-2?.$. Woodward — Mathematical Theories of the Earth. 351 



others. The doctrine requires for its application a competent 

 theory of cooling and hence cannot 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 Thomson's hypothesis, it appears that 

 the stratum of no strain moves downward from the surface of 

 the earth at a nearly constant rate during the earlier stages of 

 cooling, but more slowly during the later stages; its depth is 

 independent of the initial temperature of the earth ; and if we 

 adopt Thomson's value of the diffusivity it will be about two 

 and a third miles below the surface in a hundred million years 

 from the beginning of cooling, and a little more than fourteen 

 miles below the surface in 700,000,000 years. The most im- 

 portant 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- 

 jected, and one which some* consider crucial against it, is the 

 volumetric amount of crumpling shown by the earth at the 

 present time. This is a difficult quantity to estimate, but it 

 appears to be much greater than the theory can account for. 



The opponents of the contractional theory of the earth, be- 

 lieving it quantitatively insufficient, have recently revived and 

 elaborated an idea first suggested by Babbage and Herschelf in 

 explanation of the greater folds and movements of the crust. 

 This idea figures the crust as being in a state bordering on 

 hydrostatic equilibrium which cannot be greatly disturbed 

 without a readjustment and consequent movement of the 

 masses involved. According to this view, the transfer of any 

 considerable load from one area to another is followed sooner 

 or later by a depression over the loaded area and a correspond- 

 ing elevation over the unloaded one ; and in a general way it is 

 inferred that the elevation of continental areas tends to keep 

 pace with erosion. The process by which this balance is main- 

 tained has been called isostasy, and the crust is said to be in an 

 isostatic state. \ The dynamics of the superficial strata with 

 the attendant phenomena of folding and faulting are thus re- 

 ferred to gravitation alone, or to gravitation and whatever 

 opposing force the rigidity of the strata may offer. In a 

 mathematical sense, however, the theory of isostacy is in a less 



* Notably Rev. Osmond Fisher. See his Physics of the Earth's Crust, Chap- 

 ter VIII. 



f Appendix to the Ninth Bridgewater Treatise (by C. Babbage), second edi- 

 tion, LondoD, 1838. 



\ Button, Capt. C. E., On some of the Greater Problems of Physical Geology, 

 Bulletin Philosophical Society of Washington, vol. xi, pp. 51-64. 



