998 Wisconsin Academy of Sciences, Arts, and Letters. 
sistance to mixture at temperatures below 4° is so small that 
we need not be surprised that the whole mass of water is 
readily cooled by circulation to 3°, or even 2°. On the other 
hand, the rapid increase of resistance to mixture per degree 
as zero is neared indicates one reason why the temperature 
curve of inverse stratification is never a straight line, and 
why, even in larger lakes and at the moderate depth of 20 m. 
to 25 m., bottom temperatures are rarely so low as 1°. I 
ought to add that Wedderburn (’09) seems to understand this 
relation very fully. His paper was received just as this is 
going to press. 
Thus many of the facts of lake temperature find an easy 
explanation when the principle is accepted that the thermal re¬ 
sistance to mixture increases as the temperature departs from 4°. 
I have called especial attention to its bearing on those problems 
for which students of limnology have found only a partial 
solution. Among these are the rapid warming of the lake in 
spring and early summer; or stated in a different way, the 
rapid descent of the isotherms as the lake begins to warm, as 
compared with the slow penetration later in the season of iso¬ 
therms representing higher temperatures. Similar problems 
are the cooling of the lake below 4° ; the position, persistence, 
and stability of the thermocline in spite of disturbance by 
violent winds. In all of these and other cases which involve 
the work of the agents for distributing heat, the fact must be 
considered that a limit is always set to the efficiency of these 
agents by the thermal resistance to mixture. Water is so 
nearly a perfect fluid that if its temperature could rise with¬ 
out a change of density the distributing agents in any lake 
would quickly distribute the warmer surface strata through 
the whole mass of the water. The most effective means of 
limiting this distribution is the rapid increase of the rate of 
decline of density as the temperature rises. 
In this discussion it has been assumed that water is a per¬ 
fect fluid. This is not the case; water is viscous and its vis¬ 
cosity is not without influence on the ability of the wind to 
mix it. If a lake were composed of a perfect fluid, thermal 
resistance would be the only force opposing mixture. In a 
