992 Wisconsin Academy of Sciences, Arts, and Letters. 
liter of water at any given temperature and at a temperature 
one degree lower. Thus, a liter of water at 10° weighs 81 
mg. less than one at 9° ; at 25° a liter is 252 mg. lighter than 
at 24°. These numbers, therefore, express the differences in 
density and weight which for a temperature difference of 1°, 
(1) enable a layer of water to set up convection currents if 
it lies above a warmer stratum, and (2) which enable a 
stratum of water, warmer above and cooler below, to resist 
mixture attempted by mechanical agencies. 
It is evident that the differences shown in column III for 
a rise or fall of one degree become greater as the temperature 
rises above or sinks below 4°. From this fact it follows that 
a given mass of water—Say, a cubic decimeter—which has 
been cooled one degree below the temperature of the water 
beneath it, will act with greater energy in setting up convection 
currents in proportion as the initial temperature was distant 
from 4°. It also follows that a column of water of unit area 
and height whose upper surface has a temperature one degree 
higher than its lower surface, will offer a thermal resistance 
to mixture greater in proportion as the average rises above 
4°; it being assumed that the temperature gradient in the 
column is uniform. 
Hor is this difference a small one, as may be seen from col¬ 
umn IV. In this column the convection capacity (if I may 
coin an equivalent for the German word Auftrieb), and the 
thermal resistance to mixture corresponding to the temperature 
difference of one degree at 4°-3° or 4°-5°, is taken as unity 
and the relative value is given for the same difference at higher 
and lower temperatures. At 10° its value is more than ten 
times as great as at 4° ; at 15° it has increased eighteenfold; at 
20° more than twenty-five fold; and at 30° it is more than 
thirty-seven times larger than at 4°. 
Grolks paper (p. 48) expresses this fact in relation to con¬ 
vection by stating the number of liters of water which would 
be needed to make a mass that weighs 1 kg. less than the 
same mass of water one degree cooler. Such a mass of water 
is necessary at the given temperature to secure “1 kg. Auf- 
