Gravitation the determining force

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UNITED STATES OF AMERICA.

Chapter I

GRAVITY CAUSES INCREASE OF DENSITY, HIGHER TEMPERA- TURE, AND FLUIDITY OF MATTER.

Variations of density dependent upon variations of gravity. — The expansive tendency of heat resisted by gravity. — Density and conductivity of matter depend upon position and condition. — Conductivity varies with density. — Interdependence of temperature, density, compressibility, and resistance. — Contraction affected by pressure. — Bearing of the preceding laws upon the condition of the earth. — Sustaining strength of the crust of the earth. — Thickness of the earth's crust only approximately determined. — Tendency of heat toward the centre of the earth. — A fused nucleus. — Objections to the theory of a fused nucleus. — Conclusions of William Hopkins, F. E,. S. — The surface of the earth changed from fluid to solid by influence of gravity. — Apparent exceptions to law of increasing density. — Effect of contraction upon condition and dimensions of the earth. — Elevations and depressions, how produced. — Superficial changes now going on. — Upheavals and depressions, how caused. — Causes of fracture. — Changes in coast line. — Mountains, glaciers, moraines. — Location of progressive subsidi CONTENTS.

dences. — Origin, cause, and location of current disturbances in the earth's crust. — Subsidence and uplifting reciprocal. — Uplifting and leveling forces kept in equilibrium. — Where leveling forces are most active. — Sustaining strength of the earth's crust limited. — Causes modifying disturbance resulting from fracture. — Conditions under which earthquakes are specially liable to occur. — Varying distances, centrifugal and centripetal forces. — Volcanic vents.

— The earth's crust thin, and the interior hot. — Possible transitions of heat and matter. — Heat and gravity correlative. — Relation of gravity to cohesion.

— Effect of the removal of gravity. — Consequence of the restoration of gravity. — Process of refrigeration. — Equalization of temperature. — Direction and form of inequalities, how determined. — Ocean currents modified by earth's motion. — Inequality of temperature a cause of springs

Sections I.-XLIII. pp. 1-62

Chapter II. The Theory Of The Tides

Influence of sun and moon upon the tides, as presented by different writers. — Causes assigned inadequate to produce the effect. — Relative force of different elements. — Influence of the earth's rotation. — Resultant of the several elements. — Reciprocal motions of earth and moon. — Instability of the earth's axis, and its effect. — Result were the position of the earth's axis invariable. — Cause of axial rotation. — Projectile from a rifled gun. — Exceptions to Herschel's view. — A complex problem. — Forces considered, adequate to produce the tides. — Location of high tides Sections XLIV.-LVII. pp. G3-85

CONTENTS. Xlll

Chapter III. Precession, Nutation, And Obliquity Of The Ecliptic

Precession. — Newton's theory. — Influence of redundant matter at the earth's equator. — Fallacy of the Newtonian hypothesis. — Real causes of precession. — Causes of precession illustrated. — Amount of annual precession variable. — Maximum and minimum eccentricity. — Herschel on the stability of the earth's axis. — Variable direction of the influence of disturbing bodies. — Axis of rotation not coincident with the

geometrical axis. — Theories of nutation

Sections LVIII.-LXVTII. pp. 86-99

Chapter IV. The Secular Acceleration Of The Moon's Mean Motion

Moon's acceleration. — Hypothesis of Laplace. — Objections to the hypothesis of Laplace. — Is the earth's orbit becoming a circle ? — Moon's acceleration not due to change in orbit. — Moon's acceleration not due to ethereal resistance. — Laplace traces the cause of lunar acceleration to the sun. — Influence of the sun and moon on the stability of the earth's axis. — The sun's motion an element in the problem. — The lunar acceleration likely to continue indefinitely ....

