350 Wisconsin Academy of Sciences , Arts, and Letters. 
other method. Yet the results may be closely similar as 
may be seen from the following example, in which the same 
temperature series from Lake Mendota as that given in 
table 1 is computed by 5 m. intervals. 
TABLE 2 
Heat and work in Lake Mendota, computed by five-meter intervals. 
Depth, m. 
Temp. 
RTXZ 
1 — D 
G. cm. 
Cal. 
0-5 
23.2° 
101200 
0.002483 
250.48 
8140 
5-10 
20.6 
248100 
1895 
471.20 
5560 
10-15 
14.8 
315400 
844 
265.86 
2750 
15-20 
13.4 
274800 
647 
177.92 
1500 
20-24 
13.1 
73000 
609 
44.46 
290 
1209.92 
18240 
The results shown by table 2 are substantially identical 
with those of table 1, but the distribution of work is some¬ 
what different. This will ordinarily be the case when compu¬ 
tation is made by larger intervals. 
7. CAUSES OF DIFFERENCE IN RESULTS WHEN DIFFERENT 
THICKNESS OF STRATA ARE EMPLOYED IN COMPUTING. 
One fundamental cause for the differences between table 1 
and table 2 is the fact that the density of water does not 
vary directly as the temperature. The density of a stratum 
at its mean temperature is not the same as the mean density 
of the several subdivisions of the stratum. A second reason 
is because both density and volume change in going down¬ 
ward through a stratum and they do not change in a parallel 
way. Hence, the product of the means will differ from the 
mean of the several products. A third reason, which is not a 
necessary one, comes from the way in which mean tempera¬ 
tures of strata are usually computed. The sum of the read¬ 
ings taken at equal intervals in the stratum is ordinarily 
divided by the number of readings to give the mean tempera¬ 
ture, and this process for a stratum of, say, 5 m. is quite 
accurate enough. But if the temperature is changing rapidly 
in the stratum this mean will not be quite the same as that 
derived from the mean temperature assigned to the several 
meters of the stratum. If readings have been made at each 
