Popular Science Monthly/Volume 17/August 1880/The Interior of the Earth II
By R. RADAU.
ASIDE from the evidences of the earth's internal heat furnished by artificial excavations, we have incontestable proof thereof in hot springs and in volcanic phenomena generally. The temperature of certain springs is nearly 100° at the surface. That of the Chaudes-Aigues is 80°; the Trincheras (Venezuela), 97°; the geysers of Iceland are 85° at the surface and 127° at a depth of twenty metres. But it is plain that the temperature of hot springs does not necessarily indicate the heat of the depths they come from. Aside from purely chemical agencies, there are physical causes sufficient to account for a very high degree of heat. When we consider the size of such caverns as those of Carniola and Istria, it will not be difficult to believe that there may be in the earth's crust fissures ten or twenty kilometres in depth, that may be filled with water, like the cavity that periodically absorbs and expels the water of the Lake of Kirknitz. Even at a depth of two or three kilometres the temperature of this water is 100°, but the pressure of two or three hundred atmospheres which it sustains prevents ebullition, as at 100° steam attains a pressure equal to the weight of only one atmosphere, and it does not form unless the pressure exceeds that. Under stronger pressure a higher temperature is required before ebullition takes place (i. e., the temperature at which the pressure of steam equals the resistance, or pressure on the liquid). Thus, under a pressure of 10 atmospheres, water boils at 180°; under 25 atmospheres at 225°; beyond these limits the law that governs the phenomenon of ebullition is not accurately known, but it is known that the pressure of steam increases in a much more rapid ratio than the temperature, and it may be stated that it approximates to 1,200 atmospheres at about 600°; 5,000 atmospheres at about 1,000°, etc. From this it is clear that there is a point where the pressure of steam will equal the weight, where consequently ebullition will occur. Admitting that the temperature of the soil increases at the rate of 1° to 20 metres, we would reach at twelve kilometres a temperature of 600°; and at this depth the pressure of steam would equal the resistance. It would be necessary to go deeper if we adopt a less rapid rate of increase in temperature. Now, if water commences to boil beneath a certain level, the steam will rise through the mass and condense anew, as in a refrigerant imparting thereto a portion of its heat. The upper portion of the liquid will thus become heated more than the soil at the same level; in fact, the water may boil even at the surface, as in the Iceland geysers.
If, in volcanic regions, the temperature is 1,000° at about twenty kilometres depth, the steam forming at that point may possess a pressure greater than 5,000 atmospheres—which would be sufficient to sustain the weight of a column of lava twenty kilometres high. At a temperature of 1,300° the pressure would doubtless be equal to 10,000 atmospheres. This is very nearly the force of the gas of gunpowder in a cannon of heavy caliber, and it is evident that this force would more than suffice for the mechanical effects of which volcanoes offer the terrifying spectacle.
However we view it, volcanoes are an irrefragable proof of a subterranean fire; they truly seem to be the thousand gates of the burning hell we read of. The number of volcanoes discovered constantly increases with the progress of geographical knowledge; in the least explored countries highly volcanic regions are found. A. von Humboldt enumerated 407, of which 227 were active. We now know of several thousand, and, according to M. Fuchs, the number of active volcanoes at the present time may be set down as 323. It is difficult to draw the line between active and extinct volcanoes, because the greater portion have periods of repose, possibly a century or more in length. We know that the ancients considered Vesuvius a perfectly harmless mountain up to the time of the great eruption of a. d. 79, when Herculaneum and Pompeii were buried, and that it remained quiet for three centuries (1306-1631).
On looking at a map whereon the volcanoes are marked as red points, the attention is at once struck by the fact that almost all are found in proximity to the large bodies of water. The greater number are found to be on islands; and the remainder, with a very few exceptions, near the borders of the sea or of lacustrine basins. Around the Pacific Ocean is a vast circle of ignivomous mountains—the western coasts of America, the Aleutian Islands, Kamtchatka, the Kuriles, Japan, the Philippines, Molucca, down to the Sunda Islands and New Zealand, being comprised therein. Aside from this immense belt only isolated groups are found, but they are always disposed around the borders of the sea, or near some large body of water. Does not this geographical distribution force us to the conclusion that there exists an intimate connection between volcanic phenomena and water? Shall not we say that infiltration of water is a necessary condition of eruptions, and that the force which expels the torrents of lava is due to the pressure of steam?
