1887.] 



Distribution of Strain in the Earth's Crust. 



325 



may possibly be sanidine. It is often rounded or broken in outline, 

 is always greatly cracked, and contains many inclusions of a pale 

 brown glass. One grain, indeed, consists very largely of glass, in 

 which the crystalline parts are, so to say, embedded. This suggests 

 that the minei'al has been melted down in situ along the lines of 

 natural fracture, rather than that it has incorporated the glass in 

 crystallising. There are occasional cavities in the felspar, with 

 bubbles varying in their relative size, which do not move. Grains 

 of quartz, as observed by Tschermak (' Mineral. Mittheil.,' 1872, 

 p. 108) in specimens brought by Favre from the lava streams lower 

 down the mountain, do not ocour in this specimen. A fluidal structure 

 is barely indicated. The rock may be named a hornblende-andesite. 

 1 have compared the slide with one from the upper part of Ararat 

 (lent me by Professor Judd), and with my own collection of andesites 

 and allied rocks from Auvergne, Germany, Hungary, Italy, Old 

 Providence Island, and the Andes, but it differs varietal ly from all. 



III. " On tbe 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 

 Prof. T. G. Bonney, D.Sc, F.R.S. Received April 7, 1887. 



(Abstract.) 



The paper is founded on — 



1. Sir W. Thomson's and Professor G. H. Darwin's researches on 

 the rigidity of the earth. 



2. Sir W. Thomson's investigation on the secular cooling of the 

 earth. 



3. The contraction theory of mountain formation. 



I. The Distribution of Strain in the Earth's Crust resulting from 



Secular Cooling. 



The following problem is solved : — A globe, of radius r, is sur- 

 rounded by a number of concentric spherical shells, called A l5 A 3 , 

 A 8 . . . ., of thickness c%, a 3 , a 3 . . . . respectively. The globe remain- 

 ing at its initial temperature, the shell A l is cooled by the shell A 2 

 by t 2 °, in the same time, and so on. The linear coefficient of expan- 

 sion being e, and the same for all the shells, it is required to find the 

 distribution of strain resulting from this method of cooling. 



An expression is found giving the change of radius of the inner 

 surface of any shell. Supposing all the shells to be of equal thick- 



