158 PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 



4. Fourier's mathematical theory of the conduction of heat is a beautiful 

 working out of a particular case belonging to the general doctrine of the " Dissi- 

 pation of Energy." * A characteristic of the practical solutions it presents is, 

 that in each case a distribution of temperature, becoming gradually equalised 

 through an unlimited future, is expressed as a function of the time, which is in- 

 finitely divergent for all times longer past than a definite determinable epoch. 

 The distribution of heat at such an epoch is essentially initial — that is to say, it 

 cannot result from any previous condition of matter by natural processes. It is, 

 then, well called an " arUtrary initial distribution of heat," in Fourier's great 

 mathematical poem, because it could only be realised by action of a power 

 able to modify the laws of dead matter. In an article published about nine- 

 teen years ago in the " Cambridge Mathematical Journal,"! I gave the mathe- 

 matical criterion for an essentially initial distribution ; and in an inaugural 

 essay, " De Motu Caloris per Terrse Corpus," read before the Faculty of the 

 University of Glasgow in 184G, I suggested, as an application of these principles, 

 that a perfectly complete geothermic survey would give us data for determin- 

 ing an initial epoch in the problem of terrestrial conduction. At the meeting 

 of the British Association in Glasgow in 1855, I urged that special geothermic 

 surveys should be made for the purpose of estimating absolute dates in geology, 

 and I pointed out some cases, especially that of the salt-spring borings at Creuz- 

 nach, in Rhenish Prussia, in which eruptions of basaltic rock seem to leave traces 

 of their igneous origin in residual heat.]; I hope this suggestion may yet be 

 taken up, and may prove to some extent useful ; but the disturbing influences 

 affecting underground temperature, as Professor Phillips has well shown in a 

 recent inaugural address to the Geological Society, are too great to allow us to 

 expect any very precise or satisfactory results. 



5. The chief object of the present communication is to estimate from the 

 known general increase of temperature in the earth downwards, the date of the 

 first establishment of that " consistentior status," which, according to Leibnitz's 

 theory, is the initial date of aU geological history. 



6. In all parts of the world in which the earth's crust has been examined, at 

 sufficiently great depths to escape large influence of the irregular and of the 

 annual variations of the superficial temperature, a gradually increasing tempera- 

 ture has been found in going deeper. The rate of augmentation (estimated at 

 only TToth of a degree, Fahr., in some localities, and as much as J^th of a 

 degree in others, per foot of descent) has not been observed in a sufficient number 



* Proceedings Royal See. Edin., Feb. 1852. " On a Universal Tendency in Nature to the 

 Dissipation of Mechanical Energy." Also, " On the Restoration of Energy in an Unequally Heated 

 Space," Phil. Mag., 1853, first half year. 



t Feb. 1844. — " Note on Certain Points in the Theory of Heat." 



X See British Association Report of 1855 (Glasgow) Meeting. 



