As astronomical and seismic evidences strongly favor the view that the earth is rigid throughout, they lend support to the view that the interior retains its rigidity by the extrusion of liquid matter practically as fast as it is formed, and that this progressive extrusion adjusts the temperature to that which is consistent with solidity.

The bearing of this conception becomes evident on consideration. The shrinkage of the earth from loss of heat by conduction and by the extrusion of molten rock, affects the deep interior as well as the more superficial zones. It is even possible that the shrinkage may originate chiefly in the deeper zones. The postulated transfer of fluid rock from the deeper parts to the more superficial ones lessens the heat in the former, and adds to that in the latter. The postulated greater flow of heat from the deeper half to the outer half, than from the latter outward, gives a concordant result. If the conductivity of the deeper and denser material is appreciably greater than that of the more superficial and less dense material, as seems probable, this effect is intensified. The distribution of compressibility at the existing state of condensation may possibly be such that more new heat is generated by shrinkage in the outer parts than in the inner. Neither of these conceptions can be affirmed as actually taking place. They merely lie within the range of reasonable hypothesis in the present state of experimental data. What the real truth is must be left to further research. Present effort may be regarded as temporarily successful if it forms consistent conceptions of the applicable hypotheses, and of their consequences.

Recombination of material.—One other peculiarity of the accretion hypothesis must be recalled here. The incoming bodies must probably be assumed to have fallen in promiscuous order, and hence to have been indiscriminately mingled in the growing earth. As they became buried deeper and deeper and their temperatures and pressures were raised, much recombination, chemical and physical, may be presumed to have followed. As already noted, these changes would probably give increased density in the main. The material being, however, in a solid state, the rearrangement would be slow and its persistence in time indeterminate, and it may yet be far from complete. It is not improbable, therefore, under this hypothesis, that some notable part of the recent shrinkage of the earth has been due to the continued rearrangement of its heterogeneous internal matter. This would not be equally so in an earth derived from a molten mass, for the required adjustments of the material should have taken place while in the fluid state before solidification.

Comparison of the hypotheses.—By comparing the three hypotheses of the early states of the earth’s temperature, it will be seen that there is a radical difference, thermally, between the first and the last two. The first assumes a nearly uniform distribution of internal temperature, and hence, owing to the exceedingly slow rate of conduction, limits the movements and deformations of the crust, so far as dependent on heat, to very superficial horizons. The second and third views agree in postulating changes of temperature in the deep portions, as well as in the superficial, and hence involve the central portion of the earth in the great movements and deformations. It is not to be supposed that this of itself necessarily increases the sum-total of the effects of contraction, for, given a certain loss of heat from the surface, it may be relatively immaterial whether this loss arose from a large reduction of temperature in a shallow zone, or a small reduction of temperature in a deep zone, for, except as the coefficient of expansion varies, the total shrinkage would be the same. But the difference in distribution makes a radical difference in the resulting movements, for, in the first case, the movements are in a weak superficial shell that cannot accumulate great stresses, and hence must yield practically as fast as the stresses arise, while, in the second case, the stress-accumulating power of the thick segments may be great, and the stresses may gather for long periods and give rise to great cumulative results at long intervals. In this respect the last two views have much in common, though they differ in other important particulars.

With this general background of hypothesis, we may now turn to the direct evidences of the distribution of internal temperature which observations near the surface afford. Unfortunately they are limited to a mere film, as it were, little more than ¹⁄₄₀₀₀ of the radius of the earth.

OBSERVED TEMPERATURES IN EXCAVATIONS.