Sections LXIX.-LXXVIIL pp. 100-111

Chapter V. Gravitation In The Solar System

Laws of matter uniform throughout the solar system. — Forces that determine the moon's path. — Unequal density of the superior and inferior limbs of the moon, and of comets. — Illustrative experiments. — The iv CONTENTS.

rarer limb moves in the longer orbit. — The balanced condition of the moon and other satellites. — Conditions likely to affect the temperature of the moon's surface. — Laws determining magnitude of melted nucleus. — Varying density of the planets. — Spots and faculas on the sun's surface. — The sun not deteriorating. — Thickness of crust of the earth, Jupiter, and of the moon. — Location of the greatest inequalities. — Motion of the line of the apsides. — Exterior and interior condition of Jupiter. — Condition of the planetary envelopes. — Geological and meteorological phenomena upon Jupiter and Saturn. — Heat radiated from the earth does not pass the limits of the atmosphere .... Sections LXXIX.-XCVI. pp. 112-141

Chapter VI. Principles Of Planetary Motion, And Ethereal Resistance

Theories of resistance to planetary motion. — The ring hypothesis of Laplace. — Facts inconsistent with the ring hypothesis. — Axial rotation not explained by the ring hypothesis. — Significance of recent discoveries, etc. — Initial effects of gravitation. — Beginning of orbital motion. — Composition of forces. — Discoveries of Newton and Kepler. — Question of interplanetary resistance undecided. — Important results of experiment, and their practical application. — The distances and periodic times of planets and comets indicate the absence of a resisting medium. — Author's conclusions harmonize with Scriptural representations. — Space originally pervaded by homogeneous nebulous matter. — The consummation . .

Sections XCVII.-CXI. pp. 142-169

GKAVITATION THE DETERMINING FORCE.

Chapter I

GRAVITY CAUSES INCREASE OF DENSITY, HIGHER TEMPERATURE, AND FLUIDITY OF MATTER.

Variations* of Density Dependent upon Variations oe Gravity.

If molten matter be congealed while under pressure, the density of the congealed mass will be greater than if the congelation had taken place while the matter was free from such pressure. The greater the pressure, the greater the resulting density, until a limit is reached beyond which the density will be nearly or quite uniform. Now, as the force of terrestrial gravitation decreases as the square of the distance from the earth's center increases, it follows that its condensing power is less on the mountain heights than at the level of the sea ; and less at the equator than at distances nearer either pole. All the tests that we can apply combine to prove : That the force of gravitation determines the density of matter,

II. The Expansive Tendency of Heat Kesisted by Geavity

The expansive force of heat opposes the condensing tendency of gravitation, as is seen in the expansion of matter when the temperature is raised. But the expansion of a fluid mass resulting from an increase of temperature is less in proportion as it is subjected to greater pressure. For example, if we apply heat to a vessel of water in a receiver from which a considerable portion of the air has been removed, we shall see how much more readily it yields to the expansive force, and at how much lower temperature it will be converted into steam. Hence we conclude : That the expansive power of heat is limited by the force of gravitation and the elasticity of the matter heated.

THE DETERMINING FORCE.

m.

Density and Conductivity of Matter Depend upon Position and Condition.

In the "Principia," Book II. Prop. 20, Newton maintains that any single particle of a spherical fluid mass is pressed toward its center by the force of its own gravity, but if a second particle rests upon the first, the pressure is doubled ; a third particle will make the pressure treble ; a fourth, quadruple, and so on.

