 20 m.-21 m. 
stratum, 0.695 g. cm. of work was done in each meter above 
it, and 0.348 g. cm. within it. In a similar way, if the lake is 
divided into equal strata, the work for each stratum may be 
distributed; two shares being given to each higher stratum 
and one to the stratum in question. Of the work necessary 
to warm the 1 m.-2 m. stratum, for instance, 66.7 % belongs 
to the 0 m.-l m. stratum and 33.3% to the 1 m.-2 m. stratum; 
40% of the work belonging to the 2 m.-3 m. stratum goes to 
each of the two strata above it. 
In this way there may be computed the work done in each 
stratum. This may be platted as a curve which may be called 
the curve of distributed work. The computation of such a table 
for Lake Mendota is given in table 5, and the method of 
computing the result is explained under the table. The 
results of this computation are shown in plate VII. 
