430 Transactions of the Sotith African Philosophical Society. 



per unit area of surface by any stratum of the soil between the 

 dates and depths for which the curves are taken. That is Q = Ac. 

 Now the quantity of heat per unit area of surface which flows past 

 any level at a depth x in unit time is equal to the product of the 

 thermal conductivity k and the average temperature gradient clvjclx 

 between the two successive epochs. That is, for the depths x^ and x^ 

 and corresponding temperatures v-^ and v^ — 



Q = A; J -^^^ _ ^' ^ 

 ) dxy dx-i \ 



Whence — 



= kii say. 



k _ A. 



My own attempts to apply this formula have not been very 

 successful, even in dry weather when the diffusivity of the ground 

 has not been interfered with by moisture. For one thing I have not 

 found either A or dv/dx easy to determine from a diagram. There 

 is no doubt, however, that had my thermometers been more 

 numerous, say only 6 inches apart instead of 2 feet, there would not 

 have been much, if any, difficulty. 



The observations, nevertheless, yield in one particular a direct 

 measure of the effect of a given surface disturbance in terms of the 

 temperature and the average rate at which it travels downwards. 

 For example. Table 10 shows the average efl'ect of a heavy fall of 

 rain after a spell of dry weather in the last quarter of the year. At 

 this time the mean temperature at each depth in question is gradually 

 rising in response to the increasing heat of the sun's rays. An idea 

 of the normal rate of rise may be obtained from the extended 

 averages at the end. Table 10 shows what disturbing effect a smart 

 shower has upon these normals in the course of the following week, 

 expressed in deviations from the normal. It is based upon the 

 particulars of thirteen storms of rain. 



* H. L. Callendar, "Observations of Soil Temperatures," Trans. R. S. Canada, 

 1895, 1896. It will be understood, of course, that Callendar's method only gives the 

 diffusivity at the time of observation, vvhereas the periodic constants give the mean 

 diffusivity for the year. The two results may disagree to some extent because of 

 the varying amount of moisture in the soil. 



