574 
BULLETIN OE THE BUREAU OF FISHERIES. 
This difference between the deep and shallow lakes, however, is relatively less 
apparent in the epilimnion than in the thermocline and hypolimnion. In these regions 
the second disadvantageous factor of the shallower lake comes in with more influence. 
The gains of heat of the water in and below the thermocline depend wholly on mechanical 
mixture. There are no gains from the sun and no losses to the air and practically no 
losses by conduction. Hence the thermal resistance to mixture “ is the factor which 
resists the transfer of heat downward, and the influence of the wind, direct or indirect, 
is the force which carries the heat down. But the thermal resistance increases much 
more rapidly than the temperature rises and soon puts an end to the force of the wind 
in carrying the heat downward. If we compare the thermocline of Otisco and Canadice 
Lakes, we find that the region is included between the same levels in both lakes and that 
the temperature is not greatly different (Canadice, 12.9°; Otisco, 13.2°). The advantage 
in temperature is on the side of the shallower lake. But the reduced thickness of the 
region in Otisco Lake is only 3.05 meters as against 3.76 meters in Canadice. The 
total amount of heat in the region is therefore about 17 per cent less. 
If the thermocline of Otisco Lake were to derive as much heat from each square 
centimeter of surface as did that of Canadice, Tm-4 for that region must be 15.7°, or 
2.5° above that actually reached. A great amount of energy is needed to produce this 
increase from 13.2° to 15.7° by mixture. The increase of temperature is about 19 per 
cent but the work to be done in effecting this increase is much greater than that. 
The work to be done in warming a stratum of water which lies below the direct 
influence of the sun is done against gravity which resists the descent of the warmer and 
lighter water. The net work done in warming a stratum of water to a given degree 
may be measured by the energy which would be needed to transport the mass of water, 
thus warmed, to the place where it is found, against the resistance of denser water at a 
temperature of 4°. We may think of such a stratum as pushed down to its place through 
water at 4°, somewhat as a sheet of cork might be forced down through the water. The 
weight to be moved is the difference in weight between the warmed water and water at 
the temperature of maximum density. The distance through which it is carried is the 
mean distance of the stratum in question from the surface. 
In this case the difference in the amount of work necessary to warm the thermo- 
cline to 13.2° and 15.7° is proportional to the difference in loss of weight of water at 
these temperatures. A liter of water at 13.2° weighs 621 milligrams less than at 4°, 
and this is the weight of each liter to be used in computing the work done in warming 
the thermocline. At 15.7° the weight of a liter is 982 milligrams less than at 4°. Thus 
over one-half must be added to the work which was done in warming the water to 13.2°, 
if 2.5°, or about 19 per cent, are added to the heat. 
A similar statement may be made for the hypolimnion. If this region in Otisco 
Lake is to receive as many calories per square centimeter of the surface of the lake as 
does that of Canadice, its temperature will rise to 12°. But to effect this rise would 
require, if measured on the same basis as in the former example, more than three times 
aBirge, Edward A.: An unregarded factor in lake temperatures. Transactions Wisconsin Academy of Sciences, vol. xvi, 
pt. 2, p. 989. 1910. 
