1894.] On the Straining of the Earth resulting from Cooling. 141 



III. " On the Straining of the Earth resulting from Secular 

 Cooling." By CHARLES DAVISON, M.A., MatKematical 

 Master at King Edward's High School, Birmingham. 

 Communicated by Professor POYNTING, F.R.S. Received 

 January 10, 1894. 



(Abstract.) 



If the coefficient of dilatation (e) and the conductivity (/c) are 

 constant at every point within the earth, and if the temperature (V) 

 was initially the same throughout, the depth of the surface of zero- 

 strain after 100 million years is 2'17 miles, the total volume of the 

 crust folded and crushed above that surface is about 184,500 cubic- 

 miles, and the mean thickness of the crushed rock spread over the 

 whole surface of the earth is 4'95 ft. (taking e 0-0000057, K = 400. 

 V = 7000 F.). The smallness of these figures has been claimed by 

 some geologists as a new and strong argument against the contraction 

 theory of mountain evolution. 



In the present paper the problem is reconsidered on the supposition 

 that the coefficient of dilatation is not constant, but increases with 

 the temperature, the change in the former varying as the correspond- 

 ing change in the latter. It follows, from experiments made by 

 Fizeau, that, for a rise of one degree in temperature, the coefficient of 

 dilatation increases on an average by about 1/888. Adopting this 

 value, and taking the other constants as above, it is found that, after 

 100 million years, the depth of the surface of zero strain is 7' 79 miles, 

 the total volume of crust-folding about 6,145,000 cubic miles, and the 

 mean thickness of the layer formed by spreading it over the whole 

 earth 164-7 ft. 



If the conductivity increases with the temperature, or if the 

 material which composes the earth's interior be such that the con- 

 ductivity and coefficient of dilatation are greater in it than in the 

 surface rocks, or if initially the temperature increased with the 

 depth, the figures given in the preceding paragraph must be still 

 further increased. It follows, therefore, that calculations as to the 

 alleged insufficiency of the contraction theory to produce mountain 

 ranges are at present inadmissible. 

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