418 PROFESSOR W. THOMSON ON THE REDUCTION OF 
of Professor Forbes’ 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 (for- 
mal or physical) in the surface at the locality, or to inequalities of physical char- 
acter of the rock below. It may be remarked, in the first place, that if the rates 
of diminution 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 pro- 
portion inversely, at the greater depths. For in that case, all that would be 
necessary to reconcile the results of observation with Fouriger’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 capacities. * 
25. Now, in reality, a portion, but only a portion, of the discrepance may be 
done away with in this manner; for while the logarithmic amplitudes and the 
epochs each experience a somewhat diminished rate of variation per French foot 
of descent at the greater depths, this diminution is much greater for the former 
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 °1156 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 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 variation of conductivity and specific heat in inverse propor- — 
tion to one another at the different depths, we may take the mean of the rates 
of variation of logarithmic amplitude and of epoch at each depth, and alter the 
scale of longitudinal reckoning downwards, so as to reduce the numerical 
measures of these rates to equality. This, however, we shall not do in either the 
five years’ or the thirteen years’ term, which we have hitherto considered sepa-— 
rately, but for a harmonic annual variation representing the average of the whole 
eighteen years 1837 to 1854. 
* 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 main- — 
tained at temperatures differing by unity. In terms of this definition, the specific conductivity 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 
by a unit (or one degree) of temperature. The specific heat of a substance is the thermal capac of 
a unit quantity of it, which may be either a unit of weight or a unit of bulk. - ‘ 