This view finds a confirmation in the recent discoveries of the chemical constitution of the gases emitted by volcanoes. According to M. Charles Sainte-Claire Deville, the clouds that emanate from volcanoes consist principally of the vapor of water. M. Fouqué estimated at over 2,000,000 cubic metres the quantity of water thrown out from Etna in a gaseous form during the eruption of 1865. The clouds of vapors issuing from a crater in eruption often condense and fall in delude-like rains, which make torrents of mud of the volcanic ashes. The streams of lava are, moreover, so charged with vapors that they acquire a remarkable fluidity. These vapors are rapidly disengaged as the streams descend, and sometimes in suddenly escaping they occasion miniature eruptions in the middle of a torrent of solidifying lava. Marine salt and other elements of sea-water are found in the gaseous products of eruptions and in the deposits of fumaroles as well; and M. Fouqué's researches on the chemical composition of the emanations from Vesuvius, Etna, and the volcano of Santorin, show that they are in part the result of the decomposition of sea-water.
Such accumulated proofs no longer allow us to doubt the constant agency of water in the production of volcanic phenomena. It would seem that sea-water passes into the subterranean reservoirs either by percolation through fissures or by transudation under, the enormous pressure it sustains. Coming in contact with the incandescent lava at a great depth, it is vaporized, and the accumulation of steam causes from time to time an explosion of these subterranean boilers. Although the heat of the lava-streams is rapidly dissipated by contact with the air, the temperature of the incandescent mass at the bottom of the crater may be estimated at 2,000°, for refractory metals are known to melt in contact with the molten lava. Were it not over 1,200°, the pressure of the steam generated by matter thus heated would be ample to account for the explosive force of eruptions. It is not necessary, indeed, to assume so great a depth as twenty kilometres for the seat of this force, in order to explain the existence of matter in fusion, for there is nothing to militate against the supposition that the earth's crust is thinner in volcanic regions than elsewhere. It is quite probable that the inner surface of this crust is furrowed and fissured, especially along the lines of unequal density where the continents join the ocean-beds.
The quantity of lava that a volcano emits during an eruption surpasses anything we can imagine. The volume of the lava-stream of Kilauea, in the great eruption of 1840, was estimated at five and a half milliards of cubic metres, and a still larger mass was thrown out in 1855 from the crater at the summit of Mauna Loa, of which Kilauea is the smaller outlet. But these are trifling compared with the mass of matter emitted by the Iceland volcano of Skapta-Jökull, in 1783, which was estimated to equal the volume of Mont Blanc, or not less than five hundred milliards of cubic metres! According to the probably exaggerated estimate of Zollinger, the total volume of scoriae and ashes thrown out in 1815 from a volcano in the island of Sumbawa (Tomboro), to the distance of five hundred kilometres, equaled twice that of Mont Blanc. We have more exact data concerning the eruption of Coseguina, a small volcano of Central America, which, in 1835, rained pumice-stone on the land and sea over a radius of fifteen hundred kilometres, and discharged daily not less than fifty milliards of cubic metres. When we consider the stupendous force required to raise and throw to a distance such volumes of matter, it is difficult to believe that the underground forces that feed the volcanoes, and which we know have been active from a very remote period, are mere accumulations of matter in fusion. Still more difficult is it to suppose that the heat of these fires is due to chemical action developed in the bosom of the earth. We can not but seek, in the wide-spread, incandescent mass under the thin crust that varies, possibly, from twenty to one hundred kilometres in thickness, the proximate cause of volcanic phenomena. The objection based on the non-coincidence of eruptions of volcanoes situated in the same region disappears when the mechanism of the eruption is explained by the more or less fortuitous deposition of infiltrated water.
