Observations of Underground Temperature. 129 



a height of 350 feet above the sea. The rock is a porphyritic 

 trap, with a somewhat earthy basis, dull and tough fracture. 

 The exact position is a fev) yards east of the little transit house. 

 There are also other buildings in the neighbourhood. The ground 

 rises slightly to the east, and falls abruptly to the west at a di- 

 stance of fifteen yards. The immediate surface is flat, partly 

 covered with grass, partly with gravel*." 



I have marked by italics those passages which describe circum- 

 stances such as it appears to me might account for the discre- 

 pancies in question. 



31. Application to Semiannual Harmonic Terms. — The har- 

 monic expressions given above (§ 15) for the average periodic 

 variations for the three stations of Professor Forbes's original 

 series of five years' observations, contain semiannual terms 

 which are obviously not in accordance with theory. The retar- 

 dations 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 im- 

 possible result. The careful manner in which the observations 

 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 semiannual 

 terms are from '28° to '74? (corresponding to variations 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 

 semiannual 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 pro- 

 gress of temperature during the five years' period at the three 

 stations, from which our apparent semiannual terms have been 

 derived, have been theoretically analysed. But, as we have seen, 

 every irregularity 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 semiannual terms for the eighteen 

 years' average of the Calton Hill thermometers, which we now 

 proceed to do. 



* Professor Forbes " On the Temperature of the Earth," Trans. Rov. 

 Soc. Edinb. 1S46, p. 194. 

 Phil. Mag. S. 4, Vol. 22. No. 115. Aug. 1861. K 



