182 SEE-FURTHER RESEARCHES ON [April 24, 



1846. (" De Motu Caloris per Terras Corpus," read before the 

 faculty of the University of Glasgow in 1846; also a " Note on Cer- 

 tain Points in the Theory of Heat," February, 1844, published in 

 the Cambridge Mathematical Journal, and reprinted in the " Mathe- 

 matical and Physical Papers of Sir W. Thomson," 1882, Vol. I, 

 Art. X.) 



In a paper " On the Rigidity of the Earth " published in the 

 Philosophical Transactions of the Royal Society for May, 1862, 

 Lord Kelvin pointed out that if the matter of the earth's interior 

 yielded readily to the tidal forces arising from the attraction of the 

 sun and moon, the crust itself would respond to these forces in 

 much the same way as the waters of the sea ; and the corresponding 

 movements of the crust would mask or largely reduce the height 

 of the oceanic tides calculated for a rigid earth. By actual analysis 

 of long series of tidal observations Kelvin and Darwin subsequently 

 found the observed fortnightly tide to have very nearly its full 

 theoretical height, and hence concluded that our globe as a whole 

 possesses a very high effective rigidity. (Cf. Thomson and Tait's 

 "Natural Philosophy," Vol. I, part II, §832-847; also the article 

 " Tides," Encyclopedia Britannica, ninth edition, § 44.) 



Owing to the great importance of this work on the rigidity of 

 the earth, we must trace the successive steps in the advancement of 

 our knowledge. The assumption that the earth is made up of a 

 liquid nucleus covered with a thin crust stiff enough to maintain its 

 figure against the tide-raising forces of the sun and moon would 

 imply that the crust has a degree of strength and rigidity not pos- 

 sessed by any known substance. It was therefore inferred by Lord 

 Kelvin as early as 1862 that the crust might be 2,000 to 2,500 miles 

 thick, in order to resist distortion under the tide-producing forces 

 arising from the sun and moon. 



"If the crust yielded perfectly, there \vould be no tides of the sea, no 

 rising and falling relatively to the land, at all. The water would go up and 

 down with the land, and there would be no relative movement ; and in pro- 

 portion as the crust is less or more rigid the tides w'ould be more or less 

 diminished in magnitude. Now we cannot consider the earth to be absolutely 

 rigid and unyielding. No material that we know of is so. But I find from 

 calculation that were the earth as a whole not more rigid than a similar globe 

 of steel the relative rise and fall of the water in the tides would be only 



