THE MATHEMATICAL THEORIES OF THE EARTH. 195 



extract wheat tloiir from peascods, so pages of formuliie will not get a. 

 definite resnlt out of loose data."* 



When we pass from the restricted domain of quantitative results 

 concerning geologic time to the freer domaiu of qualitative results of a 

 general character, tlie contractional theory of the earth may be said 

 still to lead all others, though it seems destined to require more or less 

 modification if not to be relegated to a place of secondary importance. 

 Old, however, as is the notion that the great surface irregularities of 

 the earth are but the outward evidence of a crumpling crust, it is only 

 recently that this notion has been subjected to mathematical analysis 

 on anything like a rational basis. About three years ago Mr. T. Mel- 

 lard Eeadet announced the doctrine that the earth's crust from the 

 joint effect of its heat and gravitation should behave in a way somewhat 

 analogous to a bent beam, and should possess at a certain depth a 

 k' level of no strain " corresponding to the neutral surface in a beam. 

 Above the level of no strain, according to this doctrine, the strata will 

 be subjected to compressiou and will undergo crumpling, while below 

 that level the tendency of the strata to crack and part is overcome by 

 pressure which produces what Eeade calls "compressive extension," 

 thus keeping the nucleus compact and continuous. A little later the 

 same idea was worked out independently by Mr. (Charles Davison,| and 

 it has since received elaborate mathematical treatment at the hands of 

 Darwin, § Fisher,|| and others. The doctrine requires for its application 

 a competent theory of cooling, aud hence can not be depended on at 

 present to give anything better than a general idea of the mechanics of 

 crumpling and a rough estimate of the magnitudes of the resulting 

 effects. Using Thomso.n's hypothesis, it appears that the stratum of no 

 strain moves downward from the surface of the earth at a nearly con- 

 stant rate during the earlier stages of cooling, but more slowly during 

 later stages; its depth is independent of the initial temperature of the 

 earth; and if we adopt Thomson's value of the diffiisivity, it will be 

 about two and a third miles below the surface in a hundeed million years 

 from the beginning of cooling, aud a little more than fourteen miles 

 below the surface in seven hundred million years. The most important 

 inference from this theory is that the geological effects of secular cooling 

 will be confined for a very long time to a comparatively thin crust. Thus, 

 if the earth is a hundred million years old, crumpling should not extend 

 much deeper than two miles. A test to which the theory has been sub- 



' • Geological Reform (The Anniversary Address to the Geological Society for 1869). 



t Reade, T. Mellard, Origiu of Mountain Ranges, Loudon, 1886. 



t 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, with a note by G. H. Darwin, rhilosophical Transac- 

 tions, voL 178 (1887), A, pp. 231-'^49. 



(i Ibid. 



II Fisher, Rev. Osmond, Physics of the Earth's Crnst, second edition, Loudon, 1889, 

 Chapter vili. 



