424 PROFESSOR W. THOMSON ON THE REDUCTION OF. 
greater relatively will be the semi-annual term ; that within the tropics the semi- 
annual term may predominate, except at the great depths; and that at the 
equator the tendency is for the annual term to disappear altogether, and to leave 
a semi-annual term as the first in a harmonic expression of the yearly vicissitude 
of temperature. The facilities which underground observation affords for the 
analysis of periodic variations of temperature, when the method of reduction 
which I have adopted is followed, will, it is to be hoped, induce those who have 
made similar observations in other localities to apply the same kind of analysis 
to their results ; and it is much to be desired, that the system of observing tem- 
peratures at two if not more depths below the surface may be generally adopted 
at all meteorological stations, as it will be a most valuable means for investigating 
the harmonic composition of the annual vicissitudes. 
III.—Deduction of Conductivities. 
35. Notwithstanding the difficulty we have seen must attend any attempt to 
investigate all the circumstances which must be understood in order to reconcile 
perfectly the observed results with theory, the general agreement which we have 
found is quite sufficient to allow us to form a very close estimate of the ratio of 
the conductivity of the rock to its specific heat per unit of bulk. Thus, according — 
to the means deduced from the whole period of eighteen years’ observation, the 
average rate of variation of the logarithmic amplitude of the annual term through 
the whole space of twenty-one feet is ‘1157, and of the epoch of the same term, 
"1154. The mean of these, or 1156, can differ but very little from the true 
average value of <i = for the portion of rock between the extreme thermometers. 
36. Dividing = by the square of the reciprocal of this number, we find 235-1 
as the value of 2 or, as we may Call it, the conductivity of the rock in terms of the 
thermal capacity of a cubic foot of its own substance. In other words, we infer 
that all the heat conducted in a year (the unit of time) across each square foot of 
a plate one French foot thick, with its two sides maintained constantly at tem- 
peratures differing by 1°, would, if applied to raise the temperature of portions of 
the rock itself, produce a rise of 1° in 285 cubic feet. As it is difficult (although 
by no means impossible) to imagine circumstances in which the heat, regularly 
conducted through a stratum maintained, with its two sides, at perfectly constant 
temperatures, could be applied to raise the temperatures of other portions of the 
same substance, we may vary the statement of the preceding result, and obtain 
the following completely realisable illustration. 
37. Let a large plate of the rock, everywhere one French foot thick, have 
every part of one of its sides (which, to avoid circumlocution, we shall call its 
lower side) maintained at one constant temperature, and let portions of homo- 