The question appears to be reduced to deciding whether the central nucleus on which the mass of lava rests is itself liquid or whether it is solid. This is a much disputed point, and great ingenuity has been shown on both sides of the argument. The hypothesis of a liquid nucleus has long been favored, and it has many adherents. It has been objected that a liquid nucleus would be subject to tides that would break in an instant the thin envelope and produce terrific cataclysms. Ampère, in particular, felt it impossible to reconcile this consequence of the hypothesis with the calm that reigns on the surface. "Those who maintain the idea of a liquid nucleus," said he, "do not appear to have considered the effect of the moon's attraction on this enormous liquid mass, which would cause tides analogous to those of our seas, but far more terrible, by reason of their extent and the density of the liquid. It is difficult to conceive how the earth's crust could withstand the action of a kind of hydraulic lever 1,400 leagues long." He therefore maintained, with Davy, the hypothesis of a non-oxidized nucleus which becomes an inexhaustible chemical source of heat by contact with the already oxidized crust. In this view of the matter, a volcano is simply a permanent fissure and channel of intercourse between the non-oxygenated nucleus and the liquids lying upon the oxygenated bed. Whenever this passage of the liquids to the nucleus takes place, elevations of the earth occur from the increase of volume due to oxidation. The heat generated by these chemical actions is propagated at once toward the exterior and interior of the globe, and, in proportion as the oxidation of the crust progresses, the seat of these chemical actions is carried deeper. This, a difficult theory to sustain, has no longer any adherents.
To the objection of the power of the tides it may be further said that, examined more carefully, they would probably be found to produce an entirely inappreciable flexion of the solid crust far from sufficient to cause any disruption. Indeed, it is a question to be considered whether earthquake phenomena do not indicate the existence of subterranean tides. This is a matter that has formed the object of over thirty years' researches by M. Alexis Perrey, Professor of the Faculty of Sciences at Dijon. Professor Perrey has compiled all the observations of earthquakes from the middle of the last century to the present time, and, in grouping the various facts collected during these one hundred and twenty-five years, he has been able to adduce evidence of a connection between the frequency of earthquakes and the phases of the moon. If the phenomena are compared with the lunar month, two maxima will be seen at the periods of the syzigia (new and full moon), and two minima during the first and last quarter. In the following table the results of observations for three periods are given, the earthquake-days being grouped in the weeks corresponding to the moon's four phases, the new and full moon groups and the quadrature groups being separated:
It would thus appear that the shocks occur more frequently at those periods when the sun and moon can combine their action on the liquid particles of the interior of the globe.
M. Perrey has also compared the earthquake-periods with the times of perigee and apogee, that is, the moon's nearest point in her orbit to and farthest point from the earth. The following table gives the results of the comparison—periods of five days being taken—in the middle of which occurs a perigee or an apogee of the moon:
A third means of ascertaining the moon's influence on earthquake phenomena consists in comparing the latter with the lunar day. There are then found to be two maxima corresponding to the moon's passage to the upper and lower meridian, or to what may be called the lunar mid-day and midnight. The minima occur near the middle of these intervals. M. Perrey has made comparisons in this way of 824 shocks felt at Arequipa from 1810 to 1845; of the journals of four observers at Monteleone, Messina, at Catanzaro and Scilla, in the years 1783 to 1785, which were marked by great eruptions of Vesuvius; and, lastly, of the journal of M. S. Arcovito, kept at Reggio from 1836 to 1854. There is manifest, more or less markedly, in all these observations, a preponderance in favor of the hours of the moon's passing the meridian.
This constant increase in frequency of the shocks at the times when the tides are strongest would seem to prove that the producing cause extends its action below the earth's surface. The increase is small, it is true, but it is constantly apparent, however the facts may be viewed.
