30 Prof. W. Thomson on the Reduction of 



corresponding term in the other series gives us, therefore, two 

 determinations of the value of </ jr, which should agree per- 

 fectly, if (1) the data were perfectly accurate, if (2) the isother- 

 mal surfaces throughout were parallel planes, and if (3) the 

 specific heat and conductivity of the soil were everywhere and 

 always constant. 



As these conditions are not strictly fulfilled in any natural 

 application, the first thing to be done in working out the theory 

 is to test how far the different determinations agree, and to judge 

 accordingly of the applicability of the theory in the circumstances. 

 If the test thus afforded prove satisfactory, the value of the con- 

 ductivity in absolute measure may be deduced from the result 

 with the aid of a separate experimental determination of the 

 specific heat. 



13. The method thus described differs from that followed by 

 Professor Forbes, in substituting the separate consideration of 

 separate terms of the complex harmonic function for the exami- 

 nation of the whole variation unanalysed, which he conducted 

 according to the plan laid down by Poisson. 



This plan consists in using the formulae for a simple harmonic 

 variation, as approximately applicable to the actual variation. 

 At great depths the amplitudes of the second and higher terms 

 of the complex harmonic function become so much reduced as 

 not sensibly to influence the variation, which is consequently 

 there expressed with sufficient accuracy by a single harmonic 

 term of yearly period ; but at even the greatest depths for which 

 continuous observations have actually been made, the second (or 

 semi-annual) term has a very sensible influence, and the third 

 and fourth terms are by no means without effect on the varia- 

 tions at three feet and six feet from the surface. A close agree- 

 ment with theory is therefore not to be expected, until the me- 

 thod of analysis which I now propose is applied. It may be 

 added that in the theoretical reductions hitherto made, either 

 by Professor Forbes or others, the amplitudes of the variations 

 for the different depths have alone been compared, and the very 

 interesting conclusion of theory, as to the relation between the 

 absolute amount of retardation of phase and the diminution of 

 amplitude for any increase of depth, has remained untested. 



14. In Professor Forbes' s paper *, the very difficult operations 

 which he had performed for effecting the construction and the 

 sinking of the thermometers, and the determination of the cor- 



* "Account of some Experiments on the Temperature of the Earth at 

 different Depths and in different Soils near Edinburgh," Transactions 

 of the Royal Society of Edinburgh, vol. xvi. part 2. Edinburgh, 1846. 



