Earth Temperatures at Kimberley. 429 



corresponding epochs ; tc.2, tLi, V2, V'a, the ampUtudes and epochs 

 of the second harmonic terms. The last Hne, standing for condi- 

 tions below the depth at which the diurnal variation is felt, is 

 satisfactory enough. But the others are not. There is, however, 

 the circumstance that, saving the case of the retardation of the 

 epoch of the second harmonic term between 1 and 2 feet, the rate 

 of diminution of the logarithms of the amplitudes is, in depths down 

 to 4 feet, almost exactly 1*3 times the rate of retardation of the 

 epoch, expressed in circular measure. The composition of the sur- 

 face strata possibly accounts for much of this. Throughout the first 

 foot of depth the soil is a light red sand with some humus. From 

 1 to 3 feet it changes gradually into a compact red subsoil (possibly 

 washed out of the surface sand in the course of ages by the rain) 

 which is very hard when dry, but soft and plastic when wet. Under 

 this is a shallow layer of about a foot in depth of hard limestone 

 lumps overlying an indefinite depth of soft floury chalk. It would 

 appear, then, that some irregularity in the thermal capacity and 

 conductivity of the ground down to a moderate depth should be 

 expected. There is also to be taken into account the comparatively 

 short period during which observations have been taken, and also 

 the change in the position of the thermometers. 



Taking the average of the variation of the logarithms and retarda- 

 tion of the epochs between 4 and 6 feet, we get -1534 as the average 

 of the numbers in the last line of Table 9. This gives for the 

 diffusivity hjc in the chalk the value 133-33 per annum, which 

 reduces to -0044 in C.G.S. units, a value not differing greatly from 

 Angstrom's value for argillaceous sand, nor from A. Herschel's value 

 for dry clay." Professor H. E. Callendar has shown how the dif- 

 fusivity may be simply and directly computed from a graphic integra- 

 tion of the algebraic expression of the law of diffusion, i.e., of — 



dv k d^v 



dt c dx' 



For 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. Let a series of such curves for 

 successive epochs be drawn on squared paper. The area included 

 between any two of these curves when multiplied by c, the thermal 

 capacity of unit volume, gives the total quantity of heat absorbed 



*^^See " On the Eeduction of Observations of Underground Temperature," Lord 

 Kelvin, Phil. Mag., 1861; Deschanel's "Natural Philosophy" (Everett), 1891, 

 p. 425; Preston, "Theory of Heat," ch. vii, ; Fourier, passim. 