We must not lose sight of the local perturbations to which the irregularity of the earth's internal surface may give rise. As M. Perrey has said, the lower side of this shell must consist of curves and anfractuosities, mountains whose summits project into the central liquid like gigantic stalactites, and valleys which approach the outer surface. This internal orographic system must modify the propagation of the subterranean waves. As in narrow and rapid rivers, the waves will be confined, and will gain in power between two mountains that obstruct their passage; they will spread out and lose power in a plain or valley whose configuration allows them to move more freely. Beating against cliffs and other obstructions, they will cause shocks and concussions, fissures, and a partial local falling of the internal vault, the effects of which will be felt at the surface as undulations and tremblings. All these causes combine to make of earthquakes a very complex phenomenon.
We might expect to find a species of tide-movement in the lava of active volcanoes, but data on this point are lacking. The only fact we have bearing upon it is derived from the observations of Scacchi and Palmieri during the eruption of Vesuvius in May, 1855, who noticed an increase in the flow of the lava twice daily at intervals of about twelve hours' duration, and with a little less than an hour's retardation from one day to the next, as observed in the ocean-tides. The eruption commenced on the 1st of May, and the periodic swelling of the lava-stream was observed from the 5th to the 19th. Such observations could easily be made in the island of Hawaii, on the borders of the lava-lake of Kilauea.
It must not be forgotten that these subterranean tides do not by any means demonstrate the liquidity of the nucleus, but simply the existence of a liquid mass of a certain depth. It will be shown how astronomic phenomena furnish data for the solution of this question, but we will first glance at some purely physical considerations that have been advanced in elucidation of the matter.
Mr. James Thompson was the first to point out that compression would have the effect of lowering the point of fusion, and consequently of retarding the congelation of those liquids that expand in solidifying. This has been shown to be the case with water, and it would probably be found to be the same with iron. On the other hand, in the case of the far more numerous substances that contract in solidifying, compression facilitates congelation by cooling the mass. It ought, therefore, to raise the point of fusion, and this is known to occur with many bodies. Thus the melting-point of sulphur, which shrinks materially in solidifying, is raised from 107° to 140° under a pressure of eight hundred atmospheres. Now, according to the experiments of Bischof, the greater part of the rocks expand by fusion and contract in solidifying. Granite, the schists, and trachyte shrink about one fifth in solidifying. This tends to confirm the supposition, says Sir W. Thomson, that the earth's nucleus has long been solidified.
Let us conceive the earth as primarily wholly liquid. There would be established in the mass an equilibrium of temperature corresponding to a given pressure. As the mass cooled, solidification would commence, either on the surface or at the center. The question is a very complex one and can not be fully solved without a better knowledge than we have of the properties of the liquid under consideration. But assuming that solidification commences at the surface, a thin skin will first be formed, and this being by the hypothesis heavier than the liquid it covers—since its volume shrinks in solidifying—it follows that it must be broken up and the fragments be carried to the bottom or center, forming there a solid nucleus. Thus, in any event, solidification will occur at the center, and, when the entire mass has acquired a temperature near the point of solidification, a solid carapace will gradually cover the surface, beneath which here and there masses of liquid will still exist.
This argument, however, is open to question in several respects. M. Mallet's experiments, for instance, with the scoriæ of smelting furnaces, show that certain silicates contract only six per cent. The celebrated engineer, Werner Siemens, cites, as opposed to Sir W. Thomson's theory, the results of his experiments at the glass-works of his brother, Fr. Siemens, at Dresden. When the melted vitreous mass commenced to cool, contraction was at first very rapid, then more gradual as it attained a pasty consistency, and at the time of solidification it even seemed to expand slightly. From this M. Siemens concludes that the contraction resulting from the solidification of the fused silicates occurs during the change from the liquid to the pasty state; and, by Sir W. Thomson's reasoning, it would seem all the more probable that the central portions of the globe have already attained a pasty consistency.
