Chapter IX (2)

=Gravity.=—The most obvious of the concentrating forces is gravity, and in most questions relating to great segmental movements, it has been thought sufficient to consider gravity alone, but it is by no means certain that this does not lead to serious error. In studying the causes and effects of earth movements, it is necessary to consider both gravitational _energy_ and gravitational _force_. Gravitational _energy_ is greatest when the mass is most widely dispersed, and least when most concentrated. Gravitational _force_ is greatest when the mass is most concentrated, and least when most dispersed. The gravitational energy of the earth matter was at its maximum when it was most widely diffused in the supposed nebulous condition. It will perhaps reach its minimum at some future period when the shrinkage shall reach its limit. In passing from an expanded condition to a more concentrated condition, potential energy, or energy of position, is transformed into other forms of energy, chiefly heat. The heat thus developed is an important factor in the earth’s dynamics. The total amount of gravitational energy involved in the earth’s evolution is unknown, for neither the maximum dispersion of the earliest state, nor the ultimate condensation, is known. It is not difficult, however, to compute the amount of transformation of gravitational energy into heat, or other forms of energy, during a given degree of condensation. If a mass equal to that of the earth were originally infinitely scattered, the gravitational energy given up by it in condensing into a homogeneous sphere of the earth’s present size would, if all transformed into heat, suffice to raise the temperature of an equal mass of water 8900° C. (Hoskins), or an equal mass of rock (specific heat of .2), 44,500° C. If the mass were more condensed toward the center, as is the actual case, the heat would be considerably greater. If the condensation toward the center followed the Laplacian law (p. 564), the heat would be sufficient to raise the earth mass 48,900° C., assuming its specific heat to be .2, which is about the average specific heat of rock at the surface (Lunn). A further shrinkage of one mile would transform an additional amount of gravitational energy into heat about equal in amount to Tait’s estimate of the loss of heat from the surface of the earth in 100,000,000 years (see p. 572). If the radial shrinkage has been 32 miles, or even 16 miles, the amount of heat generated is very much greater than the estimated loss from the surface.

How much gravitational energy can possibly be transformed into heat and other forms of energy in the future, can only be computed by making assumptions as to the possible extent of further contraction, and that involves hypotheses as to the atomic and sub-atomic constitution of the earth’s matter, and its behavior under the prodigious pressures of the earth’s interior. All shrinkage develops added gravitational force and further tendency to shrinkage, which follows when the heat generated by the shrinkage is lost; and where the process may end, in a body of the dimensions of the earth, is beyond present determination. If there were no limit to the density that might be attained, it would be impossible to assign any limit to the energy that might be transformed. It has usually been assumed that contraction could not go on indefinitely because the atoms would come into actual contact, and prevent further increase of density. This conception rests on the recently prevalent hypothesis of the atomic constitution of matter; but the more recent hypotheses that substitute multitudes of revolving corpuscles or electrons for irreducible atoms, do not carry the same presumption of a rigorous limit to condensation. It is not therefore prudent to try to set such a limit, or to make it a feature in the dynamical doctrines of the earth. It is even less prudent to try to measure the limit of future conversion of the gravitational energy of the sun into heat, and so to set a limit to the habitability of the earth.

The _force_ of gravity may be defined as the effort of gravitational energy to change into other forms of energy. It is most familiarly expressed in terms of weight, which is the resultant of the gravitational force of the whole earth upon a given portion. Weight is determined by the distances and directions of the given portion from all parts of the attracting mass, the amount of the attraction being directly as the mass and inversely as the square of the distance, modified by the direction. It is greatest about 610 miles below the surface, where it is 1.0392 times that at the surface. Below this point it declines, and at the center it is zero. The sum total of the earth’s gravitative force at the present time is equivalent to about 6 × 10²¹ tons. This gives rise to a pressure of about 3,000,000 atmospheres at the center of the earth.

Gravitational force is also expressed in terms of the earth’s ability to accelerate the velocity of falling bodies at its surface, which is now approximately 32 feet per second. For certain purposes, the force of gravity may be better pictured by means of the velocity required to overbalance it, which is 6.9 miles per second; e.g. a body shot away from the surface at a speed exceeding 6.9 miles per second, would escape from the control of the earth if the influence of the atmosphere and other bodies is neglected; while a body shot away at less than this speed would return to the earth.

