1919-20.] Effect of Weather Changes on Soil Temperatures. 71 
(b) The Conductivity of Frozen Soil, and the Depth frozen for 
Various Surface Temperatures. 
As soon as we begin to deal with frozen soil the question of latent heat 
becomes all-important. The soil in which my observations have been made 
was found, after many experiments in November 1918, and again in 
November 1919, to contain about 45 per cent, by volume of water in its 
normal winter condition. Thus one cubic centimetre of soil contains 
*45 c.c. of water, and 36 calories are liberated in freezing it. 
If K' = the conductivity of frozen soil, 
x = total depth frozen, 
h = hours of frost, 
d 0 = average temperature of surface during li, 
then, when once the surface is frozen, the heat escaping from the 
bottom of the frozen layer to the surface must equal the sum of the latent 
heat liberated and the heat conducted to the bottom of the frozen layer 
from the 4-inch depth. From this relation the following values were 
obtained for K' : — 
1919. 
March 22/23 
' „ 23/24 
„ 24/25 
„ 25/26 
„ 28/29 
Nov. 13/14 
„ 14/15 
K' = -0046 
K/= *0040 
K' == 0050 
K' = 0048 
K' = ’0040 
K' = *0044 
K' = -0043 
giving an average value of K = -0045. 
If now we neglect the upward conduction from the 4-inch depth, which 
must in any case be small, then the latent heat liberated in freezing a 
small depth dx must be conducted upwards from the frozen layer to the 
surface in time dt. 
x 
. ’. 36 xdx= K '6 0 dt 
Integrating, x 2 = 1 = '9 0 o h, 
giving us the depth frozen in terms of the mean surface temperature below 
0° C. and the duration of the frost. 
In Table XI the calculated and observed values of the depth frozen on 
