Geology, Vol. 1 [of 3]

by Thomas C. Chamberlin; Rollin D. Salisbury

The volume of the earth is at all times dependent on two sets of antagonistic forces, (1) the attractive or centripetal, consisting of gravity and the molecular and sub-molecular attractions, and (2) the resistant forces—which are not necessarily centrifugal—consisting of heat and the resistant molecular and sub-molecular forces.

1. The centripetal agencies.

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.