=Molecular and sub-molecular attractions.=—In addition to gravity, there are at least three additional classes of attractive agencies whose laws appear to differ from those of gravity, viz. cohesion, chemical affinity, and sub-atomic attraction, using these terms in their comprehensive generic senses. The thought has been entertained that these might be reducible to forms of gravity in ulterior analysis, but it does not appear from existing evidence that the laws of their attractions are conformable to the Newtonian law of the inverse square of the distance, to which gravity conforms. Apparently the forces of the molecular, atomic, and sub-atomic attractions increase at higher rates, and have individual peculiarities of action quite different from gravity. It would be of the utmost service to geological philosophy if these laws of molecular and sub-molecular attractions were firmly established, and could be applied to the conditions of heat and pressure under which the matter of the interior of the earth exists. In the absence of such determinations, we can do little more than recognize that the matter of the interior of the earth tends to condense itself by the aid of molecular and sub-molecular attractions, supplemental to the attraction of gravity.

=Cohesion and crystallization.=—The force of gravity between small bodies is exceedingly feeble, but it is cumulative, every particle in a mass attracting every other particle, so that in great masses the force becomes enormous. In cohesion, and probably in the other molecular and sub-molecular attractions, the particles attract very strongly the particles with which they are in close relations, but beyond minute distances their effects are insensible. The force of crystallization is felt for a very short distance from the crystal, and “mass action” is probably dependent on a function of similar kind, acting at a very small distance, but the range of these forces is very limited in comparison with that of gravity.

Rock matter, as a rule, tends to become crystalline by the assembling of like molecules in systematic order. The general effect is condensation, though this is not universally the case, for in some instances the crystalline arrangement results in expansion. The crystallizing force may be regarded as a specialized variety of cohesion which usually coöperates with gravity to produce increased density. In cases of expansion it seems clear that the organizing force does not act according to the law of gravity. The intensity of the force exhibited in the formation of ice illustrates the superiority of the molecular force over the gravitative force in small masses; but in a planet of ice of very moderate dimensions, the internal pressure of gravity would overcome the crystalline force, which illustrates the superiority of gravity in large masses.

While the crystalline force may thus in exceptional cases operate against gravity, it is known that in most cases it not only operates with it, but is controlled by it, in this sense—that where a substance has two forms of crystallization, it will take the denser one when the pressure is great. The inference is that if the less dense form of crystallization takes place under slight pressure, and subsequently the pressure is greatly increased, the form of crystallization will change from the less to the more dense.[247] It is probable that in general those forms of molecular arrangement will be assumed in the deep zones which give the greatest density, and this probably includes concretionary, colloidal, and other forms of aggregation, as well as crystallization.

=Diffusion.=—The same law probably holds relative to diffusion, though in a molecular sense diffusion is the opposite of crystallization, for in crystallization, like comes to like, while in diffusion the molecules distribute themselves among those of unlike nature. Diffusive action, quite familiar in gases and liquids, takes place to some extent in solids. The molecules of plates of gold and lead brought into intimate contact under pressure mutually diffuse among one another. So gases seem to be very generally diffused or “occluded” in rocks, though the nature of this relation is imperfectly determined. It is known that pressure upon gases promotes their diffusion through liquids and solids. It is inferred that pressure upon a solid tends to the diffusion of the entrapped gases within it, but it is not to be inferred from this that pressure upon rock promotes the absorption of gases into it, but rather the opposite. It is probable that great pressure with high heat promotes the diffusion of entrapped gases or other diffusible substances through the rock-mass, and at the same time tends to their extrusion along lines of least resistance; but this is an inference rather than a demonstration.

=Chemical combination.=—The general effect of chemical combination under pressure is greater density. In reversible reactions capable of conditions of chemical or physical equilibrium, pressure invariably favors the formation of the denser of any possible products.

