850 R. S. Woodward — Mathematical Theories of the Earth . 



this matter, I feel bound to state that, although the hypothesis 

 appears to be the best which can be formulated at present, the 

 odds are against its correctness. Its weak links are the unver- 

 ified assumptions of an initial uniform temperature and a con- 

 stant diffusivity. Very likely these are approximations, but of 

 what order we cannot decide. Furthermore, if we accept the 

 hypothesis, the odds appear to be against the present attain- 

 ment of trustworthy numerical results, since the data for calcu- 

 lation, obtained mostly from observations on continental areas, 

 are far too meager to give satisfactory average values for the 

 entire mass of the earth. In short, this phase of the case 

 seems to stand about where it did twenty years ago, when 

 Huxley warned us that the perfection of our mathematical 

 mill is no guaranty of the quality of the grist, adding that " as 

 the grandest mill will not extract wheat flour from peas-pods, 

 so pages of formulae will i:ot get a definite result out of loose 

 data.''* 



When we pass from the restricted domain of quantitative 

 results concerning geologic time to the freer domain of quali- 

 tative results of a general character, the contractional theory of 

 the earth may be said to still lead all others, though it seems 

 destined to require more or less modification, if not to be rele- 

 gated 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. 

 Mellard Reade 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 pos- 

 sess at a certain depth a " level of no strain," corresponding to 

 the neutral surface in a beam.f Above the level of no strain, 

 according to this doctrine, the strata will be subjected to com- 

 pression and will undergo crumpling, while below that level 

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

 pressure which produces what Reade calls "compressive exten- 

 sion," thus keeping the nucleus compact and continuous. A 

 little later the same idea was worked out independently by 

 Mr. Chas. Davison,:}; and it has since received elaborate mathe- 

 matical treatment at the hands of Darwin,§ Fisher, | and 



* Geological Reform (The Anniversary Address to the Geological Society for 

 1869), Lay Sermons, Addresses and Reviews. D. Appletoa &Co. New York, 1871. 



f Reade, T. Mellard, Origin of Mountain Ranges, London, 1886. 



% 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, Philo- 

 sophical Transactions, vol. clxxvhi (1887), A, pp. 231-249. § Ibid. 



flFislier, Rev. Osmond, Physics of the Earth's Crust, second edition, London, 

 1889, Chapter VIII. 



