352 Wisconsin Academy of Sciences, Arts, and Letters. 
In most cases, when general results only are desired com¬ 
putation by 5 m. intervals gives sufficient accuracy; especially 
if single meters are used in the thermocline where the tem¬ 
perature (and therefore the value of 1 — D) is changing rapidly. 
8. MATHEMATICAL STATEMENT OF THE WORK OF 
THE WIND. 
In the preceding discussion I have treated the subject in a 
way essentially non-mathematical,—a manner suited to my 
small mathematical knowledge, and, I imagine, to that of 
most students of lakes. The matter may, however, be stated 
in mathematical form and has been so stated for me by Dr. 
C. S. Slichter, professor of applied mathematics, University 
of Wisconsin. His kind assistance in this matter, as in 
many others, is gratefully acknowledged. His report is as 
follows: 
It is desirable to change somewhat the notation used in 
the preceding pages, if the results and formulas are to be 
stated in strict mathematical form. The symbols “RT” 
for reduced thickness and “D n ” for density at depth n are 
likely to give a misleading impression when used in formal 
mathematics. The following notation is therefore em¬ 
ployed, which is essentially that used by Schmidt (T5) 
in a paper to be discussed more fully on a later page (see 
p. 365): 
z = depth of any layer of water measured from the surface 
z o = depth of any layer of water measured from the center 
of gravity of the lake 
z= depth of the center of gravity of the lake below the 
surface 
h = total depth of the lake 
jx (z) =the reduced thickness of any layer 
d z = density of the layer of water at depth z 
D =the mean density of the lake 
A = total area of the surface of the lake 
W =work per sq. cm. of lake surface necessary to produce 
the given vertical distribution of temperature from 
a uniform density of unity at 4°G. 
W 3 = Schmidt’s measure of stability 