As the earth is penetrated below the zone of seasonal changes by wells, mines, tunnels, and other excavations, the temperature is almost invariably found to rise. The rate of rise, however, is far from uniform. If we set aside as exceptional the unusually rapid rise near volcanoes and in other localities of obvious igneous influence, the highest rates are still six times the lowest. A large number of records have been collated by the Committee on Underground Temperatures, of the British Association for the Advancement of Science. These range from 1° F. in less than 20 feet to 1° F. in 130 feet, with an average of 1° F. in 50 to 60 feet, which has usually been taken as representative. The more recent deep borings that have been carefully measured with due regard to sources of error indicate a slower rate of rise. Some of the more notable records are as follows:[257]

It is to be noted that even these selected records vary a hundred per cent. Very notable variations are found in the same mine or well, and often much difference is found in adjacent records, especially those of artesian wells. Some of these are explainable, but the full meaning of other variations is yet to be found.

Explanations of varying increment.—Certain apparent variations are merely due to inequalities of topography. The isogeotherms, or planes of equal underground temperature, do not normally rise and fall with every local irregularity of the surface, but more nearly strike an average. A well on a bluff 500 feet high would probably reach nearly the same temperature at 1000 feet, as a well 500 feet deep in the adjacent valley, giving a gradient twice as great in the one case as in the other.

In interpreting the temperatures of artesian flows, regard must be had to the depths of rock under which the waters have passed, as well as the depths at the location of the wells. Darton has found[258] unusually high and varying temperatures in the artesian wells of the Dakotas, some part of which may be due to this cause, though a full explanation of their singular variations is not yet reached.

The permeation and circulation of water affect the temperature in two important ways: (1) wet rocks are better conductors than dry ones, and (2) the convective movement of water is a means of conveying heat from lower to higher horizons. As the circulation of underground water is very unequal, much irregularity of thermal distribution in the upper zones probably arises from this source. The general effect of water circulation is to reduce the thermal gradient where the circulation is relatively rapid, as it is near the surface and in the main thoroughfares of circulation, and hence to cause a relatively rapid rise in the gradient just below the zone of effective water influence. Some records conform to this theoretical deduction, but in general it is masked by other influences.

Chemical action, especially oxidation, carbonation, hydration, solution, and precipitation, modify the normal temperature gradient, but how effectively is not well determined. With little doubt the first three mentioned above raise the temperature, while solution and precipitation in some large measure offset each other.[259] The sum-total is probably an appreciable rise in temperature. It has even been conjectured that the heat of volcanic action is due to chemical combination in the lower reaches of water circulation, but this is obviously an over-estimate.

Differences in the conductivity of rock are an obvious source of varying underground temperature gradients. If an outer formation conducts heat more freely than those below, it tends to lower the gradient within itself and to cause a relative rise in the gradient just below. If a lower formation is more conductive than that above, it tends to lower the gradient within itself, and to raise it in the one above, because it carries heat to the outer one faster than the latter carries it away.

The compression to which rocks have been subjected affects their temperature. At the surface the variation from this source is chiefly dependent on the lateral thrust suffered.

When allowances are made for all these and other known causes of local variation of temperature, it is still not clear that a uniform average gradient remains as the true conception. If the earth were once a molten spheroid, there would be a strong presumption that, aside from local variations, there would be a normal curve applicable to all regions. On the other hand, if the internal heat has arisen chiefly from compression, and if the compression has varied in different regions, as the inequalities of the surface render probable, there would be no such definite normal curve in the accessible zone of the earth, but rather a varying rate in different regions. In either case, the later movements, compressions and strains of the crust, must modify the original thermal gradients.

Gradients projected.—It is not probable that these gradients, even when corrected for local variations, continue unmodified to the center of the earth. If they did, 1° F. in 60 feet continued to the earth’s center would give 348,000° F., and 1° F. in 100 feet would give 209,000° F. It is much more probable that the rates of rise fall away below the superficial zone. If water circulation in the fracture zone is the most efficient agency cooperating with conductivity in the outward conveyance of heat, as seems probable, the gradient in that zone should rise at an abnormal rate, and hence the average gradient in the deeper portions not affected by this circulation should be lower. It will be recalled that the central temperature deduced from an extension of Barus’ fusion curve is 136,800° F. (76,000° C.), which, high as it is, gives a lower average gradient than the surface observations. The computations from compression by Lunn, giving a central temperature of 36,000° F. (20,000° C.), imply a still lower average rate, while the convection hypothesis postulates no sensible increase at all below 200 or 300 miles.