This law of Newton respecting pressure, like the laws given in some of our text-books to explain the expansion and contraction resulting from an increase or diminution of temperature, is only applicable to matter in certain positions. Let the earth be the spherical mass to which the law is applied, and suppose the first particle to be located on the earth's surface at its mean distance from the center, as on the 45th degree of latitude ; a second particle placed above this would practically double the pressure, but as we go on building up particle upon particle, it is evident that the law, in order to be accurate, must take account of the decrease of gravitation with the increase of distance from the center. The expansion and contraction with, or without, a variation of temperature, contrary to the laws given in the tables of many of our text-books, vary with the pressure. Since the above was first written, the principle here laid down has been repeatedly demonstrated by striking practical experiments. In the " Scientific American " for January 1, 1876, under the heading, " Expansion and Contraction by Change of Temperature under great Strain," we find the following : " It is well known that metals expand or contract by the rise or descent of temperature, according to co-efficients found by careful experiments, and laid clown in the books; but it appears that the amount of this effect of heat and cold can only be correctly determined beforehand in cases where the metals are under no great strain of extension or expansion. . . . This has been forcibly illustrated in the case of the great steel bridge in St. Louis, Mo., with its arches of 500 feet span. Calculations and allowances were made for expansion and contraction by heat and cold through a range of 140° Fall., and the difference to be expected in the elevation of the center arch of the upper chord, above the City Directrix, from the hottest clay of summer to the coldest day of winter, was calculated to be about 18 inches. . . . The result of almost daily observations ranging through 106° of temperature showed an actual difference in height of 8A inches. The difference for this range of temperature, according to the tables, should have been about 14 inches. But we observe that, in the case of the Victoria Bridge at Montreal, the expansion in summer and contraction in winter is in perfect accord with the calculation; in this bridge, however, the expansion is only longitudinal, and is not counteracted by any strain ; while in the case of the St. Louis bridge the expansion has to overcome the immense strain exerted by the weight of the structure itself and the load upon the arch, ... so that for an arch with slight elevation in the center, the strain becomes very great, and often surpasses the actual weight many times. . . .

" In the case of the Suspension Bridge at Niagara, it was found that the elevation by contraction was less than the calculation gave ground to expect ; here, too, the material acts under an immense strain."

The effect of an increase or diminution of pressure upon expansion and contraction may not be perceptible in bodies of small mass, but could be very readily detected in a body of such magnitude as that of the earth. Without attempting to determine the amount of the variation in pressure, density, expansion, or contraction due to the superposition of matter at different altitudes, I conclude : That the density of matter, in all its forms, depends on the force of gravitation and the weight of particle on particle. The expansive force of heat must be taken into account in this connection.

If we take a tube a few feet in length, closed at both ends, fill it with molten matter while the tube is in a horizontal position, close the aperture, and then raise one end till the tube is vertical, the molten matter will no longer fill it, because the increased pressure has increased the density of the fluid mass. If the matter contained in the tube were not heated, its density would not be sensibly affected by the change of position and slight increase of pressure. This experiment shows, That the expansive force of heat is more readily overcome ivhen matter is molten, and that the density of matter depends, in a measure, on the pressure of particle on particle ; for by placing the tube of molten matter in a vertical position, gravitation acts less on the matter ; for, as a whole, it is removed farther from the center of the earth, but the pressure and density are greater.

rv.

Conductivity Yaeies with Density.

When the density of matter is uniform, its conducting power is also uniform ; but if we pulverize a solid body, or in any way increase or diminish the density of a body, we increase or reduce its conducting power. It is evident then, That the conductivity of matter increases ivith the density.

If we apply condensing force to a mass of liquid matter, such force affects equally every portion of the entire mass. But if the liquid mass have considerable depth, its density cannot be uniform, since the density of the lower portion would be increased by the weight of the upper.

If we apply heat to homogeneous matter of uniform density, the conducting power tends to diffuse the heat equally through the mass ; if the density is not uniform the denser portion will receive the larger measure of heat, since the conductivity of the successive strata tends to convey the heat from the rarer to the denser part.

Interdependence of Temperature, Density, Compressibility, and Besistance.

If we compress a cubic foot of air, or of other matter, into a smaller space than it previously occupied, it will, henceforth, be less easily compressed. The general result may therefore be thus stated: The capacity of matter to sustain a crushing force increases with the density. As heat, the equivalent of force, is made apparent by resistance, the temperature of matter is increased by compression, as all substances indicate. It has been said that if a mixture of ice and water be compressed the temperature of the mixture will be lowered. This may seem to be an exception to the above law, but we should remember that the formation of ice affords a partial exception to the law that cold contracts all bodies, since the greatest density is reached above the freezing point. It is evident, too, that a portion of the heat resulting from compression is utilized in melting the ice.