=Sub-atomic forces.=—Recent investigation has made it probable that atoms are composite, embracing many exceedingly minute bodies—corpuscles or electrons—in a state of extremely high activity and possessed of marvelous energy notwithstanding their minuteness. This discovery possesses deep interest to the geologist because it seems to reveal sources of energy of almost incalculable potency, some portions of which at least are being constantly freed and added to the previously recognized supplies of energy. Attempts have been made during the past few decades to limit the habitable age of the earth, both retrospectively and prospectively, by the smallness of the sum total of energy derivable from gravity. In these estimates slight recognition has been given to the resources of molecular and atomic energy, and none at all to the possibilities of sub-atomic energy. It would be going quite too far to assume that these sub-atomic energies are all available for the perpetuation of habitable conditions on the earth or in the solar system, but we are doubtless justified in appealing to them as an offset to all dicta restricting the period of the earth’s habitability by supposed insufficiencies of energy deduced merely from the estimated resources of gravity. The banishment of the idea of the atom as a minute, incompressible, undecomposable sphere takes away the theoretical limit of compressibility, and by so doing cuts away the groundwork for assigning definite limits even to the resources of gravity, since, as already indicated, unlimited condensation gives theoretically unlimited transformation of the potential energy of gravity.

While we must await with such patience as we can command the development of fuller knowledge concerning the nature and laws of the molecular, atomic, and sub-atomic energies, and their applicability to the activities resident in the interior of the earth, it is permissible even now to assume that, besides the simple compressive action of gravity, there are at work varied forms of molecular aggregation, of atomic combination, and perhaps of sub-atomic change, tending toward increased density, and that the ulterior limit of these processes is quite undetermined. The condensational forces are now restrained at certain temporary limits by the antagonistic resistant forces, some of which, such as heat, are the products of the condensational forces, and are gradually being dissipated, permitting further condensation. Where the process may ultimately end, we dare not attempt to say. On the other hand, we are not compelled to accept assigned limits that seem to be inconsistent with the phenomena which the earth actually presents.

2. _The resisting agencies._

=Heat.=—The most familiar of the active agencies that resist condensation is heat. Upon this the existing volume of the earth is immediately dependent, in some large part at least. As this heat is dissipated, the earth shrinks. This shrinkage increases the force of gravity, and hence the internal pressure increases, and, if further compression takes place as the result of this increased pressure, additional heat is developed, which checks further condensation until it is dissipated. It is this kind of creative and self-checking action that determines the volume of great gaseous bodies like the sun. Though their matter is far from its ultimate density, and their self-gravity is enormous, they condense slowly, because, with every stage of condensation, heat is generated which antagonizes gravity and checks condensation, until at least a part of the heat is radiated away. As the force of gravity increases with every stage of condensation, the heat developed to hold it in check must increase, and hence the famous law of Lane, that a gaseous body like the sun grows hotter as it condenses. This law holds good while the body remains in a gaseous state in which the maintenance of the volume is essentially dependent on heat. When a body becomes liquid or solid, its volume is dependent in part on forms of resistance other than heat, and the force of the law is abated, though the principle still holds good. In small solids, the principle has little application, since the force of self-gravity is slight compared to the resisting forces, and very little new heat is generated as the body loses that which it has; but in large bodies, like the earth, where the condensational forces are enormous and the internal temperature is very high, it is not improbable that the heat generated at every stage of condensation is relatively large. It has been inferred by some students of the phenomena that the conditions in the interior of the earth are essentially those of gaseous matter, so far as molecular relations are concerned, because the temperatures are thought to be above the critical temperatures of the substances composing it. If this be true, the new heat generated with each stage of condensation is large. However this may be, it seems safe to infer that in so far as the volume of the interior mass is dependent on heat resistance, _the loss of existing heat leads to the generation of new heat_. The amount of this new heat must be enough, together with the residual heat and the other forces of resistance, to match the new condensational forces. The molecular and sub-molecular forces of resistance other than heat, are probably responsible for some large part of the resistance to the increased condensational force, but how much is not determined.

=All resistance perhaps due to motion.=—As now interpreted, the force of resistance of heat is due to the impact of the flying particles of the heated matter. The other forms of resistance to compression have not usually been interpreted in this way, but the tendency of recent investigation is to place them in the same dynamic class. A cold solid body offers resistance to compression that is in no obvious way dependent on heat motion. In small bodies this resistance is immeasurably greater than the self-gravity of the body. It is so great that it can only be partially overcome by any force which human ingenuity can bring to bear upon it. This form of resistance has thus, not unnaturally, come to be regarded as approximately immeasurable, and perhaps as grading into actual immeasurability, and as resting back upon the actual contact of irreducible atoms. But the recent researches which have developed grounds for the conception that even the atoms are composite, lead to the further conception that their resistance to compression is dependent on the movement of their constituent corpuscles or electrons. This encourages the broad conception that the whole of the resistance to compression arises from molecular, atomic, and sub-atomic _motions_, of which heat is merely one form.