On the supposition that the solid crust has but a slight thickness, many phenomena are explained, notably the ascent of lava in volcanic vents, which might thus be due to the hydrostatic pressure caused by the weight of masses of rock. This same cause may even have contributed to the elevation of mountains, by forcing the lighter solid masses above the level of a sea of heavier lava. Again, the slow changes of level of the land, as seen in the changes in certain coastlines, indicate a mobility of the solid crust, which would naturally experience oscillations in consequence of a secular displacement of its center of gravity, and this displacement may result from modifications of the exterior surface by the action of water, and of the inner surface by the action of lava. Indeed, do not earthquakes—whose cause may be found as well in the falling of masses of rock, or the action of subterranean waters, as in purely volcanic phenomena—constantly show that great changes are occurring in the depths of the ground?
Sir George Airy has lent the weight of his great authority to the hypothesis of a liquid nucleus, in his recent interesting address at Cockermouth, before an audience of miners and others. The illustrious astronomer royal holds the opinion that the earth's crust is formed of more or less compact rocks that float on a mass of fluid or semifluid lava. The heaviest of the rocks form the ocean-beds; lighter ones the continents; and the mountains are composed of the portions that project the farthest into the lava, in exactly the same way that large ships draw more water than small ones. It follows from this that beneath the mountains a considerable volume of relatively dense lava has been displaced by lighter masses, which would account for the slight effect produced by certain ranges—the Himalayas, for example—on the plummet.
Again, it is on the hypothesis of an internal fire that such theories of the elevation of mountains as that of M. Elie de Beaumont are founded. The earth's crust in cooling undergoes a contraction, causing ruptures on the arcs of great circles; the lava, as it is compressed by the contracting solidified crust, is forced through these fissures, folding back and elevating the edges, and forming, as it solidifies, long ridges which constitute the mountain-chains. The waters, displaced from their old beds, seek new basins, and, as a state of calm is reestablished, they deposit the matter with which they become charged during the period of disturbance; and it is thus that sedimentary deposits, spreading over the more ancient disruptions, are formed. The existing configuration of the surface would thus be the resultant of a series of elevations separated by long intervals of time. The chronology of these occurrences M. de Beaumont has endeavored to establish by the aid of geometric laws, by virtue of which chains of contemporary formation assume a parallel direction. This theory of mountain upheavals has its weak features, especially that relating to the synchronism of its formations. It has been vigorously combated by the Sir Charles Lyell school, which attributes all the changes of the earth's surface to the slow action of forces that are still in operation about us. In considering the prodigious effects of volcanic eruptions and earthquakes, the secular oscillations of the ground, the changes of the earth's surface even in our day by the action of the sea and of rivers, the partisans of uniformity in geological changes reject the theory of cataclysms, as held by the opposite school. Still, it can not be denied that the earth has grown old, and that its energy must have diminished. On this point Sir W. Thomson makes a judicious remark: "It might be surprising but strictly admissible to assert that volcanic activity as a whole has never been more intense than at the present time. But it is not less certain that the earth contains to-day a smaller store of volcanic energy than it did a thousand years ago, as a ship of war, after a sharp engagement for five hours without replenishing its ammunition, contains less powder in its magazine than before the combat." Again, M. Charles Sainte-Claire Deville, in his lectures at the College of France, cited, in opposition to the uniformity theory, some considerations borrowed from an article of M. J. Bertrand's, on similitude in mechanism, from which it appears impossible, in accounting for a displacement of a given magnitude, to compensate for a deficit in energy by an indefinite extension of the time employed.
There is thus no lack of argument drawn from geognosy to sustain the hypothesis that changes in the earth are attributable to the mobility of the liquid nucleus; but we now pass to an examination of those furnished by astronomy.
Emanuel Swedenborg left behind him as a souvenir only a theosophy and a thaumaturgy; he was, however, a distinguished engineer, and before becoming the leader of a sect of visionaries, as the assessor of the Stockholm College of Mines published some researches that are not without value. In his great work of 1734 ("Principia Rerum Naturalium"), to which M. Nyren has recently called the attention of the scientific world, is for the first time elaborated a theory of the universe closely resembling the celebrated cosmogonic hypothesis of Laplace. Swedenborg postulates a solar vortex, from which is gradually detached a ring, by the disruption of which the planetary globes and their satellites are formed. Twenty years later analogous ideas were held by Immanuel Kant, who, it would seem, merely commented on and developed the views of Thomas Wright. In this system the planets are formed directly by the condensation of nebulous matter without the intermediate formation of rings. These theories are curious in the light of the history of science. There is also the theory of Buffon, who imagined that a comet, striking the sun, forced from it a stream of matter that agglomerated to form the planets. But Laplace was the first to offer a theory of the origin of the solar system that was founded on rigorously scientific principles, and that conformed to the data of celestial mechanics. That which distinguishes the conceptions of his genius is, that the discoveries since made, far from weakening his hypothesis, seem on the contrary to daily strengthen it.
