
OBSERVATIONS OF UNDERGROUND TEMPERATURE. Ain 
As these conditions are not strictly fulfilled in any natural application, the 
first thing to be done in working out the theory is to test how far the different 
determinations agree, and to judge accordingly of the applicability of the theory 
in the circumstances. If the test thus afforded prove satisfactory, the value of 
the conductivity in absolute measure may be deduced from the result with the 
aid of a separate experimental determination of the specific heat. 
13. The method thus described differs from that followed by Professor ForBEs 
in substituting the separate consideration of separate terms of the complex har- 
monic function for the examination of the whole variation unanalysed, which he 
conducted according to the plan laid down by Potsson. 
This plan consists in using the formule for a simple harmonic variation, 
as approximately applicable to the actual variation. At great depths the ampli- 
tudes of the second and higher terms of the complex harmonic function become 
so much reduced as not sensibly to influence the variation, which is consequently 
there expressed with sufficient accuracy by a single harmonic term of yearly 
period; but at even the greatest depths for which continuous observations have 
actually been made, the second (or semi-annual) term has a very sensible in- 
fluence, and the third and fourth terms are by no means without effect on the 
variations at three feet and six feet from the surface. A close agreement with 
theory is therefore not to be expected, until the method of analysis which I now 
propose is applied. It may be added, that in the theoretical reductions hitherto 
made, either by Professor Forzes or others, the amplitudes of the variations for 
the different depths have alone been compared, and the very interesting conclu- 
sion of theory, as to the relation between the absolute amount of retardation of 
phase and the diminution of amplitude for any increase of depth, has remained 
untested. 
14. In Professor ForBgs’s paper,* the very difficult operations which he had 
performed for effecting the construction and the sinking of the thermometers, and 
the determination of the corrections to be applied to obtain the true temperatures 
of the earth at the different depths from the readings of the scales graduated on 
their stems protruding above the surface, are fully described. The results of 
five years’ observations—1837 to 1842—are given, along with most interesting 
graphical representations and illustrations. A process of graphic interpolation, 
for estimating the temperatures at times intermediate between those of observa- 
tions, is applied for the purpose of obtaining data from which the complex har- 
monic functions expressing the temperatures actually observed for the different 
depths are determined. I am thus indebted to Professor Fores for the mode of 
procedure (described below) which I have myself followed in expressing the 
variations of temperature during the succeeding thirteen years for the Calton Hill 
* Account of Some Experiments on the Temperature of the Earth at Different Depths and in 
Different Soils near Edinburgh; T'ransactions R.S.E., Vol. XVI. Part II. Edinburgh, 1846, 