The amount of loss of heat.—The amount of loss of interior heat which the earth suffers may be estimated by that which is observed to be passing outward through the rock, or by computing the amount which should be conveyed outwards with the estimated gradients and with the conductivity of rock as determined by experiment. The latter method is usually employed in general problems. Taking the mean thermometric conductivity of rock as 0.0045, the gradient as 1° C. in 30 meters, the average specific heat of rock as 0.5 small calories per cubic centimeter, it is computed that in 100,000,000 years the loss of heat would amount to 45° C. (81° F.) for the whole body of the earth.[261] Tait makes the more conservative estimate of 10° C. (18° F.) in the same period.[262] This is an exceedingly small result, and emphasizes the low conductivity of rock.

The amount of shrinkage from loss of heat.—To compute the amount of shrinkage for a given amount of cooling, the average coefficient of expansion of rock is required. This has been experimentally determined by several investigators. By combining the determinations of others with his own, T. Mellard Reade found the linear coefficient to be .000005257 per 1° F., equivalent to .00002838 per 1° C. per volume. In this the proportions of the different rocks in the crust were roughly estimated. To secure an independent result from the best available estimate of what constitutes the average rock, W. H. Emmons has reduced Clarke’s average of the chemical constituents of the crust to the norm minerals under the new system of Cross, Iddings, Pirsson, and Washington (see p. 454) and made a weighted average of the conductivities of these, as shown in the following table:

Subtracting the stated volume from the volume at a temperature of 1° C. higher, the difference is found to be .0006708125, which divided by the volume gives .0000199, which is the coefficient of expansion of the theoretical, average, surface rock of the earth.

With this coefficient, the radial shrinkage resulting from an average loss of 10° C. (18° F.), (Tait’s estimate), is a little over a quarter of a mile (.2572); and for a loss of 45° C. (81° F.), (estimate of Daniell’s Physics), a little over a mile (1.1574). The shortening of the circumference for 10° C. loss is 1.6 miles, and for 45° C., 7.27 miles. Computations based on the coefficient of expansion adopted by Reade give 2.35 miles circumferential shortening for a loss of 10° C. and 10.5 miles for a loss of 45° C. In both these cases, the whole contraction is assumed to take a vertical direction, and hence these are maximum results. They are exceedingly small.

Unless there is a very serious error in the estimated rate of thermal loss, or in the coefficients of expansion, cooling would seem to be a very inadequate cause for the shrinkage which the mountain foldings, overthrust faults, and other deformations imply. This inadequacy has been strongly urged by Fisher[264] and by Dutton.[265] In view of the apparent incompetency of external loss of heat, the possibilities of distortion from other causes invite consideration.

OTHER SOURCES OF DEFORMATION.

Transfer of internal heat.—It is theoretically possible that deformation of the subcrust may result from the internal transfer of heat without regard to external loss. It has already been shown (p. 539) that under certain possible conditions more heat would flow from the inner parts to higher horizons than would be conveyed through these latter to the surface and there lost, and that, as a result, the temperatures of the inner parts might be falling, while those of the outer parts (except the surface) might be rising. With the more conservative coefficient of expansion previously given, a lowering of the average temperature of the inner half of the earth 500° C. and the raising, by transfer, of the outer half to an equal amount would give a lateral thrust of about 83 miles, which is about the order of magnitude thought to be needed. It is not affirmed that this takes place, but some transfer of this kind is among the theoretical possibilities under the accretion hypothesis. The process could not continue indefinitely; but, for aught that can now be affirmed, it may still be in progress.

Denser aggregation of matter.—As already noted, matter under intense pressure tends to aggregate itself in the forms that give the greatest density. If the earth were built up of heterogeneous matter arranged at haphazard, the material would probably readjust itself more or less, as time went on, into combinations of greater and greater density. This process may be one of the important sources of shrinkage, for an average change of density of 1 percent., affecting the matter of the whole globe, would probably meet all the demands of deformation since the beginning of the Paleozoic period.

