TRANSACTIONS OF THE SECTIONS. 



55 



ditions of uniformity as to surface, or by possible inequalities of underground con- 

 ductivity existing in the localities of observation. When those conditions of unifor- 

 mity are perfectly fulfilled both by the surface and by the substance below it, the 

 law of variation in the interior produced by a simple harmonic variation of tempera- 

 ture at the surface, as investigated by Fourier, may be stated in general terms in the 

 three following propositions :— (1) The temperature at every interior point varies 

 according to the simple harmonic law, in a period retarded by an equal interval of 

 time, and with an amplitude diminished in one and the same proportion, for all equal 

 additions of depth. (2) The absolute measure in ratio of arc to radius, for the retar- 

 dation of phase, is equal to the diminution of the Napierian logarithm of the ampli- 

 tude; and each of these, reckoned per unit of length as to augmentation distance 

 from the surface, is equal to the square root of the quotient obtained by dividing the 

 product of the ratio of the circumference of a circle to its diameter, into the thermal 

 capacity of a unit of bulk of the solid, by the thermal conductivity of the same esti- 

 mated for the period of the variation as unity of time. (3) For different periods, the 

 retardations of phase, measured each in terms of a whole period, and the diminutions 

 of the logarithm of the amplitude, all reckoned per unit of depth, are inversely pro- 

 portional to the square roots of the periods. 



The first series of observations examined by the method thus described were those 

 instituted by Professor Forbes, and conducted under his superintendence during five 

 years, in three localities of Edinburgh and the immediate neighbourhood : (1) the 

 trap rock of Calton Hill ; (2) the sand below the soil of the Experimental Gardens ; 

 and (3) the sandstone of Craigleith Quarry. In each place there were, besides a 

 surface thermometer, four thermometers at the depths of 3, 6, 12, and 24 French 

 feet respectively. The diminution in the amplitude, and the retardation of phase in 

 going downwards, have been determined for the annual, for the half-yearly, third- 

 yearly, and the quarterly terra, on the average for these five years for each locality. 

 The same has been determined for the average of twelve years of observation, conti- 

 nued on Calton Hill by the staff" of the Royal Edinburgh Observatory. 



The following results with reference to the annual harmonic term are selected for 

 example : — 



Average of five years, 1837 to 1842. 



