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]
| 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 of crust (Clarke’s tables).[260] | Norm minerals calculated from Clarke’s average. | Mineral equivalent (C.I.P.W. system). | Axis. | Linear expansion. | Volume expansion. | ||
|---|---|---|---|---|---|---|---|
| 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 Ilmenite | 6.8 | c | −.000001707 | ||
| Na2O | 3.20 | Augite (used for hypersthene) | a | +.000013856 | |||
| TiO2 | .55 | Minor constituents omitted | 2.5 | ||||
| Minor constituents omitted | 2.52 | ||||||
——— | b | +.00000272 | .0000245 | ||||
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:
| Percentages of norm minerals. | Sp. Gr. of norm minerals. | Volume proportions of norm minerals. | Volume proportions of temp. 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.