OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 175 



Fourier to be equal to I™ log.e, where a = ./-. Hence, if A and B could be 



determined from the curves showing the range at different depths, and if c, the specific 

 heat, were determined by laboratory experiment, the conductivity of the strata at the 

 three stations could be deduced. Specimens of the three varieties of strata were 

 submitted to M. Kegnault of Paris, who determined their specific heats by experiment, 

 and from these values, combined with the values of B obtained from the curves, the 

 values of k the conducting power of the strata were computed, "which," Prof. Forbes 

 remarks, " has rarely been so accurately determined for any form of matter." 



This research of Prof. Forbes has a special interest, to which no later investigation 

 of the rock thermometer observations in Edinburgh can aspire, inasmuch as the 

 existence of the three sets enabled him to compare the different circumstances depend- 

 ing on the locality of the instruments, more particularly the relative conducting powers 

 of the different rocks or soils in which they were buried. The destruction of two of the 

 sets prevents any redetermination of these quantities by this method from a longer 

 series of observations so far as these two stations are concerned, and the loss at a later 

 date of t 2 at Calton Hill still further restricted the material for investigation. After 

 the Calton Hill set. however, had been in existence for a further period of thirteen 

 years, Lord Kelvin (then Prof. William Thomson) and Prof. Everett, in papers read 

 before the Koyal Society of Edinburgh on the 30th April 1860, re-discussed the whole 

 of the physical phenomena concerned, both from the theoretical and practical points of 

 view. Lord Kelvin, specially, shows how the theory of periodic variations can be 

 applied to the particular case of terrestrial temperature. As Prof. Forbes had already 

 done, he adopts Fourier's solution of the problem, and applies it in a more elaborate 

 form than Prof. Forbes had attempted. Fourier's solution of the problem of the 

 deduction of the conductivity of the strata from the retardation of epoch, and the 

 amplitude at different depths, may be stated in Lord Kelvin's own words : "If the 

 temperature at any point of an infinite plane, in a solid extending infinitely in all 

 directions, be subjected to a simple harmonic variation, the temperature throughout the 

 solid on each side of the plane will follow everywhere according to the simple harmonic 

 law, with epochs retarded equally, and with amplitudes diminished in a constant pro- 

 portion for equal augmentations of distance. The retardation of epoch expressed in 

 circular measure (arc divided by radius) is equal to the diminution of the Napierian 

 logarithm of the amplitude ; and the amount of each per unit of distance is equal to 



/ ,, if c denote the capacity for heat of a unit bulk of the substance, and k its 



conductivity. 



" Hence if the complex harmonic functions expressing the varying temperature at 

 two different depths be determined, and each term of the first be compared with the 



corresponding term of the second, the value of ~ may be determined either by 