Laplace conceived all the stars formed by the gradual concentration of a nebulosity diffused in space, which became luminous in proportion as it condensed, under the force of gravitation. The sun itself was at first nebulous, with a brilliant nucleus. Supposing the system endowed with a rotary movement—and this is an unavoidable postulate—the solar atmosphere at first assumed a figure of spheroidal equilibrium, much flattened, and limited in its dimensions by the zone where the centrifugal force counterbalanced the weight. The molecules situated beyond this limit ceased to belong to the atmosphere proper, and revolved freely around the central star as planetary masses. Now, a law of mechanics teaches that in proportion as the cooling contracts the atmosphere and condenses the molecules in the vicinity of the nucleus, the rotation becomes more rapid; the centrifugal force thereby augmenting, the point where the weight counterbalances it is brought nearer the center, and the particles banished to the outskirts become planets. Contracting little by little, the solar atmosphere became separated from the zone of vapors in the plane of its equator. These abandoned vapors, wrecks of the solar ocean, must first have formed concentric rings circulating around the sun, comparable to the rings of Saturn. These rings would soon break up into several masses, which, speedily conglobulating, assumed, a rotary movement in the direction of their revolution around the sun. It is thus that the planets originate, and give birth, in cooling, to the satellites that accompany them. "Hence," says Laplace, "the notable phenomenon of the slight eccentricity of the orbits of the planets and their satellites; of the slight inclination of these orbits to the plane of the solar equator; and of the identity of movement, in rotation and revolution, of all these bodies with that of the sun, giving to the hypothesis we offer a high degree of verity." This also explains why the duration of the sun's rotation, twenty-five clays, is less than that of the revolution of the various planets. And the triple ring of Saturn seems to be an ocular proof of the original extension of the atmosphere of that planet, and of its successive contractions. So many analogous phenomena certainly render Laplace's cosmogonic hypothesis highly probable.
A final confirmation of the theory is supplied by spectrum analysis. The study of the spectra of the nebulae has demonstrated that, if many of them are merely agglomerations of stars, others are still gaseous bodies—veritable specimens of the primitive chaos, exemplifying perfectly Kant's, W. Herschel's, and Laplace's conception of the beginnings of worlds as they left the Creator's hands. Of the nebulæ two appear to be composed of a central globe with a ring like Saturn's, and in many others it seems possible to discern the gyratory movement by means of which planetary systems are formed.
Of recent investigations that have served to establish the basis and develop the results of Laplace's theory, we must place in the first rank the valuable researches of M. Edouard Roche, on the form of the heavenly bodies, which the author has recently supplemented by an essay on the constitution and origin of the solar system. M. Roche first demonstrates that by virtue of the particular form of the "free surface" bordering the atmosphere—a surface having a projecting ridge at the equator—as the nebula contracts a fluid stratum will slide from the poles toward the equator and be thrown off over the equatorial ridge as through an opening. It is thus that an equatorial zone, independent of the central body, will be formed and become an outer ring.
But the theory shows that inner rings will be formed from portions of the mobile matter brought toward the equator from the poles, and it is thus that Saturn's two inner rings would be formed, their radius being less than twice that of the planet. The equatorial extent of the planet's atmosphere being at present equal to 2, there can not have been a ring thrown off inside this distance. Laplace's theory, not admitting inner rings, accounts only for the formation of the largest of the three. M. Roche also holds that the moon was formed from an inner ring, and that it was developed in the bosom of the earth's atmosphere, which, withdrawing little by little, left its satellite free.
