72 ROYAL SOCIETY OF CANADA 
viously equivalent to a graphic integration of the differential equation 
dv AU Jen Pe Np, , ‘ 
k i= Ce which is the mathematical expression of the law of diffu- 
sion of temperature, 
Applying the method above described to the curves given in Fig. 6, 
and choosing depths in each case at which tangents can be drawn to the 
curves with tolerable certainty, we deduce the following values between 
the depths of 20 and 100 inches : 
k 
April 23rd to 29th ; e = ‘00587 C. G.S. 
k 
April 29th to May 5th; = = ‘00592 CCS. 
k 
May 5th to May 10th; = = ‘00635 C. G.S. 
With these we may compare— 
k 
Dec. 2nd to Dee. 9th ; = = 00648 C. G. S. 
between the depths of 20 and 66 inches. 
These values agree more closely among themselves than those ob- 
tained from the observations on the annual range previously referred to. 
They are in equally close agreement with other results obtained for the 
same soil, in a similar condition, at different dates, during the fall and 
winter months. Rainfall, however, is found to raise the value of the dif- 
fusivity very considerably. ‘Taking, for instance, the interval, April 21st 
to 23rd, including a fall of nearly half an inch of rain on the 22nd, we 
h at 
find for the mean value of à between the depths of 15 and 100 inches, the 
much larger result, ‘0110 C. G. S. The increase in the value found is no 
doubt due to percolation. A similar, and often very much larger, increase 
is observed in other cases to be due to rain, but time has not yet sufficed 
to reduce the observations to rule. 
In order to determine by this method the diffusivity of the surface 
layers, in which the temperature is constantly and rapidly varying, a 
slight modification is required. By drawing tangents at any suitably 
selected epoch to the curves of diurnal variation, the instantaneous values 
dv ; 
of a À different depths may be found. These are plottted in the form 
of a curve, with the corresponding depths as abscissæ, giving the rate at 
which the ground is absorbing heat at different depths. The integration 
of this curve between limits à 
Ci 
rate at which the stratum x, x, is absorbing heat. This is equated to k 
and x,, when multiplied by €, gives the 
dv 
times the difference between the values of de at the depths x, and x,, ob- 
tained from the temperature depth curve corresponding to the same 
