Birge—An Unregarded Factor in Lake Temperatures. 995 
average temperature remains the same, the thermal resistance 
will rise and fall in proportion to the difference in temperature 
between the upper and lower surfaces. If, under these con¬ 
ditions, the temperatures of the surfaces are 11° and 8° re¬ 
spectively, the resistance will be three times as great as if 
they were 10° and 9°; the average temperature being the same 
in both cases hut the gradient being steeper in the first example. 
If the temperature gradient is not a uniform one, then the 
temperature, T, is not a linear function of z. In such cases 
f(z) |z —can be plotted and the value of W found by 
means of v a planimeter. 
The fact that the thermal resistance to mixture increases as 
the temperature rises has important and wide applications. 
First, it has much influence on the rapid distribution of heat 
through the lake in the spring as compared with its slow pene¬ 
tration later in the season. Even in our deepest Wisconsin 
lakes, like Green Lake (72 m.) the temperature of the bottom 
water goes up to 5°, or even 6°. So, too, the water at all 
depths of the lake acquires heat most rapidly in spring and 
early summer. A lake of considerable depth gains little heat 
after the first of July. Its gains are greatest in April, May, 
and the early part of June. Yet the surface receives more 
calories during July and August than during the earlier months. 
This rapid gain and distribution of heat in spring has forced 
some students of lake temperatures to conclude that the water 
is more diathermous in spring than in summer. So Ule (’01, 
p. 126) says that from the rapid gains of heat in spring we 
must draw the conclusion that the diathermancy becomes less 
.in the course of the summer. This may or may not be the 
case, but it never happens to a degree which makes any not¬ 
able difference; since in all lakes and at all times the upper 
meter of water receives most of the heat. 
But the wind and the currents derived from its influence 
are mixing agencies which become less efficient as the lake 
warms, if equal temperature gradients are assumed. At 10° 
they are 10 times less efficient than at 5°; only one-third as 
efficient as at 6° ; and less than one-half as efficient as at 7°. 