While all this is yet on the frontier of physical progress, these conceptions may well be recognized in framing interpretations of the agencies which determine the volume of the earth, and which control the changes that take place in it from age to age. The result of their combined action at any stage is _a state of temporary equilibrium_ between gravity, aided by the molecular, atomic, and sub-atomic attractions, on the one hand, and heat, aided by the molecular, atomic, and sub-atomic resistances, on the other. The vital problem is to ascertain _the original condition of balance_ between these antagonistic forces, and the changes which have affected that balance since. The original state of balance is necessarily a matter of hypothesis, and the best that can be done at present is to picture as clearly as possible the different hypotheses that have been entertained, and the different consequences that logically flow from them. The most important factor in the case is the original amount and distribution of internal heat.

ALTERNATIVE VIEWS OF ORIGINAL HEAT DISTRIBUTION.

The hypothetical modes of origin of the earth will be treated in the historical section. Suffice it here to say that one view is that the earth was once gaseous, passed thence into a liquid, and later into a solid state. Under this view, there are two hypotheses as to the original distribution of internal heat, dependent on the mode of solidification. According to the one, solidification began at the surface after convection had brought the temperature of the whole mass down nearly to the point of congelation; according to the other, solidification began at the center at a high temperature, because of pressure, and proceeded thence outwards. The former only has been much developed in the literature of the subject, though the latter is now generally regarded as the more probable.

Another view of the globe’s origin is that the earth was built up gradually by the infall of matter, bit by bit, at such a rate that though each little mass became hot as a result of its fall, it cooled off before others fell on the same spot, the rain of matter not being fast enough to heat up the whole mass to the melting-point. Under this view, the internal heat arose chiefly from compression due to the earth’s gravity.

A clear conception of the three hypotheses of thermal distribution which rest on these two views of the origin of the earth is important to the further discussion.

=1. Thermal distribution on the convection hypothesis.=—It was formerly the prevailing opinion that the molten condition of the earth persisted in the interior until after the crust had formed, and that solidification proceeded from the surface downwards. It was a natural corollary of this view that, previous to the beginning of solidification, convection stirred the liquid mass from center to circumference and equalized the temperature so that the whole mass cooled down equably until it approached the point of solidification and became too viscous for ready convection. The temperature should, therefore, have been nearly the same from center to surface at the stage just preceding incipient solidification. This conception forms the basis of most discussions involving internal temperatures.[248] The famous studies of Lord Kelvin are based on the assumption of a uniform initial temperature of 7000° Fahr.[249] Other temperatures have been assumed in similar studies by others, but the results do not differ materially. On this hypothesis there would be no deep-seated change of temperature until a temperature-gradient, extending to the deeper horizons, had been developed by surface cooling. In the earliest eras, the loss of heat would be felt solely in the outer zone. By surface cooling, a temperature gradient would be slowly developed, and gradually changed from age to age, as shown by the curved lines in Fig. 450, each of which shows the temperature at the successive stages stated in the legend. The computations for these curves were based on the methods and assumptions of Lord Kelvin. The two lower curves represent greater periods than those usually assigned by geologists to the whole history of the earth. It will be seen that the modification of the original temperature line extends only about 160 miles below the surface for the 100,000,000-year period, only about 240 miles for the 237,000,000-year period, and only about 320 miles for the excessive period of 600,000,000 years. The superficial nature of the whole thermal problem under this hypothesis is thus made clear and impressive.

After the outer shell had cooled so as to be in approximate equilibrium with the environment of the earth, it suffered practically no contraction.

So also it appears from the diagram that there was practically no contraction below 160 miles up to the end of the 100,000,000-year period, because cooling had not yet reached that depth. Between these two non-contracting horizons the greatest rate of contraction at the close of the 100,000,000-year period lay about 60 miles below the surface. The contraction of this middle zone, while the outermost shell and the interior body remained constant, is held to have developed a state of horizontal thrust in the outer shell, because this shell, being too large for the shrinking subcrust, tended to settle, and to crowd upon itself horizontally. The wrinkling and other modes of deformation of the outer part of the earth are referred, under this view, to the thrust so developed. This is the view which has been most generally accepted.

