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. |
|---|---|---|---|
| 1.00 | 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.
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.