176 MR THOMAS HEATH ON 



dividing the difference of the Napierian logarithms of the amplitudes, or the difference 

 of the epochs by the distance between the points. The comparison of each term in the 

 one series with the corresponding term in the other gives us, therefore, two determina- 

 tions of the value of / j~, which should agree perfectly, if (l) the data were perfectly 



accurate, if (2) the isothermal surfaces throughout were parallel planes, and if (3) the 

 specific heat and conductivity of the soil were everywhere and always constant." 



By the method thus indicated Lord Kelvin applied the general theory — 1st, to the 

 five years' observations at the three stations ; 2nd, to the thirteen years' observations 

 at Calton Hill alone. The result he brought out was that the figures representing the 



conducting power of the rock at Calton Hill, the values of / -,-, as deduced from the 



diminution of amplitude, and from the retardation of epoch, appear to diminish as the 

 deeper thermometers are approached. There are thus outstanding discrepancies from 

 Fourier's theory, which supposes that the values should come out alike for all depths. 

 Lord Kelvin states his opinion that " 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 

 formula." Later on he says : " I can only infer that the residual discrepancies .... 

 are not with any probability attributable to variation of conductivity and specific heat 

 in the rock, and conclude that they are to be explained by irregularities, physical and 

 formal, on the surface." Some of these irregularities he specifies, the ground rising 

 slightty to the east and falling abruptly at a distance of about 15 yards on the west, the 

 immediate surface being flat, partly covered with grass, partly with gravel. 



It thus appeared to be of great interest to see whether the reduction of the whole 

 series of forty years' observations of the old thermometers, and the series of twenty years 

 of the new thermometers erected in 1879 would bring out a similar or a more satis- 

 factory result. In carrying out this work I have availed myself largely of the elegant 

 methods of procedure detailed in the paper by Prof. Everett mentioned already. The 

 readings of the thermometers have throughout been made once a week, on Mondays at 

 noon, and the corrected readings for 1837-76, which were published in the Edinburgh 

 Astronomical Observations, have now been taken out and arranged in four series of ten 

 years, under each Monday of the year. The means of the columns so formed give the 

 temperature of each thermometer for the mean date of the Monday to which it belongs. 

 The average of the four series of ten years were then taken as the final temperatures 

 from which the annual curves of the old set of thermometers were obtained. 



In computing the equations of these curves, or the harmonic function of the 

 temperature at any time represented by the fraction of the year, I have followed Prof. 

 Everett in dividing the year into twelve parts instead of thirty-two, the division Lord 

 Kelvin adopted. I have done so for two reasons — (1) because the labour involved is 

 much less, the equations being solved by a simple method of elimination, and the 



