THE CAUSES OF MOVEMENT.
General Considerations.
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.
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.