348 J?. S. Woodward — Mathematical Theories of the Earth. 



tion that there exist hot foci in space was advanced also in 

 another form in 1852 by Rankine, in his interesting specula- 

 tion on the reconcentration of energy. But whatever we may 

 think of the hypothesis as a whole it does not appear to be ade- 

 quate to the case of the earth unless we suppose the epoch of 

 transit through the hot region exceedingly remote, and the 

 temperature of that region exceedingly high. The continuity 

 of geological and paleontological phenomena is much better 

 satisfied by the Leibnitzian view of an earth long subject to 

 comparatively constant surface conditions but still active with 

 the energy of its primitive heat. 



Notwithstanding the indefatigable and admirable labors of 

 Fourier and Poisson in this field, it must be admitted that they 

 accomplished little more than the preparation of the machinery 

 with which their successors have sought and are still seeking 

 to reap the harvest. The difficulties which lay in their way 

 were not mathematical but physical. Had they been able to 

 make out the true conditions of the earth's store of heat they 

 would undoubtedly have reached a high grade of perfection in 

 the treatment of the problem. The theory as they left it was 

 much in advance of observation, and the labors of their succes- 

 sors have therefore necessarily been directed largely toward 

 the determination of the thermal properties of the earth's crust 

 and mass. 



Of those who in the present generation have contributed to 

 our knowledge and stimulated the investigation of this subject 

 it is hardly necessary to say that we owe most to Sir William 

 Thomson. He has made the question of terrestrial tempera- 

 tures highly attractive and instructive to astronomers and 

 mathematicians, and not less warmly interesting to geologists 

 and paleontologists. Whether we are prepared to accept his 

 conclusions or not, we must all acknowledge onr indebtedness 

 to the contributions of his master hand in this field, as well as 

 in most other fields of terrestrial physics. The contribution of 

 special interest to us in this connection is his remarkable me- 

 moir on the secular cooling of the earth.* In this memoir he 

 adopts the simple hypothesis of a solid sphere whose thermal 

 properties remain invariable while it cools by conduction from 

 an initial state of uniform temperature, and draws therefrom 

 certain striking limitations on geologic time. Many geologists 

 were startled by these limitations and geologic thought and 

 opinion have since been widely influenced by them. It will 

 be of interest, therefore, to state a little more fully and clearly 

 the grounds from which his arguments proceed. Conceive a 

 sphere having a uniform temperature initially, to cool in a 



* Transactions of the Royal Society of Edinburgh, 1862. Thomson and Tait's 

 Natural Philosophy, vol. i, Part II, Appendix D. 