Extravasation of lavas.—It is obvious that if lavas are forced out from beneath the crust and spread upon it, a compensating sinking of the crust will follow. This, however, is rather a mode than an ulterior cause, for a cause must be found for the extrusion of the lavas, and this cause may be one of the other agencies recognized, such as a transfer of heat, a reorganization of matter, or a change of pressure. The more practical question, however, relates to its competency. Can the amount of lava that has been extruded have had any very appreciable effect on the descent of the crust? The great Deccan flow is credited with an area of 200,000 square miles, and a thickness of 4000 to 6000 feet. Vast as this is for a lava-flow, it would form a layer only about 5 feet thick when spread over the whole surface of the globe, and hence the sinking to replace it would cause a lateral thrust, on any great circle, of about 31 feet only. It requires a very generous estimate of the lavas poured out between any two great mountain-making periods since the beginning of the well-known stratigraphic series to cause a horizontal thrust of any appreciable part of that involved in mountain-making. The case is different, however, if we go back to the Archean era, in which the proportion of extrusive and intrusive rocks is very high. Very notable distortion may then be assigned to the extravasation of lavas. The outward movement of lava must also be credited with some transfer of heat from lower to higher horizons, and this is probably one of the agencies that have produced the relatively high underground temperatures in the outer part of the earth.

If lavas are thrust into crevices of the crust they contribute to its extension, but causes for the crevices and for the intrusion must be found, and these are probably only expressions of one or another of the more general agencies.

Change in the rate of rotation.—As previously noted, the tide acts as a brake on the rotation of the earth. The oblateness of the present earth is accommodated to its present rate of rotation. It is assumed that such accommodation has always obtained, and that if the rotation has changed, the form of the earth has changed also. Now, the more oblate the spheroid, the larger its surface shell and the less the total force of gravity. Hence if the earth’s rotation has diminished, its crust must have shrunk, because the form of the spheroid has become more compact, and the increase of gravity has increased its density. There is at present a water-tide chiefly generated in the southern ocean, and irregularly distributed to more northerly waters. This irregularity interferes with its systematic action as a brake, and its average effects are difficult of estimation. The water-tides of past ages are still more uncertain, as they must have depended on the configuration and continuity of the oceans. There are geological grounds for the belief that the southern ocean was interrupted by land during portions of the past at least, and it is unknown whether there were elsewhere ocean-belts well suited to the generation of large tides. The ocean-tide, therefore, furnishes a very uncertain basis for estimating the retardation of rotation.[266] The theoretical case rests largely on the assumption of an effective body-tide. The earth doubtless has some body-tide, but whether it is sufficiently great to be effective, and whether its position, which depends on its promptness in yielding and in resilience, is favorable to the retardation of rotation, are yet open questions. The existence of an appreciable body-tide has not yet been proved by observation.