=Level of no stress.=—As the outer shell is thus held to be in a state of thrust while the zone below is in a state of shrinkage, there must be, between these two zones, a _level of no stress_, where there is neither compression nor stretching. Above this level, the thrust increases to the surface, and below it, the stretching increases to the depth of most rapid change of temperature, below which it decreases and finally vanishes at the lower limit of temperature change. In the earliest stages of cooling, the level of no stress must have been near the surface, and must have descended gradually as the cooling proceeded. The depth of this level has been repeatedly computed on the basis of assumed times and rates of cooling. Fisher, assuming the temperature of solidification to have been 4000° Fahr. and the period of cooling 33,000,000 years, computed its depth at only ⁷⁄₁₀ of a mile below the surface.[250] T. Mellard Reade, with somewhat different assumptions, placed it at 2 miles after 100,000,000 years of cooling.[251] Davison (1897) placed it at 2.17 miles,[252] and G. H. Darwin at 2 miles after the same period.[252] In a later computation, based on the assumption that the coefficient of dilatation increases with the temperature, Davison placed the level of no stress at 7.79 miles, and stated that if the coefficient of conductivity and the initial heat also increased down wards, the zone would lie still deeper. To suppose the initial heat to increase downwards, however, is to abandon the hypothesis we are now considering. These computations seem to show that, at the very utmost, the level of no stress, under this hypothesis, lies at a very slight depth, and that the thrust zone above is, therefore, very shallow. This should be kept constantly in mind in all deductions drawn from this hypothesis. If the thickness of the thrust zone be taken at 8 or 10 miles, it will apparently be conceding to the view all that can legitimately be claimed for it.

=2. Thermal distribution on the hypothesis of central solidification.=—When the previous conception was first formed, the effect of pressure on the melting-points of lavas was neglected, as little or nothing was known on the subject. Experiment, however, has shown that pressure, as a rule, raises the melting-points of lavas, and out of this has grown the doctrine that the earth solidified first at the center, where the pressure was greatest, and gradually congealed outwards. Barus has shown that the melting-point of diabase,[253] selected as a representative rock, rises directly with the pressure. If this rate holds good to the center of the earth, the melting temperature of diabase there would be 76,000° C. (136,800°F.). The range of the experiment is, however, very small compared with the range of the application, and little confidence can be felt in the special numerical result reached. The rate of rise of the fusion-point may be much changed as the extraordinary conditions of the deep interior are invaded. Still there is good ground for the hypothesis that solidification took place at some very high temperature at the center, because of the very great pressure there. The inference then is that when the temperature of the center of the supposed molten globe reached the appropriate point, solidification began there, and that it took place at lesser depths in succession as the appropriate temperatures were reached. This view _excludes convection_ in the successive zones from the center outward after the time when their temperatures of solidification were reached, or after these were approached sufficiently near to develop prohibitive viscosity. Some loss of heat from these horizons would be suffered while the outer parts were solidifying, but on account of the exceedingly slow conductivity of rock, it is improbable that the amount of loss would be sufficient to change the general character of the internal distribution of heat previous to solidification at the surface, the time when the existing phase of the earth’s history by hypothesis began. Fig. 451 shows the theoretical distribution of heat under this view. The consequences of this assumption are very important to geological theory and, carried out to their logical consequences, lead to the conclusion that cooling and shrinkage _affected the deep interior of the earth_, for the high central heat must have been constantly passing out toward the surface. Instead, therefore, of the contraction being concentrated in and limited to the outer 200 miles or so, as under the preceding hypothesis, it was deeply distributed. The contraction within the outer zone would be less than under the preceding view, because the flow of heat from within would partially offset the flow outwards, and a corresponding part of the contraction would be distributed below.

COMPUTED PRESSURES, DENSITIES, AND TEMPERATURES WITHIN THE
EARTH BASED ON LAPLACE’s LAW.

