126 Proceedings of the Royal Society of Edinburgh. [Sess. 
the soil is frozen to a depth x centimetres is calories per square 
centimetre. 
If therefore the soil is frozen to a depth x at the beginning of the obser- 
vations and x' at the end, the latent heat liberated = 36(cc / — x) calories. 
(c) Upward Conduction. 
In calculating the upward conduction from the warmer and lower strata, 
the question of the depth at which it would be best to take our observations 
has to be settled at the outset. 
I have chosen a depth of 4 in. (10 centimetres) for the following 
reasons : — 
(1) The surface soil only extends to a depth of 6 in. ; below this the 
subsoil is of quite a different character. The conductivity at depths of 
4 in. and 6 in. was found to be in each case equal to *004 ; below 6 in. depth 
it varied from place to place. 
(2) The lag of the maximum temperature at a depth of 4 in. is about 
3| hours, and so roughly coincided with sunset during the greater part of 
the winter. This much simplified the calculation of the average temperature 
at that depth during the night. 
(3) Since 4 in. = 10 centimetres, the computations were simplified. 
To obtain a measure of the upward conduction, the difference between 
the temperature at the surface and 4 in. depth at various times during the 
night seemed necessary ; but it also appeared reasonable to suppose that the 
mean difference would not vary much from the difference between the 
mean temperatures at the surface and at a depth of 4 in. 
If this were so, then the conduction upwards equals 
x - calories per sq. centimetre per second 
10 9 c a r 
-55^ x - x 0 m x 60 x 607i calories during the night 
10 9 
= ’80 m h calories ........ (1) 
I therefore tested, by taking hourly readings of the temperature at the 
surface and 4 in. depth, on two nights, November 21, 1918, and February 26, 
1919, whether there was likely to be any serious discrepancy in taking <f> m — <p m 
as the mean difference of the surface and 4 in. temperatures during the night. 
It would appear that </> m — cp m is a very close approximation to the 
mean difference of the surface and 4 in. temperatures. Thus on November 
21, (p' m — <p m was equal to 6'0° F., whilst the average of the hourly 
differences of surface and 4 in. temperatures was 6T° F. Similarly, on 