G. H. Darwin, assuming that the earth is viscous enough to give a body-tide of appreciable value and of effective position, has deduced a series of former rates of rotation of the earth and has computed the corresponding distances of the moon.[267] C. S. Slichter has shown that the lessening of the area of the surface and the increase of the force of gravity corresponding to these assigned changes of rotation are large, and that if the changes were actually experienced they must have involved much distortion of the crust.[268] These distortions would, however, be of a peculiar nature, and should thereby be detectible, if they were realized; for in passing from a more oblate to a less oblate spheroid, the equatorial belt shrinks, and the polar tracts rise and become more convex. Wrinkles should, therefore, mark the equatorial belts, and tension the high latitudes. Slichter has computed that in a change from a rotation period of 3.82 hours to the present one, the equatorial belt must shorten 1131 miles and the meridional circles lengthen 495 miles. If we take Heim’s estimate of the crust-shortening involved in forming the Alps—74 miles—as a standard, the 1131 miles of equatorial shortening would be sufficient for the formation of 15 mountain ranges of Alpine magnitude. If, as some geologists urge, the estimate of mountain folding is too great, the quotient would be still larger. These ranges should run across the equator and be limited to about 33° N. and S. latitude. The high-latitude tension would be sufficient to cause the earth to gape more than two hundred miles at the poles, if there were simple ideal shrinkage. The amounts and the distribution of thrust and shrinkage are shown in Fig. 453. If the change of rotation were no more than from 14 hours to the present rate, there would still be 52 miles of thrust in the equatorial belt, and 40 miles of shortage in the meridional circles. There are no clear signs of such a remarkable distribution of thrust and tension as this hypothesis requires. Mountains are about as abundant and as strong north of 33°, the neutral line, as south of it, and they extend to high latitudes. The Archean rocks, in which this agency should have been most effective because of their early formation, are crumpled and crushed in the high latitudes much the same as in low latitudes. Furthermore, if there had been appreciable change in the form of the earth to accommodate itself to a slower rotation, the water on the surface, being the most mobile element, should have gathered toward the poles, and the less mobile solid earth should have protruded about the equator, but the distribution of land and water, present and past, gives no clear evidence of this. The equatorial belt contains a less percentage of land than the area north of it and more than that south of it. It varies but slightly from the average for the whole globe.

While the doctrine of tidal retardation is theoretically sound, and while the relations of the moon to the earth have probably been appreciably affected by tidal action, geological evidence indicates that it has not been sufficiently effective in producing crustal deformations to be clearly detected by its own distinctive results. This may be due (1) to the fact that there are compensating agencies that tend to acceleration of rotation, and (2) to the probable fact that the central rigidity of the earth is too high to give a very effective body-tide. Hence the process of retardation may have been too slow to have been geologically appreciable in the known period. The recent estimates of the effective rigidity of the earth are greater than former ones, and they may need to be modified yet further in the same direction.

Distribution of rigidity.—An important consideration in this connection is the distribution of interior rigidity. It is certain that the rigidity of the outermost part, taken as a mass, is somewhat less than that of rock of an average surface type, for it is fissured, and there is no reason to suppose that the rigidity of the rock next below the fissure zone rises at once to the rigidity of steel, and hence if the average rigidity of the whole earth is equal to that of steel, a portion of the interior must have a rigidity much higher than steel. There is probably some law of increase from surface to center, and there are theoretical grounds for thinking that it is in some way connected with the laws of pressure, density, compressibility, and temperature. All of these factors probably affect rigidity, but in different ways. The modulus of rigidity of steel is about 770 × 10⁶ grms. per sq. cm. Milne and Gray[269] found that of granite to be 128 × 10⁶. The ratio of the rigidity of steel to that of rock is, therefore, about 6 : 1. If it be assumed that the rigidity increases in depth directly as the density, the rigidity will nowhere reach that of steel, being only about two-thirds as much at the center. If it be assumed that the rigidity increases as the squares of the density ratios, the following values are obtained:

These values seem fairly consistent with the apparent requirements of the case.

If the distribution of rigidity were of this nature, the average rigidity would be much less than that of steel, for more than half the volume lies in the outer division, between 1.00 and .75 radius, and yet the effective resistance to tidal deformation would be high, for, according to G. H. Darwin,[270] the tidal stress-differences are eight times as great in the center as at the surface. The rigidity would, therefore, be distributed so as to be much more effective in resistance than if it were uniform. The suggestion arises here that the tidal stresses and other analogous stresses arising from astronomical sources may be in themselves the causes of some such distribution of rigidity as this. The tidal stresses are rhythmical and give rise to a kind of kneading of the body of the earth, small in measure to be sure, but persistent and rapidly recurrent. Since these stress-differences at the center are eight times those at the surface, and since also the gravitative stress at the center is 3,000,000 times that at the surface, there is a series of persistently recurring stress-differences, greatest at the center and declining outwards, superposed on enormous static stresses, also intensest at the center and declining outwards. Now, if the earth material were once made up of a mixture of minerals of different fusibility, some of which became more mobile (whether fluid or viscous) than others under the rising temperature of the interior, it seems that the more mobile portion must have tended to move from the regions of greater stress-differences to those of lesser stress-differences. The persistence and the rhythmical nature of the tidal stress-differences seem well suited to aid the mobile parts in gradually working their way outwards. At the same time the more solid and resistant portions should remain behind, and thus come to constitute the dominant material of the central regions where stress-differences were greatest, and so, as it were, concentrate rigidity there. The process may still be in action.