Solid substances are more easily compressed when their temperature has been raised. The compressibility of congealed matter, therefore, increases with the temperature.

VI.

Contraction Affected by Pressure.

Fused matter, as a rule, under ordinary atmospheric pressure contracts one eighth of an inch per foot in congealing. If the pressure is lessened before and during the process of congelation, the resultant density will be diminished, but the amount of contraction will be increased. But if the pressure be augmented before and during the process of congelation, the resultant contraction will be less than one eighth of an inch per foot, the expansive force of heat having yielded to the pressure before congelation took place. Hence we deduce the proposition : The amount of contraction in matter, consequent upon refrigeration, depends, in a measure, upon its density.

VII.

Bearing of the Preceding Laws upon the Condition of the Earth.

By the application of the preceding laws we are led to the conclusion that as we go down toward the center of the earth we must reach a level where matter ceases to contract by pressure, or to expand by heat. Compression increases the density of matter, but as the ultimate molecules are supposed to be incompressible, the distance between them must decrease,. until the expansive force of heat is overcome, and the molecules are forced into contact by the superincumbent mass, causing what may be termed perfectly condensed matter ; and as heat is the equivalent of the intense force resisted, this matter must be intensely hot. Some scientists maintain that no amount of pressure could bring the ultimate molecules into actual contact. Were this to be conceded, our conclusion would not be affected, since under the condition supposed all known forces tending to keep the molecules asunder have given way to pressure.

vni.

Sustaining Strength of the Crust of the Earth.

Many experiments have been tried to determine the sustaining strength of the various rocks of which the crust of the earth is composed ; but experiments have not been sufficiently extended upon matter varying in density and temperature, like the earth's crust, to furnish data for a definite estimate of the height to which a column of such matter could be built up before its base would be crushed. The height of the column would vary with its position on the earth's surface ; for the weight of matter increases as we approach the poles, and decreases as we go toward the equator, or ascend a mountain. If we suppose the column to have been congealed from a molten state, its height would vary with the locality, since its density would depend, in a measure, upon the varying force of gravitation at these different places. If the column were cast in a vertical position in the earth, it would increase in density toward the center of the earth : the increase in density would add to its sustaining strength ; but as there is more or less heat in the surface stratum, the temperature must be increasing with the density as we descend, and the sustaining strength would decrease as the temperature became very high.

IX.

Thickness of the Earth's Crust only Approximately Determined.

Further experiments may be necessary to determine, or approximate very nearly, the distance below the surface of the earth where a stratum would be crushed by the superincumbent mass. This stratum, at whatever depth it is located, is the boundary between the rigid crust and the fluid interior of the earth. Since the density, conducting power, and temperature increase as we descend in the earth, and the sustaining strength decreases as the temperature rises, it is probable that this boundary between the solid crust and the fluid interior is comparatively near the surface. It has been shown that matter increases in density as the pressure to which it is subjected increases; but this increase of density may not continue to any very oreat depth, for, if it did, the earth would be much heavier than it is estimated to be. We may suppose the earth's crust to be made up of an infinite number of columns all pointing toward the earth's center ; the variation in the length of these columns would represent the thickness of the crust in their several localities.

The combined surface of the exterior bases of these columns would make up the surface of the earth, while the combined surface of their bases toward the earth's center would make up the boundary surface of the fluid sphere, or melted nucleus. That we should have the melted nucleus is evident ; for when the base of the solid column is crushed, the resistance to the intense force is great, and the crushed portion must be intensely hot, even to fluidity. As each column of which the earth's crust is supposed to be made up is perfectly wedged in by the columns around it, the crushed portions of one could not escape in a lateral direction, for the surrounding matter on the same level would also be crushed, and must therefore be equally hot and equally dense. If we should attempt to lengthen the shaft by adding matter to the exterior base, the interior base would be crushed. If we should remove a portion of the superincumbent weight from the exterior base, the heat would expand a portion of the matter of the crushed interior base ; the intense fluid heat, the equivalent of the crushing force, would disappear, and the matter would be refrigerated. Hence we see that the length of the column would not be increased or diminished by overloading or lightening its exterior base.

