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.

Fig. 450.—Diagram showing the original distribution of heat assumed by the convection hypothesis and the modifications of this distribution near the surface in successive long periods. The base-line of the figure represents divisions of the earth-radius with center at the left and surface at the right. The vertical lines represent temperatures ranging from 0° C. to 5000° C. The assumed initial temperature 3900° C. (7000° F.) is represented by the horizontal line TC, full at the left and dotted at the right to indicate the original extension of the initial temperature to the surface. The upper curve at the right shows how much the temperature will have been modified at the end of 100,000,000 years, computed according to the method of Lord Kelvin. The middle curve shows the change at the end of 237,000,000 years, and the lower curve the change at the end of 600,000,000 years. Similar curves may be found in an article by Clarence King, Am. Jour. of Sci., XLV, 1893, p. 16.

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.

Fig. 451.—Diagram illustrating the internal temperatures of the earth when it first became solid, under the hypothesis that it solidified from the center outward, and assuming that the fusing-point rose directly as the pressure, in accordance with Barus’ experiments with diabase. The divisions of the base-line represent fractions of the earth’s radius. The divisions of the vertical lines represent pressures in atmospheres at the left, and temperatures in degrees C. at the right. The lower curve, PC, represents the interior pressures, ranging from one atmosphere at the surface to 3,000,000 atmospheres at the center, derived from Laplace’s law of density. The upper curve, FC, represents the fusion-points of diabase at the various depths and pressures, and hence the temperatures at which the interior would become solid at the various depths, or, in other words, the initial temperatures of the solid earth. The lower curve is derived from Slichter; the upper is formed by directly plotting the temperatures given by Barus (Am. Jour. Sci., 1893, p. 7).

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.

Distance from
center in terms
of radius.		Pressure in
megadynes
per sq. cm.[254]		Density.Temperature
in degrees C.
1.0002.800
.9597,0003.37320
.90215,0003.951,110
.85353,0004.542,190
.80510,0005.133,470
.75684,0005.714,880
.70874,0006.286,350
.651,077,0006.847,860
.601,289,0007.389,360
.551,507,0007.9010,830
.501,727,0008.3912,250
.451,944,0008.8413,590
.402,154,0009.2614,840
.352,353,0009.6415,980
.302,535,0009.9817,000
.252,698,00010.2717,880
.202,836,00010.5118,610
.152,947,00010.7019,190
.103,029,00010.8419,610
.053,078,00010.9219,870
.003,095,00010.9519,950

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.

Fig. 452.—Diagram illustrating the distribution of temperature under the accretion hypothesis (neglecting the heat from infall and other external sources). The divisions of the base-line represent fractions of the earth’s radius. The vertical divisions represent both pressure in megadynes per sq. cm., nearly the same as atmospheres per sq. in., at the left, and temperatures in degrees C. at the right. It is to be noted that the temperature scale is 2000° C. per division, while that of [Fig. 451] is 5000° C. per division. The upper curve at the left, PC, is the pressure curve. The middle curve, DC, is the density curve, beginning at 2.8 at the surface and reaching nearly 11 at the center. The lower curve, TC, is the temperature curve, rising from the surface temperature, 0° C., at the right, to 20,000° C. at the center. It is to be noted that the portion of this curve at the left representing the deeper part of the earth is convex upwards, while the portion at the right is concave. It will be seen that the gradient increases from the center to a point between .6 and .7 radius, and then decreases, and that between .8 radius and the surface, a distance of about 800 miles, the decrease is notable. This means that with an equal coefficient of conductivity the flow from the center outward to .6 or .7 radius will be faster than the flow from .8 radius to the surface, neglecting the immediate surface effects of external cooling. These curves were worked out by Mr. Lunn.

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.