1919-20.] The Cooling of the Soil at Night. 
17 
Table VI. — Differences of Air and Surface Minimum ° C. 
(a) 
Surface frozen. 
(6) 
Surface not frozen. 
(10 nights.) 
(28 nights.) 
Average difference between air 
minimum and surface -soil > 
-2-7° C. 
+ *4° C. 
minimum J 
Greatest and least differences \ 
of above J 
— 3-2° C. ; — ‘3° C. 
+ 1 *0° G. ; — T - 0° C. 
If the surface does not freeze it would appear that the air minimum 
over open soil follows the surface-soil minimum very closely. 
VI. The Forecast Equation. 
Let us suppose we wish to forecast the minimum surface temperature 
to-night, the conditions being favourable for a calm clear night. By about 
6 p.m. we should know — 
(1) The maximum surface temperature = M 0 . 
(2) The maximum 4-in. depth temperature = M 4 . 
(3) The ratio of ranges of surface and 4-in. temperature from minimum 
to maximum = a. 
(4) The probable average relative humidity of the coming night. 
(5) The number of degrees which the surface temperature can fall 
below the 4-in. depth temperature read off Table V = 0. 
If R 0 and 1L are the ranges from maximum to minimum on the coming 
night, we may assume that R 4 = aR 0 . When the surface has reached its 
minimum the 4-in. depth is still considerably above its minimum, the 
amount depending on the value of the lag. 
Thus the surface temperature at time of minimum = M 0 — R 0 
The 4-in. depth „ „ „ =M 4 — /3R 4 
= M 4 — a/3R 0 
where f3 is a fraction depending on the value of the lag. 
Now the surface temperature cannot fall more than 0° below the 4-in. 
temperature, 
.-. , M 0 - R 0 = M 4 - a/3R 0 - 0, 
• t> _ M 0 — M 4 + 6 / -I \ 
1 — a{3 (1) 
If we assume that for an average spring day the maximum at the 
surface occurs about 2.30 p.m. and the minimum at about 4.30 a.m. — 
VOL. XL. 2 
