From this table it will be seen that for domes of continental dimensions the supporting strength equals only a very small fraction of the dome’s own weight. Increasing the thickness of the shell increases its actual supporting power, but the proportion is somewhat less when the whole sphere is concerned. The problem has not been worked out for domes of limited extent. For rough estimates, where the dimensions of the dome are of continental magnitude, each mile of thickness may be taken as supporting a layer of about 10 feet of its own material. If the hypothetical level of no stress be placed at 8 miles depth, the shell above this, by reason of its domed shape, could relieve its own pressure on that below to an amount equal only to the weight of about 80 feet of rock over its surface, even if its form and structure were ideal. If the shell were thick enough (817 miles) to embrace one-half the volume of the earth, its supporting power would be a little more than the weight of one and one-half miles of rock. As the radius of the earth is less than 4000 miles, the extreme supporting power reckoned on this basis would be only about 8 miles of rock-depth. It is interesting, if not significant, to observe that this depth barely reaches the minimum shrinkage that will serve, according to current estimates, to account for the crustal shortening of the great mountain-making periods. It is as if the shrinkage stresses accumulated to the full extent of the stress-resisting power of the whole sphere, and then collapsed. It is not safe, however, to give much weight to this coincidence, for higher densities and probably higher resistances to distortion come into play in the deeper horizons. If these resistances are proportional to the higher densities of the interior, the deductions would remain the same. If the effective rigidity of the earth as a whole is that of steel, as deduced by Kelvin and Darwin from tidal and other observations, or twice that of steel, as inferred by Milne from the transmission of seismic vibrations, the supporting power of the body of the earth dependent on its sphericity would be appreciably higher.

It would seem clear from the foregoing considerations that something more than the mere crust of the earth has been involved in the great deformations. Indeed it is not clear that the fullest resources of stress-accumulation which the spheroidal form of the earth affords are sufficient to meet the demands of the problem, unless the rigidity of the earth be taken at a much higher value than that of surface-rock, and this is perhaps an additional argument for the high rigidities inferred from tides and seismic waves.

In view of the doubtful competency of even the thickest segments to accumulate the requisite stresses, there is need to consider modes of differential stress-accumulation other than those dependent on sphericity.

Stress-accumulation independent of sphericity.—The principle of the dome is brought into play whenever an interior shell shrinks away, or tends to shrink away, from an outer one which does not shrink. In this case, there is a free outer surface and a more or less unsupported under surface toward which motion is possible. The dome may, therefore, yield by crushing or by contortion. The computations given above are for cases of this kind. But where the thickness becomes great and the dome involves a large part or even all of a sector of the earth, freedom of motion beneath is small, and to readjust the matter to a new form, strains must be developed widely throughout the sector, and must involve regions where the pressure is extremely great on all sides, and crushing in the usual sense impossible. Assuming the correctness of the modern doctrine that such pressure increases rigidity, instead of the older doctrine that it gives plasticity, it becomes reasonable to assume that stress-differences would be distributed throughout the mass, and bring into play a large portion of its stress-accumulating competency. When the mass yielded, it would not be by crushing, but by “flowage,” which would be more or less general throughout the mass. It might, however, be partially concentrated, as, for example, on the borders of sectors of different specific gravity.

Stress-differences may arise from physical changes within the rock itself. Whenever there is a re-aggregation of matter, or a change of any kind which involves change of volume, a change of stress is liable to be involved. It may be of the nature of relief or of intensification. In an earth built up by the haphazard infall of matter, a very heterogeneous mass must result, and the subsequent changes may be supposed to be intimately distributed through the mass, being slight at any point, but present at innumerable points. An immeasurable number of small stress-differences may, therefore, be developed throughout the mass. Until these overmatch the effective strength of the mass, they may continue to accumulate. These are not necessarily connected with stresses that arise from sphericity, and may work more or less independently of them. It is not improbable that the great stress-accumulating power of the globe finds an essential part of its explanation in supplemental considerations of this kind, and not wholly in its spheroidal form.

The actual configuration of the surface.—The foregoing computations relative to the power of shells of the earth to sustain pressures are based on ideal forms and structures that are not realized in fact. How far the earth fails to conform to these conditions must now be considered. When compared with the earth as a whole, the inequalities of its surface are trivial. If the great dynamic forces acted through the whole or the larger part of the body of the earth, the configuration of the surface can be supposed to have done little more than influence the location of the surface deformations and their special phases. But if the forces were limited to a crust of moderate thickness, the configuration of the surface is a matter of radical importance.

