Birge—Work of Wind in Warming a Lake. 359 
This comparison shows the state of the facts more clearly 
than the other. The deep water of lake Geneva has over 80% 
as much heat as Green lake has, and this difference is a meas¬ 
ure of the disadvantage in gaining heat which the shallower 
lake finds, so far as one observation can indicate this. The 
work needed to distribute this smaller quantity through the 
water below 20 m., is more than 25% greater than that needed 
by Green lake. 
By comparisons of this sort it is not difficult to ascertain 
whether the limitations of the heat budget of a given lake 
are due to area or to depth, and to state, roughly, the 
amount of such limitations. 
13. OTHER METHODS OF EXPRESSING THE WORK OF THE WIND. 
In the preceding pages both heat and work have been 
stated in units referred to a unit of area of the surface of the 
lake. This is in general the most convenient way of stating 
the facts; but other units may be employed if desirable. 
If the total quantity of work done on a lake is desired, this 
may easily be derived from the results already reached. 
These are given in gram-centimeters per square centimeter 
of the surface of a lake having a certain area and mean depth. 
If this amount is divided by 10 the result will show the num¬ 
ber of kilogram-meters per square meter of the surface. This 
result again multiplied by the area of the lake in square 
meters will give the total work done in kilogram-meters. In 
the example from lake Mendota we have: 
W = 1208.9 g. cm. per sq. cm. of surface. 
Dividing by 10 we have W = 120.89 kg. m. per sq. m. 
of surface. 
But the area of lake =39.4 X10 6 sq. m. 
Hence, W = 120.89 X (39.4 X10 6 ) kg. m. =4759 X10 6 kg. m. 
This is the total amount of work represented by the warm¬ 
ing of the lake from 4° to 19.11° in 1910. 
The volume of the lake is 478.4 X10 9 kg. and this number 
multiplied by 15.11 cal. gives a summer heat-income of 
7229 X10 9 large calories. It will be noted that the ratio be¬ 
tween quantity of work and of distributed heat is the same 
by this computation as by the first method. It is also obvious 
that if work is stated as a total amount for the entire lake, 
it is possible to compare the work done in the same lake in 
