128 Proceedings of the Royal Society of Edinburgh. [Sess. 
When the surface freezes to a depth x', the number of calories used 
up is — 
■8x-x area LMNOP 
9 
= ‘44 x (area LMNO — area LPO) 
I -44 + 0')- l^V r ) 
= -22[lO(0' + 0")-(lO-<)0' r ] .... (4) 
The accuracy of formula (4) is only approximate, and is greater the 
nearer the surface and 4 in. temperatures are to freezing-point at the 
beginning of the period of observations. 
Formula (4) becomes the same as (3) where the surface does not freeze, 
i.e. when x' and d' F both become zero. 
IV. Available Data. 
The results of observations on calm clear nights during the winter of 
1918-19 are given in Table III. The observations are grouped into two 
separate divisions — the nights when the temperature of the surface was 
almost wholly above 32° F. and the nights when the surface temperature 
was almost wholly below 32° F. being grouped separately. 
If we analyse the values given in column 7 of the table we see that, 
in all cases when the surface did not fall below 32° F., the whole of the 
radiation has not quite been accounted for. This is to be expected, since 
we have not taken into account the cooling of those layers of soil below 
the 4 in. depth. 
But choosing the nights on which the temperature of the 4 in. depth 
was close to 32° F. during the period of observations, and so could fall 
little lower without freezing, we see that the radiation on these nights has 
been accounted for to a close degree of approximation. 
Thus on the following nights on which (p' m was about 33° F. the 
differences between the actual computed radiation and the amount of that 
radiation accounted for by conduction, latent heat, and cooling of the soil 
are as follows : — 
Calories. 
January 19, 1919 . . . . +2*7 
February 9, „ . . . . +0‘5 
„ H „ +2*9 
March 3, „ . . . . — 5‘6 
„ 4 , „ - 2*8 
