382 Wisconsin Academy of Sciences , Arts, and Letters. 
Plate VII. Direct curve of work and curve of distributed work. 
The full line, A B D D, is the direct curve. To obtain this the 
value of W for each meter is taken from table 1 and is platted in 
the middle of the space assigned to the meter. These points are 
then connected by a curve. Each horizontal space equals 10 g. 
cm. and each vertical space equals 1. Then the area MA 1 gives 
the value of W for the stratum 0 m.-l m.; 1 AB 2 gives the value 
of W for the lm.-2 m. stratum, etc. The area enclosed by the entire 
curve will give the total value of W. This curve shows the work 
done in behalf of each stratum. 
The broken line, RR, gives the curve of distributed work, 
showing the work done in each stratum. It shows graphically 
the results given in table 5 col. F. The total area enclosed by the 
curve is the same as that of the direct curve. The dotted area in 
the 1 m.-2 m. stratum shows the amount of work done in that 
stratum in warming it (table 5 col. E). The remainder of the 
area 1 CD 2 shows the amount of work done in it in order to carry 
heat to deeper strata (col. D). 
The numbers from which the curves are platted are given in g. 
cm. per sq. cm. of the surface of the lake. They can be converted 
into g. cm. per sq. cm. of the area at any depth and the results 
would be similar to those shown in pi. 8. 