Every conception that favors Laplace's theory clearly tends to confirm the hypothesis of the earth's original fluidity, but without settling the question of the liquidity of the nucleus at the present time. Let us see to what extent this obscure question has been elucidated.
The equatorial swelling, which changes so slightly the spherical form of the globe, has nevertheless a very appreciable effect on the globe's rotation on its axis. If the earth were an exact sphere and entirely homogeneous, or if it were composed of homogeneous concentric spheres, the sun's attraction would have no effect on the movement of rotation; the axis of the earth would always remain parallel to itself—i. e., always point to the same place in the heavens; but the sun's action on the equatorial protuberance gradually effects a change of direction in the earth's axis, and the moon produces an analogous effect. These perturbations constitute the phenomena of the precession of the equinoxes and nutation, by virtue of which the celestial pole is continually displaced among the stars.
It is from such considerations as these that Mr. Hopkins has drawn a serious argument against the fluidity of the earth's interior. In considering the effect of the sun's and moon's action on the equatorial swelling, says Mr. Hopkins, we look upon the earth as a solid body, with all of its parts joined together, which ought to experience in its entirety the effects of these perturbing causes. But, if the earth is a liquid mass covered by a solid shell, these effects will be exerted only on the solid portion, which will in a manner slide on the liquid nucleus. As the perturbing forces will thus act on so small a portion of the globe, the effect on the rotary movement of the crust ought to be much greater than if the earth were viewed as a solid mass, and these forces will be the more intense in proportion as the crust is thin. In order to reconcile the possible effect of luni-solar action on the equatorial protuberance with the known amount of precession and nutation, Mr. Hopkins calculates the requisite thickness of the crust at not less than thirteen hundred to sixteen hundred kilometres, or from a fifth to a quarter of the earth's radius.
Mr. Hopkins's calculations were revised twenty years later by Sir W. Thomson in his "Memoir on the Rigidity of the Earth," in which this illustrious physicist gives to Mr. Hopkins's views all the weight of his authority. "Whatever objection may be made to the mathematical portion of Mr. Hopkins's work," he says, "I can see no force in the reasoning employed to refute his conclusions, and I am happy to see my opinion in the matter confirmed by such an eminent authority as Archdeacon Pratt. It has, indeed, always seemed to me that Mr. Hopkins might have carried his argument further, and concluded that no completely liquid mass, approximating to a spheroid six thousand miles in diameter, can exist in the interior of the earth without being accompanied by a very different rate of precession and nutation from that which actually exists."
These arguments grew in favor with geologists, and the hypothesis of a liquid nucleus was gradually relegated to the limbo of superannuated prejudices, when the lamented M. Delaunay undertook to demolish the principal argument, and declared that in his opinion Mr. Hopkins's reasoning had no real foundation. "To make clear our idea," said M. Delaunay, "let us take a glass globe filled with water. If it is admitted that this liquid is endowed with an absolute fluidity, it is evident that, by giving the globe a brisk rotary movement on a vertical axis, it will turn without carrying the liquid around with it. This may be readily verified by giving it a more or less rapid movement of rotation. Light substances suspended in the water will appear to remain still, despite the ball's rotation. But will this always be the case, whatever the speed of rotation? If the globe were very slowly revolved, would the liquid still be unaffected by the movement of its envelope? In conceding the perfect fluidity of the liquid, its viscosity has been lost sight of. Now, this viscosity, though slight, is not nil; hence, if the rotation be sufficiently slow, the liquid will be carried around with the glass globe, the whole revolving as one piece, or solid ball." This rotation of the liquid under the conditions described has been demonstrated by M. Champagneur in a series of experiments undertaken, by request of M. Delaunay, in the laboratory of the Sorbonne.