Tendency of Heat toward the Center of the Earth.

Heat being the equivalent of the force resisted tends toward the earth's center, not only by the force of compression, but this tendency is also favored by conduction, for heat inclines toward the denser strata which, if undisturbed, underlie the rarer. Both these causes favor the concentration of heat in the deeper regions of the earth. Although heat is being constantly conveyed from the central portions to the surface, by thermal springs, volcanoes, and other similar agencies ; and beyond the surface by the shifting currents of the atmosphere, it is not lost, as it is being constantly conducted back toward the center of the earth by the increasing density, and the consequent greater conductivity of the strata in that direction. The prevailing direction of the currents indicates that they are tending to produce an equalization of temperature; as a general rule, therefore, they move in opposition to conduction.

That heat tends to accumulate in the central portions of the earth may be confirmed still further by observations upon a tube of molten matter, such as we noted in Section III. We found that, by changing it from the horizontal to the vertical position, the bulk of the molten mass was diminished, but its quantity of heat remains undiminished ; therefore it contains more heat per cubic foot than before. We shall also note an accumulation of heat in the lower portion, caused both by the increase of density and by the consequent increase of conductivity in that direction.

Again : for an additional confirmation of the tendency of heat to concentrate in the interior portions of the earth, let us examine different strata in a vertical column of sand. We find that as we descend from stratum to stratum, there is a perceptible increase in the number of grains per cubic inch, as well as an increase of sustaining strength ; we must, therefore, admit that there is a corresponding increase of force, the equivalent of heat. If we cast a molten shaft in a vertical position, the conditions being such that all portions may be refrigerated as nearly as possible at the same instant, we shall find, as we test the shaft from the top downward, an increase of density, and of crushing force ; we shall also find an increase of conducting power, and a consequent increase of heat in the same direction. Now, let us suppose that our refrigerated shaft is one of the infinite number of columns that make up the solid crust of the earth, as in Section IX. If we could apply our tests to it in this position, we should find the same continual increase of crushing force, density, conducting power, and heat, as far as we could go ; and as these properties increase in matter, according to the pressure, we must infer that the same law of increase holds good for the depths that are beyond our penetration.

XI.

A Fused Nucleus.

Could we penetrate these depths we should find a melted nucleus which must be more dense than the crust, for a solid will not be supported by a fluid of less specific gravity than itself. It would sink, as ice on a lake would sink, if it should be overloaded ; and if the solid crust were subject to a compressing force equal to that which acts on the melted nucleus, it would itself be crushed, and be made fluid by the condensation. The crust rests on partially fused matter, and that on the melted nucleus, and heat is not conducted from the nucleus to the surface, since matter decreases in density and conducting power in that direction. As the crust has been disturbed, the decrease in density is not regular ; but the conductivity of the strata decreases very regularly, owing to the interjection of comparatively rare matter, in veins, dikes, and fissures, at the times of the various disturbances.

xn.

Objections to the Theory of a Fused Nucleus.

The theory of a melted nucleus seems to be discarded by many scientists. The " American Encyclopaedia " says: "It is controverted by Sir Charles Lyell, M. Poisson, and other eminent authorities, on these grounds. When substances, as metals, are melted, their temperature cannot be raised a single degree above the point of fusion, so long as a piece of the material remains unmelted. The same principle is exemplified in the impossibility of raising water to a higher temperature than