+------------+--------------+----------+-------------+
| Distance | Pressure | | |
|from center | in megadynes | | Temperature |
|in terms of | per sq. | Density. | in |
| radius. | cm.[254] | | degrees C. |
+------------+--------------+----------+-------------+
| 1.00 | 0 | 2.80 | 0 |
| .95 | 97,000 | 3.37 | 320 |
| .90 | 215,000 | 3.95 | 1,110 |
| .85 | 353,000 | 4.54 | 2,190 |
| .80 | 510,000 | 5.13 | 3,470 |
| .75 | 684,000 | 5.71 | 4,880 |
| .70 | 874,000 | 6.28 | 6,350 |
| .65 | 1,077,000 | 6.84 | 7,860 |
| .60 | 1,289,000 | 7.38 | 9,360 |
| .55 | 1,507,000 | 7.90 | 10,830 |
| .50 | 1,727,000 | 8.39 | 12,250 |
| .45 | 1,944,000 | 8.84 | 13,590 |
| .40 | 2,154,000 | 9.26 | 14,840 |
| .35 | 2,353,000 | 9.64 | 15,980 |
| .30 | 2,535,000 | 9.98 | 17,000 |
| .25 | 2,698,000 | 10.27 | 17,880 |
| .20 | 2,836,000 | 10.51 | 18,610 |
| .15 | 2,947,000 | 10.70 | 19,190 |
| .10 | 3,029,000 | 10.84 | 19,610 |
| .05 | 3,078,000 | 10.92 | 19,870 |
| .00 | 3,095,000 | 10.95 | 19,950 |
+------------+--------------+----------+-------------+

=3. Thermal distribution under the accretion hypothesis.=—The accretion hypothesis assumes that the internal heat was gradually developed from the center outwards as the earth grew and the internal compression was progressively developed. The heat, therefore, continued to rise at the center as long as compression continued, or at least as long as the compression was sufficient to generate heat faster than it was conducted outwards. As the conduction of heat through rock is exceedingly slow, the central heat may be assumed to have continued to rise so long as the infall of matter caused appreciable compression. In the same way, heat was generated progressively in the less central parts, and these parts also received the heat that passed out from beneath. It is assumed under this hypothesis that the degree of interior compression stands in close relation to interior density, for while there would probably be some segregation of heavier matter toward the center and of lighter toward the surface by means of volcanic action and internal rearrangement under stress differences, the interior density is regarded as due mainly to compression. The distribution of internal pressure and density generally accepted is that of Laplace, who assumed that the increase of the density varies as the square root of the increase of the pressure. This law gives a distribution of density that accords fairly well with the phenomena of precession of the equinoxes, which require that the higher densities of the interior shall be distributed in certain proportions between the center and the equatorial protuberance whose attraction by the sun and moon causes precession. The increases in pressure, density, and temperature have been computed as follows by Mr. A. C. Lunn,[255] the average specific gravity of the earth being taken at 5.6, the surface specific gravity at 2.8, and the specific heat at .2.

The temperatures are shown graphically in Fig. 452, in which the curves of pressure and density are also given. The nature of the curve of temperature is such that, if the thermometric conductivity of the material is uniform at all depths, the temperature _will fall in the deeper portions and rise in the outer ones_, excluding the surface portions subject to outside cooling. The curve indicates that the rising temperature would affect somewhat more than 800 miles of the outer part of the spheroid, or about half its volume, i.e. the inner half during the initial period had a falling temperature and the outer half, except the immediate surface, a rising temperature. This introduces a very singular feature into the problem, for the outer zone must shrink to fit the inner portion that is losing heat, while its own material is expanding because of its increase of temperature. A double distortional effect must result.[256] If the conductivity of the dense interior is greater than that of the outer parts, the effect is intensified. The redistribution of heat resulting from this unequal flowage would in time change the curve so that more nearly equal flowage would result. It would probably take a very long period for this to be effected, on account of the very slow conductivity of rock.

