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VII. On the Distribution of Strain in the Earth's Crust resulting from Secular 
Cooling; with special reference to the Growth of Continents and the Formation of 
Mountain Chains. 
By Charles Davison, M.A., Mathematical Master at King Edward's High School, 
Birmingham. 
Communicated by Professor T. G. Bonney, D.Sc., F.P.S. 
Received April 7,—Read May 5, 1887. 
(1) The reasoning of this paper is based upon the results of Sir W. Thomson’s and 
Professor G. H. Darwin’s well-known and independent researches on the rigidity of 
the Earth, upon Sir W. Thomson’s investigation on the secular cooling of the Earth, 
and, lastly, upon the beautiful contraction theory of mountain evolution which these 
researches lead up to and support. Its objects are to determine the distribution of 
strain in a solid globe resulting from secular cooling, and to examine the effects 
which this distribution must have upon the form of the great features of the Earth’s 
surface. 
In the first part of the paper I shall suppose the Earth to be bounded by a smooth 
spherical surface, and to be made up of a very great number of very thin concentric 
spherical shells, each shell being so thin that the loss of heat throughout it may be 
considered uniform. In the latter part the effects of inequalities on the Earth’s 
surface upon the results so obtained will be alluded to. The argument urged 
against the contraction theory by the Bev. Osmond Fisher will also be incidentally 
considered. 
I. The Distribution of Strain in the Earth's Crust resulting from Secular Cooling. 
(2) In his memoir on the secular cooling of the Earth, Sir W. Thomson works out 
the case of the conduction of heat in “a solid extending to infinity in all directions, 
on the supposition that at an initial epoch the temperature has had two different 
constant values on the two sides of a certain infinite plane,” and he shows that, for 
“a globe 8000 miles in diameter of solid rock, the solution will apply with scarcely 
sensible error for more than 1,000,000,000 years.” The solution he gives is 
« = % + 
2 V pnnot) 
jr\ dz.e 
v (tt) J ) 
29.8.87 