Concave tracts.—There is need, therefore, to inquire if any considerable breadth of the crust is outwardly plane or concave, for the principle of the dome is obviously not applicable to a plane or concave surface. To be a source of fatal weakness, the concavity must be broad enough to cause the planes of equal cooling, the isogeotherms, to be concave to considerable depths. For example, if the hypothetical level of no stress is eight miles below the surface, as computed on certain assumptions, the concave portion must be so broad that the isogeotherms will also be concave outward at something near that depth; in other words, the main part of the zone of thrust must be concave. A narrow concavity at the surface, such as an ordinary valley in a portion of the crust that has the average convexity, would not seriously depress the isogeotherms, or affect the zone of thrust, but a valley several times eight miles (level of no stress) in breadth would. For inspecting the surface of the earth in this regard, it is convenient to know what amounts of fall below the level surface give a true plane for given distances. These are shown in the following table:[274]

Applying these criteria to the surface of the lithosphere, it is found that concave tracts from 100 to 300 miles in breadth are not uncommon. The more notable of these are shown in black on the accompanying map, Fig. 454, and two typical ones are shown in cross-section in Figs. 455 and 456. It is to be observed that concave tracts border the continents very generally. They are connected with the descent from the continental shelf to the abysmal basins, and are unsymmetrical. Notable concavities are found in some of the great valleys on the continental platforms. The basins of Lake Superior, Michigan, Huron, and Ontario are in part concave; so are Puget Sound, the Adriatic, and the Dead Sea; so also are the valleys of California, of the Po, and of the Ganges, when the adjacent mountains are included. Some of the “deeps” of the bottom of the ocean are notably concave. Fig. 455, a cross-section of the Challenger Deep, drawn to true scale and convexity, shows the nature of the phenomenon. The breadth is here 300 miles, and the depression below a true plane is 11,400 feet. The lower line of the figure shows the approximate position and form of the normal isogeotherm about ten miles below the surface. Assuming equal conductivity in all parts, it is clear that the isogeotherms must be concave upwards for a considerable distance below ten miles. Unless the shell of thrust is much more than ten miles thick, these concave portions should yield as fast as cooling below them permits, and no stresses arising from convexity could be accumulated.

These concavities of surface are so extensive and so widely distributed over the globe that no part of the outer shell can be supposed to be capable of accumulating notable stresses unless rigidly attached to the earth-body below. In other words, so far as sphericity is concerned, the crust must ease all its stresses nearly as fast as they accumulate, if, as usually assumed, it rests on a contracting or mobile substratum.

Surface cooling under these conditions should give only feeble thrusts, developed and eased nearly constantly. Such movements should be admirably adapted to give those gentle, nearly constant subsidences that furnish the nice adjustments of water-depth required for the accumulation of thick strata in shallow water, and those slow upward warpings that renew the feeding-grounds of erosion, the necessary complement of the deposition. These gentle, nearly constant movements mark every stage of geological history, and constitute one of its greatest though least obtrusive features. But if superficial stresses arising in this way are eased in producing these effects, they cannot accumulate to cause the great periodic movements.

Even where the crust is not concave, it is so warped and so traversed by folds and fault-planes that its resistance to thrust is relatively low, and it should, therefore, warp easily and at many points, if the thrust be confined to a superficial crust.

General conclusion.—When to the weakness of the crust, as computed under ideal conditions, there is added the weakness inherent in these concave and warped tracts, the conclusion seems imperative that while the crust is the pliant subject of minor and nearly constant warpings, such as are everywhere implied in the stratigraphic series, it is wholly incompetent to be the medium of those great deformations which occur at long intervals and mark off the great eras of geologic history. These great deformations apparently involve the whole, or a large part, of the body of the earth, and seem to require a very high state of effective rigidity.

General references on crustal movements.—Babbage, Jour. Geol. Soc., Vol. III (1834), p. 206 Lyell, Principles of Geology, Vol. II, p. 235; Mallet, Phil. Trans. (1873), p. 205; Reade, Origin of Mountain Ranges, and Evolution of Earth Structure; Fisher, Physics of the Earth’s Crust; Dutton, Greater Problems of Physical Geology, Bull. Phil. Soc. of Washington, Vol. XI, p. 52, also Amer. Jour. of Sci., Vol. VIII (1874), p. 121, and Geology of the High Plateaus of Utah (1880); Jamieson, Quar. Jour. Geol. Soc. (1882), and Geol. Mag. (1882), pp. 400 and 526; Heim, Mechanismus der Gebirgsbildung; Marjerie and Heim, Les Dislocations de l’Écorce terrestre (1888); Shaler, Proc. Boston Soc. Nat. Hist., Vol. XVII, p. 288; Dana, Manual of Geol., 4th ed., p. 345 et seq.; Woodward, Mathematical Theories of the Earth, Smithsonian Rept. for 1890, p. 196; Willis, The Mechanics of the Appalachian Structures, 13th Ann. Rept. U. S. Geol. Surv., Pt. II (1893), pp. 211–282; LeConte, Theories of Mountain Origin, Jour. Geol. Vol. I (1893), p. 542; Gilbert, Jour. Geol., Vol. III (1895), p. 333, and Bull. Phil. Soc. of Washington, Vol. XIII (1895), p. 31; Van Hise, Earth Movements, Trans. Wis. Acad. Sci., Arts and Let., Vol. II (1898), pp. 512–514; Estimates and Causes of Crustal Shortening, Jour. Geol., Vol. VI (1898), pp. 29–31; Relations of Rock Flowage to Mountain Making, Mon. XLVII, U. S. Geol. Surv. (1904), pp. 924–931; A. Geikie, Text-book of Geology, 4th ed., pp. 672–702.