The accretion hypothesis assumes that, during the growth of the earth, large amounts of heat were carried by volcanic action from deeper horizons to higher ones and to the surface, and that this still continues at a diminished rate. It assumes that whenever the interior heat raised any constituent of the interior matter above its fusing-point under the local pressure, it passed into the liquid state, _and was forced outwards by the stress differences to which it was subjected_, unless its specific gravity was sufficiently high to counterbalance them. It is conceived that the more fusible portions were liquefied first, and that in so doing they absorbed the necessary heat of liquefaction and began to work their way outward, carrying their heat into higher horizons and temporarily checking the development of more intense stresses in the lower horizons. They thus served to keep the temperature there below the fusion-point of the remaining more refractory substances. Meanwhile the extruded portions were raising the temperatures of the higher horizons into which they were intruded or through which they were forced to pass. There was thus, it is thought, an automatic action that tended to reduce the heat-curve to the fusion-curve. _The actual curve of internal temperature may, therefore, be practically the fusion-curve._ This is identical with the curve supposed to arise from solidification by pressure from the center outward under the molten hypothesis, except so far as the two would vary as the result of variations in the distribution of matter, which would not be quite the same under the two hypotheses. The curve of fusion deduced by an extension of the results of Barus’ experiment has been given. It is necessary to recognize that the rate of rise of the fusion-point may, and very likely does, change in the deep interior. The curve given represents much higher temperatures in the central parts than those given by Lunn’s computations from compression, which seem inherently more probable than the higher ones.

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:[1]

Depth. Rate of rise.
Sperenberg bore (Germany) 3492 feet. 1° F. in 51.5 feet.
Schladeback bore (Germany) 5630 „ 1° F. in 67.1 „
Cremorne bore (N. S. Wales) 2929 „ 1° F. in 80 „
Paruschowitz bore (Upper Silesia) 6408 „ 1° F. in 62.2 „
Wheeling well (W. Va.) 4462 „ 1° F. in 74.1 „
St. Gothard tunnel (Italy-Switzerland) 5578 „ 1° F. in 82 „
Mt. Cenis tunnel (France-Italy) 5280 „ 1° F. in 79 „
Tamarack mine (N. Mich.) 4450 „ 1° F. in 100 „[257]
Calumet and Hecla mine (N. Mich.) 4939 „ 1° F. in 103 „[257]
Ditto, between 3324 feet and 4837 feet 1° F. in 93.4 „

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.

----------------+------------------+-------------+-----+-----------+---------- Average material| | Mineral | | | of crust | Norm minerals | equivalent | | Linear | Volume (Clarke’s | calculated from | (C.I.P.W. |Axis.| expansion.|expansion. tables).[260] |Clarke’s average. | system). | | | ----------------+------------------+-------------+-----+-----------+---------- SiO₂ 58.59 |Quartz 11.4|Quartz | |+.00001206 |.00003618 Al₂O₃ 15.04 |Orthoclase 17.2| | _a_ |+.00001906 | Fe₂O₃ 3.94 |Albite 27.3|Anorthite | _b_ |-.000002035| FeO 3.48 |Anorthite 17.8| | _c_ |-.000001495|.00001553 CaO 5.29 |Diopside 6.8| | _a_ |+.000008125| MgO 4.49 |Hypersthene 10.2|Diopside | _b_ |+.000016963|.0000234 K₂O 2.90 |Magnetite and | | _c_ |-.000001707| Na₂O 3.20 | Ilmenite 6.8|Augite | _a_ |+.000013856| TiO₂ .55 |Minor | (used for | | | | constituents | hypersthene)| | | Minor | omitted 2.5| | | | constituents | ——————| | _b_ |+.00000272 |.0000245 omitted 2.52 | 100.00|Magnetite | _c_ |+.00000791 | —————— | | | |+.000009540|.00002862 100.00 | | | | | ----------------+------------------+-------------+-----+-----------+----------

=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:

--------------+-----------+---------+-----------+--------------
| | | Volume | Volume
|Percentages| Sp. Gr. |proportions| proportions
| of norm | of norm | of norm | of temp.
| minerals. |minerals.| minerals. | 1° C. higher.
--------------+-----------+---------+-----------+--------------
Quartz | 11.4 | 2.66 | 4.28 | 4.2801548504
Feldspars[263]| 62.3 | 2.7 | 23.07 |23.0703582771
Diopside | 6.8 | 3.3 | 2.06 | 2.0600482040
Hypersthene | 10.2 | 3.45 | 2.95 | 2.9500722750
Magnetite | 6.8 | 5.17 | 1.3 | 1.3000372060
| ———— | | ————— |-------------
Total | 97.5 | | 33.66 |33.6606708125
--------------+-----------+---------+-----------+--------------

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.