428 Transactions of the South African Philosophical Society. 



the solstice, precedes that of the maximum temperature of the air by 



quite a week. This effect also seems not to be propagated to any 



depth. But the epoch of the annual wave of mean temperature 



M + m\ 



of the surface of the ground falls about January 3, and 



it is this which determines the annual wave at considerable depths. 

 This wave appears to travel more slowly as it penetrates deeper, for 

 while it traverses the first 2 feet in twelve days, it takes sixteen days 

 for the next 2, and eighteen days for the last. The semi-annual 

 wave penetrates more quickly than the annual wave, but it lags also 

 as it gets deeper, like the other. One curious fact should be noticed : 

 While the amplitudes of the first and third harmonic terms decrease 

 as the depth increases with some approach to regularity from the 

 surface downwards, the amplitude of the second harmonic term for 

 surface temperatures is actually less than the amplitude at 1 foot, 

 and scarcely greater than that at 2 feet. The reason is not obvious. 

 It seems not to be due to the longer period for which the average 

 temperatures of the deeper levels are computed. Attention may, 

 however, be recalled to Table 1, which shows that the surface of 

 the ground is much warmer than the air by day throughout the year, 

 and that possibly, therefore, a great part of the heat of the surface is 

 devoted to warming the air rather than the lower levels of the 

 ground. 



To determine the quantity (7rc/^)% where c denotes the capacity 

 for heat and h the conductivity of the ground at various individual 

 depths down to 6 feet, we have, from a comparison between the 

 amplitudes and epochs of the harmonic terms at each depth, the 

 numbers of Table 9 : — 



TABLE 9. 

 Values of 



/ttC 



V T- 



Depth. 



log — 



Vi - v; 



-? 



V2 - v'. 





per foot 

 •1432 

 •1904 

 •1559 



per foot 

 •1062 

 •1466 

 •1520 



per foot 

 •1778 

 •1765 

 •1558 



per foot 

 •0665 

 •1.326 

 •1500 



Two to four feet ..." 



Four to six feet 



In this Table %t^ and 7i^ represent the amplitudes of the first 

 harmonic terms at any two successive depths, Vj and Vi the 



