422 PROFESSOR W. THOMSON ON THE REDUCTION OF 
the east, and falls abruptly to the west at a distance of fifteen yards. The imme- 
diate surface is flat, partly covered mith grass, partly with gravel.”* 
I have marked by italics those passages which describe circumstances such 
as it appears to me might account for the discrepancies in question. 
31. Application to Semi-annual Harmonic Terms.—The harmonic expressions 
given above (§ 15) for the average periodic variations for the three stations of Pro- 
fessor ForBEs’ original series of five years’ observations, contain semi-annual 
terms, which are obviously not in accordance with theory. The retardations of 
epochs and the diminutions of amplitudes are, on the whole, too irregular to be 
reconcileable by any supposition as to the conductivities and specific heat of the 
soils and rocks involved, or as to the possible effects of irregularity of surface ; 
and in two of the three stations, the amplitude of the semi-annual term is actually 
greater as found for the six feet deep than for the three feet deep thermometer, 
which is clearly an impossible result. The careful manner in which the observa- 
tions have been made and corrected, seems to preclude the supposition that these 
discrepancies, especially for the three feet and six feet thermometers, for which the 
amplitudes of the semi-annual terms are from ‘28° to ‘74° (corresponding to varia- 
tions of double those amounts, or from ‘56° to 1°48), can be attributed to errors in 
the data. It must be concluded, therefore,.that the semi-annual terms of those 
expressions do not represent any truly periodic elements of variation, and that they 
rather depend on irregularities of temperature in the individual years, of the term 
of observation. Hence, until methods for investigating the conduction inwards 
of non-periodic variations of temperature are applied, we cannot consider that 
the special features of the progress of temperature during the five years’ period — 
at the three stations, from which our apparent semi-annual terms have been 
derived, have been theoretically analysed. But, as we have seen, every irregu- 
larity depending on individual years is perfectly eliminated when the average 
annual variation over a sufficiently great number of years is taken. Hence 
it becomes interesting to examine particularly the semi-annual terms for the 
eighteen years’ average of the Calton Hill thermometers, which we now proceed 
to do. 
32. Calculating as above (§ 26), for the coefficients A,, B,, the average values — 
of A, and B,, from Professor ForBes’ results for his first five years’ term, and 
from the averages for the next thirteen years shown in Table V. above, we 
find the values of A, and B, shown in the following table. The amplitudes — 
and epochs are deduced as usual by the formule aif (4? ag B,’) and tan ®:. 
2 
These reductions I only make for the three feet deep and the six feet deep ther- 
mometers, since, for the two others, as may be judged by looking at the thirteen 
years’ average, shown in the former table, the amounts of the semi-annual varia- 
* Professor Forsxs on the Temperature of the Earth, Trans. R.S.E., 1846, p. 194. 

