was 86° F. on 5th January, 1948 (the mean maximum for January is 

 77° F.). Similarly, the lowest soil temperature recorded during the 

 period at the 3 in. depth was 28° f. on 6th July, 1947 (the mean 

 minimum for July is 31° F.), and at the 5 in. depth the lowest value 

 recorded was 30° f. on 5th, 6th and 7th July, 1947 (the mean minimum 

 for July is 32° f.). In January it appears that the soil temperature at 

 the 3 in depth never falls below about 55° f., and at the 5 in depth it 

 never falls below about 58° f. In July, however, no soil temperature 

 in excess of 47° f. was recorded at the 3 in. depth, and no value in excess 

 of 39° F. occurred at the 5 in. depth. Table 3 shows for every month 

 the greatest, least, and mean diurnal ranges of soil temperatures 

 observed at the depths of 3 in. and 5 in. respectively, together with the 

 ratios of the mean diurnal ranges at these two depths. Extreme values 

 are given only to the nearest half degree. For purposes of comparison 

 the mean diurnal range of air temperature derived from seventeen 

 years' observations in the screen at Alexandra (near Earnscleugh) is 

 included in Table 3. 



Discussion of the Earnscleugh Results 



Assuming that heat is transferred in the soil in accordance with the 

 normal theory of conduction, it is possible to use the above results to 

 determine the diffusivity of the soil and thence to calculate its thermal 

 conductivity. If K is the diffusivity, p the density and S the specific 

 heat of the soil, then the thermal conductivity is given by the quantity 

 KpS. In this paper most attention is given to the determination of 

 the quantity K. 



Diffusivity of the Soil 



The temperature of the surface of the soil will vary periodically with 

 the altitude of the sun and may be regarded as the sum of several 

 harmonics of rather rapidly decreasing amplitude. In these circum- 

 stances the normal theory of conduction of heat shows that each 

 harmonic wave is transmitted downward with amplitude decreasing 

 exponentially with the depth and is subject to a phase retardation 

 proportional to the depth. Thus with increasing depth below the surface 

 of the soil the harmonics of small amplitude will become negligible, and 

 the temperature may be expressed more and more accurately by a 

 simple sine curve. Assuming a simple sine curve, the quantity K can 



be computed from the equation K =„-4— — p ^^ 2 where R^ and Ro are 



the daily ranges at depths Zj^ and z^ below the surface, z^ in our case 

 being 3 in. and z.^ 5 in. 



Table 4 shows the result of such calculations for z^ — z^ = 2 in. 



i a r; 



practice. 



■p 



and a range of values of the ratio r = ^ that commonly occurs in 



52 



