ÎCALLENDAR] OBSERVATIONS OF SOIL TEMPERATURES 71 
ever, very likely that the discrepancies from year to year, and between 
similar soils in different localities, may be due to percolation of rain and 
movements of underground water, which are shown to have a very 
marked effect on the changes of temperature occurring at such depths. 
These factors might operate systematically in such a way as either to 
increase or diminish the annual ranges at any depth. They are, in any 
vase, sufficient to explain the fact that the mean annual ranges at differ- 
ent depths do not agree with the geometrical series indicated by theory. 
Results founded on the annual range, even if extending over a consider- 
able period of years, are necessarily liable to constant errors from these 
sources. 
By making use of the diurnal wave, instead of the annual, it might 
be possible, by a proper choice of dates, to avoid such accidental disturb- 
ances, and to calculate the value for the surface soil under different con- 
ditions of moisture. To apply this method successfully, it would be 
necessary to analyse a large nnmber of such waves into their simple har- 
monic components, and apply the usual formule to each. Sufficient 
observations have not yet been taken, however, in the present case for 
the application of this method. 
Direct Meruop. 
A much simpler and more direct method, which can be applied to the 
observations at any date, without complicated and troublesome analysis, 
is the following. From the observations with the different thermometers 
at any, date a curve may be drawn showing the variation of temperature 
at different depths for that epoch. <A series of such curves, taken as 
samples from the observations, are shown in Fig, 6. The area included 
between any two of these curves when multiplied by €, the thermal capa- 
city of unit volume, gives the total quantity of heat absorbed per unit 
area by any stratum of the soil between the dates and depths for which 
the curves are taken. The quantity of heat per unit area which passes 
by conduction into any stratum of the soil at a depth x, in any time, is 
equal to the product of the thermal conductivity k and the mean tem- 
; dv ; 
perature gradient ae at the depth x, throughout the interval of 
AL 
sar 1 
time considered. The quantity of heat absorbed by a stratum of soil 
; 3 { dv dv | 
between the depths x, and x, is therefore equal to 4 4 | — | — | — | }. 
F | | dx : dx 4 
dv : : 
The mean value of ree the temperature gradient at any depth, for any 
interval of time, is easily found by drawing tangents to the temperature- 
depth curves. By equating the two expressions for the quantity of heat 
k 
absorbed, the value of the diffusivity — is found. This process is ob- 
5 
