OBSERVATIONS OF UNDERGROUND TEMPERATURE. 417 
TABLE VI.—AVERAGE OF THIRTEEN YEARS, 1842 To 1854; Trap Rock 
oF CALTON HILL. 
Diminution of Napierian 
Depths below surface, | logarithm of amplitude 
in French feet, per French foot of de- 
scent, 
Retardation of epoch in 
circular measure, per 
French foot of descent. 




8 to 6 feet ‘1310 +1233 
+ 6to12 ,, 1163 1140 
12 to 24 ,, ‘1121 1145 
3 to 24 feet ‘1160 ‘1156 
22. The numbers here shown would all be the same, if the conditions of uni- 
formity supposed in the theoretical solution were fulfilled. Although, as in the 
previous comparisons, the agreement is on the whole better than might have been 
expected, there are certainly greater differences than can be attributed to errors 
of observation. Thus, the means of the numbers in the two columns are for the 
three different intervals of depth in order as follows :— 
Mean deductions from amplitude 
: and epoch, 
orto .G'ieet, >: : ; , : 27 
6tol2 ,, 7G - : : : 115 
12 to 24 ,, : : . : : "113 
_ —numbers which seem to indicate an essential tendency to diminish at the greater 

depths. This tendency is shown very decidedly in each column separately; and 
it is also shown in each of the corresponding columns, in tables given above, 
of results derived from Professor Forbes’ own series of a period of five years. 
23. There can be no doubt but that this discrepance is not attributable to 
errors of observation, and it must therefore be owing to deviation in the natural 
circumstances from those assumed for the foundation of the mathematical for- 
mulz. In reality, none of the conditions assumed in Fourier’s solution is rigor- 
ously fulfilled in the natural problem; and it becomes a most interesting subject 
for investigation to discover to what particular violation or violations of these 
conditions the remarkable and systematic difference discovered between the deduc- 
tions from the formula and the results of observation is due. In the first place. 
the formula is strictly applicable only to periodic variations, and the natural 
variations of temperature are very far from being precisely periodic; but if we 
take the average annual variation through a sufficiently great number of years, 
it may be fairly presumed that irregularities from year to year will be eliminated ; 
and that the discrepance we have now to explain does not depend on residual 
inequalities of this kind seems certain, from the fact that it exists in the average 
VOL. XXII. PART II. oP 