Applying this reasoning to the earth, we will assume that it is composed of a liquid mass covered by a solid pellicle. It is first of all evident that, if we set aside the perturbations caused by the equatorial enlargement, the entire mass will turn as one piece on its axis; if any difference whatever could exist between the rate of the envelope's rotation and that of the nucleus, friction will speedily annul it. The perturbing influence of precession and nutation imparts to the solid envelope's proper movement of rotation an extremely slight acceleration. The question is, Does the internal liquid participate in this additional movement, or is the crust only affected by it? "As for me," says M. Delaunay, "there is no room for the slightest doubt. The acceleration due to the causes indicated is so slight that the fluid of the interior must follow the inclosing shell exactly as though the whole were a solid mass. So enormous is the pressure to which the various parts of the liquid mass are subjected that we can form no idea of its effect on the viscosity of the fluid in question. But if that fluid is in the condition of those we are familiar with, what we have described would occur." M. Delaunay concludes by stating that, in his opinion, the phenomena of precession and nutation can furnish no data concerning the greater or less thickness of the earth's crust.
Sir William Thomson again considers the question, and from a new point of view. In theoretically determining the height of the tides, the water only is supposed to yield to the luni-solar attraction—the solid shell of the earth being unaffected by it. Now, it is evident that even an entirely solid sphere will be slightly changed in form by these forces, and that the change will be still greater in a partially liquid sphere. We will first suppose that the entire mass of the globe yields to the attracting forces as readily as if it were liquid. In this case sea and solid land will be raised alike, and, the surface of the sea always being at the same distance from the bottom, no tides will be seen. Granting that the average rigidity of the globe's mass is comparable to that of glass, we see that it must undergo a change of form equal to 0·6 of that which it would experience if it were liquid; and, deducting this elevation from the rise of the oceanic sheet, the height of the tide is not more than 0·4 of what it would be on a perfectly rigid ball.
Assuming the rigidity of the terrestrial mass to be that of steel, Sir W. Thomson estimates that it would still undergo a change from sphericity equal to one third of that of a liquid sphere, and the apparent height of the tides is thus found to be reduced to two thirds of that which would be produced on an absolutely rigid ball. Sir W. Thomson, while fully recognizing the uncertainty in which this question of the height of the tides rests, still deems it inadmissible that the actual height is only 0·4 of the theoretical height on the hypothesis of a globe of absolute rigidity. He accordingly concludes that our globe possesses a rigidity greater than that of glass, and perhaps than that of steel. Regarding the influence on the phenomena of precession and nutation due to the globe's elasticity, the deductions from the hypothesis of absolute rigidity accord with observation, and this would tend to confirm the conclusions drawn from the observations of the tides. Even if the variability of form tends directly to diminish the effect called precession, there still exists an indirect effect of this variation which tends to augment it, so that possibly these two contrary effects may nearly counterbalance each other.
Everything considered, it is not impossible to reconcile these conclusions with the existence of an intense heat in the central portions of the globe. It must not be forgotten that these central beds are subjected to a pressure increasing in intensity toward the center. By M. Roche's law of densities, we find that the pressure at the center exceeds 3,000,000 kilogrammes per square centimetre (3,000,000 atmospheres). We can form no idea of the physical condition of substances exposed to such a pressure. Experiments on the resistance of various substances have shown that small cubes of granite crumble under a weight of 700 atmospheres; basalt and porphyry under 2,000 and 2,500 atmospheres respectively. Under such pressure the rocks disintegrate and are pulverized. Copper, steel, and cast iron resist twice or thrice this pressure, but what will be the state of the metals under a pressure one hundred or one thousand times greater? What is the action of molecular forces, in solids or liquids, subjected to a pressure of several millions of atmospheres, and, at the same time, to a temperature of some thousand degrees? What is the solid or the liquid state under these conditions? Data on this point are absolutely lacking, and anything advanced thereon must be purely hypothetical. "We may compare mathematics," Professor Huxley aptly says, "to a mill of admirable construction, capable of grinding to any degree of fineness, but what comes from it depends upon what has been put into it, and, as the most perfect mill conceivable will not produce flour if only pea-pods are put into it, pages on pages of formulas will not give an exact result from inexact data."