If it be assumed that the rhythmical stresses have thus developed a resistance to deformation proportional to their intensity, we may combine this with density to form the basis of another hypothetical distribution of rigidity, as follows:

The average rigidity is here also much less than that of steel, but its distribution is such as to render it ideally fitted to resist tidal distortion.

These hypothetical distributions of rigidity have no claims to special value in themselves, for the grounds on which they are based are quite inadequate, but they are not without importance in giving tangible form to considerations that bear vitally not only on tidal problems, but on many others connected with the internal constitution and dynamics of the earth.

Sphericity as a factor in deformation.

It is obvious that if the earth shrinks, its crust must become too large for the reduced spheroid, and must be compressed or distorted to fit the new form. The amount of distortion required for any given shrinkage is easily computed from the ratio of the radius to the circumference of a sphere, which is approximately 1 : 6.28. If, for example, the radius shortens 5 miles, each great circle must on the average be compressed, wrinkled, or otherwise distorted to the extent of about 31 miles, or, in reversed application, if the mountain foldings on any great circle together show a shortening of 100 miles, the appropriate radial shortening is 16 miles. The ratio of 1 : 6+ furnishes a convenient check on hypotheses that assign specific thrusts to specific sinkings of adjacent segments. A segment 3000 miles across, for example, such as the bottom of the North Atlantic basin, sinking three miles, about the full depth of the basin, would give a lateral thrust of about 2.2 miles, a little over a mile on each side, a trivial amount compared with the foldings on the adjacent continental borders.

The influence of the domed form of the surface.—Because of the spheroidal form of the earth, each portion of the crust is ideally an arch or dome. When broad areas like the continents are considered, it is the dome rather than the arch that is involved, and in this the thrust is ideally toward all parts of the periphery. It is probably for this reason that mountain ranges so often follow curved or angulated lines, or outline rude triangles or polygons. The sigmoidal courses of the ranges of southern Europe, the looped chains of the eastern border of Asia, and the curved ranges of the Antillean region, are notable examples. The border ranges of the Americas, of the Thibetan plateau, and of other great segments, illustrate the polygonal tendency. The general distribution of the great ranges is such that a nearly equal portion of crustal crumpling is thrown across each great circle, as theory demands. The common generalization that mountain ranges run chiefly in oblique directions, as northeast-southwest, northwest-southeast, is but a partial view of the more general fact that the lines of distortion must lie in all directions to accommodate the old crust to the new geoid, if there be equable contraction in all parts.

Theoretical strength of domes of earth-dimensions.—As the domed form of the crust has played an important part in theories of deformation, it is important to form quantitative conceptions of the strength of ideal domes having the figure and dimensions of segments of the earth’s crust. According to Hoskins,[271] a dome corresponding perfectly to the sphericity of the earth, formed of firm crystalline rock of the high crushing strength of 25,000 pounds to the square inch, and having a weight of 180 pounds to the cubic foot, would, if unsupported below, sustain only 1⁄525 of its own weight.[272] This result is essentially independent of the extent of the dome, and also of its thickness, provided the former is continental and the latter does not exceed a small fraction of the earth’s radius. If this ideal case be modified by supposing the central part of the spherical dome to rise above the average surface, the supporting power will not be materially changed unless the central elevation is a considerable fraction of the radius of the dome. Assuming a central elevation of two miles—to represent the protrusion of the continental segments—the results for domes of different horizontal extent are as follows:[273]