Birge—Work of Wind in Warming a Lake. 
353 
Then it follows at once that 
w= xJo z (1_dz) M (z) dz (1) 
This is the same result as that reached by more ele¬ 
mentary methods in the preceding pages. The simpler 
methods of computing the result are better, however, 
than any method of mechanical quadrature. 
Schmidt’s measure of stability is the work necessary to 
mix the water at any time to a uniform mass of the then 
mean density, or 
W S = J\ (1—d.) M (Z) dz (2) 
Reducing this result to unit area of surface we obtain 
Ws 1 A= xj ! z ° (i _dz) m (z) dz (3) 
Now since z — z =z 0 , we can write 
J z(l — d z ) [jl (z) dz — 1 z(l—dz)/z(z) dz 
o Jo 
= j\ 0 (1 — d z ) n (z) dz (4) 
Hence substituting (1) and (2) in (3), 
W,/A+W = iJ^(l-d z ) ix ( z)dz 
= |x'zXh(l-D) (5) 
We therefore see that Schmidt’s measure of stability 
(divided by the area A) can be found by subtracting Dirge’s 
result from the expression zh (1 — D) / A. 
This forms a ready way of computing Schmidt’s measure 
of stability after the measure of work has been found by 
the methods set forth by Birge in the preceding pages. 
9. DETERMINATION OF WORK AND HEAT FROM DIAGRAMS. 
A second method of determining the amount of work, 
and one that is quite as accurate as computation, if general 
answers are desired, is to plat the results on a diagram and 