32 F., so long as a fragment of ice remains in it."

These objections to a melted nucleus may at first seem unanswerable, but they vanish before thoughtful investigation. When a portion of matter on the surface of the earth is melted, the melted portion is usually rarer than the remaining solid part, and if the two remain in contact, the solid portion must be melted, provided that there is sufficient heat, as heat is naturally conveyed from the rarer to the denser portion. Solids that neither expand by fusion nor contract by refrigeration, have the same density whether in the fluid or solid state, and owing to the tendency of heat to diffuse itself equally the solid and fluid parts soon come to be of equal temperature when they are brought together. If the fused portion of any substance were denser than the remaining solid portion, the latter would take a superior position when they were brought together ; but the temperature of each would approach as near that of the other as does the density of inferior and superior strata of little thickness. Under such conditions, it may be said that the whole mass must be fused, or the whole be congealed, for there would be no appreciable difference of temperature between the opposite surfaces of a stratum of so little thickness.; but a descent of from fifty to sixty feet gives us a difference of a degree of temperature, if we leave out of account the varying surface influences. Water, unlike solid substances in general, expands when it congeals ; the line of transition between the solid and fluid is definite and sharply drawn, although the variation of the thermometer in passing from one to the other may not be perceptible. The water is denser and warmer than the particles of ice that rest upon it. Let us suppose a mass of ice composed of several horizontal strata, the lowest stratum being the densest, and each one above it rarer than the one upon which it rests ; then the lowest would have the largest measure of cohesive and resisting force, the equivalent of heat ; the cohesive and resisting force would ptow less and less from the lowest to the uppermost stratum, and the temperature would follow the same law. Like the water, the melted nucleus is denser and hotter than the crust that rests upon it, but as the variation of temperature — unlike the case of the water and ice — is considerable, between what may be termed solid and fluid, so the distance in the earth is considerable, between perfect fluidity and the solid crust, comprising some miles of thickening matter, until we arrive at congealed matter, or a crust twenty miles, more or less, in thickness.

XIII.

Conclusions of William Hopkins, F. K. S.

From the results of experiments upon several different kinds of rock, William Hopkins, F. R. S., of London, concluded that the density and conducting power of the inferior strata greatly exceed those of the superior, and hence inferred that the melted nucleus must be hundreds of miles from the surface. The temperature of the surface strata is variable ; but if, lower down, the density and conducting power of the crust were uniform, the temperature would be uniform also. In this case, an inferior stratum at a great depth would have the same temperature as a stratum near the surface. But as the density of the different strata increases with the pressure to which they are severally subjected, and their conducting power increases with the density, the nucleus must be intensely hot.

The more rapidly the conducting power increases as we descend, the nearer the surface of the earth should we find the surface of the fluid nucleus. In a paper read in 1860 before the Royal Institution, London, by William Hopkins, F. R. S., be gives some of tbe cod elusions that he had reached as the result of investigations to ascertain how far the observed amount of precession might be consistent with the existence of a fluid nucleus, and among them is this : " In assuming the recognized period of precession, the shell in question, in order that it promote such a result, must be at least one fifth of the earth's radius in thickness." The reasonableness of this conclusion will be considered in a subsequent chapter.

XIV.

The Surface of the Earth Changed from Fluid to Solid by Influence of Gravity.

As the density of matter depends on the force of gravitation, matter must have existed prior to its condensation by gravitation. And as resistance increases with the increase of density, the matter of which the earth is composed must have been made hot by condensation. There must have been a time, therefore, when the earth ivas in a molten condition.

Ever since the creation, gravitation has been producing its effects on the earth, and has by its powerful and all pervading influence increased the density of matter ; but this increase of density has been unequal in different portions of the earth in consequence of the pressure of superior upon inferior masses, hence we have as a necessary result that the central portions of the earth are the more dense. Heat, being more readily conducted by the denser matter, receded from the surface, producing gradual refrigeration, and ultimately a solid crust : the same causes that produced this crust would continue to increase its thickness until the refrigeration had reached a depth at which its effects are overcome by pressure, and heat ceases to recede. With the density and conducting power of the different strata as they are, the present thickness of the solid crust is about what we ought to expect, if we suppose it to have been in a fluid state at creation.