280 Mathematical Theories of the Earth. — Woodward. 
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 later stages. Its depth is independent of the 
initial temperature of the earth ; and if we adopt Thompson'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 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 subjected, 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 
alone can account for. 
The opponents of the contractional theory of the earth, believing it 
quantitatively insufficient, have recently revived and elaborated an 
idea first suggested by Babbage and Herschel 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 can- 
not be greatly disturbed without a readjustment and consequent move- 
ment 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 corresponding eleva- 
tion 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 maintained has been called 
"isostacy," and the crust is said to be in an isostatic state. The dyna- 
mics of the superficial strata with the attendant phenomena of folding 
and faulting, are thus referred 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 satis- 
factory state than the theory of contraction. As yet we can see only 
that isostacy is an efficient cause if once set in action; but how it is 
started and to what extent it is adequate remains to be determined. 
Moreover isostacy alone does not seem to meet the requirements of 
geological continuity, for it tends rapidly towards stable equilibrium, 
and the crust ought therefore to reach a state of repose earh- in geologic 
time. But there is no evidence that such a state has been attained, 
and but little if any evidence of diminished activity in crustal move- 
ment during recent geologic time. Hence we infer that isostacy is 
competent only on the supposition that it is kept in action by some 
othercausetendingconstantly to disturb the eciuilibrium which would 
otherwise result. Such a cause is found in secular contraction, and it 
