Observations of Underground Temperature. 125 



pend on residual inequalities of this kind seems certain, from 

 the fact that it exists in the average of Professor Forbes's first 

 five years' series no less decidedly than in that of the period of 

 thirteen years following. 



24. For the true explanation we must therefore look either to 

 inequalities (formal or physical) in the surface at the locality, 

 or to inequalities of physical character of the rock below. It 

 may be remarked, in the first place, that if the rates of diminu- 

 tion of logarithmic amplitude and of retardation of epoch, while 

 less, as they both are, at the greater depths, remained exactly 

 equal to one another, the conductivity must obviously be greater, 

 and the specific heat less in the same proportion inversely, at 

 the greater depths. For in that case, all that would be neces- 

 sary to reconcile the results of observation with Fourier's formula, 

 would be to alter the scale of measurement of depths so as to 

 give a nominally constant rate of diminution of the logarithmic 

 amplitude and of the retardation of epoch ; and the physical 

 explanation would be, that thicker strata at the greater depths, 

 and thinner strata at the less depths (all of equal horizontal 

 area), have all equal conducting powers and equal thermal capa- 

 cities*. • 



25. Now in reality, a portion, but only a portion, of the dis- 

 crepance may be done away with in this manner; for while the 

 logarithmic amplitudes and the epochs each experience a some- 

 what diminished rate of variation per French foot of descent at 

 the greater depths, this diminution is much greater for the for- 

 mer than for the latter ; so that, although the mean rates per 

 foot on the whole 21 feet are as nearly as possible equal for the 

 two (being "1160 for the logarithmic amplitudes, and 'HoG for 

 the epoch), the rate of variation of the logarithmic amplitude 

 exceeds that of the epoch by about 6 per cent, on the average of 

 the stratum of 3 to 6 feet; and falls short of it by somewhat 

 more than 2 per cent, in the lower stratum, 12 to 24 feet. To 

 find how much of the discrepance is to be explained by the varia- 

 tion of conductivity and specific heat in inverse proportion to 

 one another at the different depths, wc may take the mean of the 



* The "conducting power" of a solid plate is an expression of great 

 convenience, which I define as the quantity of heat which it conducts per 

 unit of time when its two surfaces are permanently maintained at tempera- 

 tures differing hy unity. In terms of this definition, the specific conduc- 

 tivity of a substance may be defined as the conducting power per unit area 

 of a plate of unit thickness. The conducting power of a plate is calculated 

 by multiplying the number which measures the specific conductivity of its 

 substance by its area, and dividing by its thickness. 



The thermal capacity of a body may be defined as the quantity of heat 

 required to raise its mass a unit (or one degree) of temperature. The 

 specific heat of a substance is the thermal capacity of a unit quantity of it, 

 which may be either a unit of weight or a unit of bulk. 



