As to how far the internal surface is from the centre, it may be possible to designate a position, or region, from which it cannot be very far distant, although we can never expectto be able to point out exactly where it is. Going back to the time when the whole earth was in a molten liquid state, and just before the outer surface began to become solid, it is certain that the interior surface must have been in the same liquid condition, whatever may have been the condition of the mass of matter between the two surfaces, owing to the pressure of superincumbent matter; nay, we may be sure that whatever may be its state now, it continued liquid long after the other became solid, because it had no outlet by which to get rid of its melting heat by radiation, nor weight of superincumbent matter to consolidate it; and it would always be much hotter than the outer surface. At that time we have every reason to believe that the outer surface was at least as dense as it is now, there being no water upon it to lower its average density, as is the case at the present day; and we have equal reason to consider that the density at the inner surface, whether liquid or solid, is now at least equal to what the outer surface was then. Duly considering, therefore, the absence of water from the interior surface, we shall suppose that the first layer of 25 miles thick upon it will have an average density of 2½ times that of water, terminating at 3 times, which is the density we have taken for the outer surface at 9 miles deep. But there is another contingency, which it will be necessary to take into consideration before going any farther.
It has been understood—as it is certainly the truth—in the calculations made with respect to the outer half of the mass of the earth, that the increase of density in descending was due to the pressure of the superincumbent matter, caused by the attraction for it of the inner half, as well as that of the whole of both the outer and inner halves on the other side of the hollow interior. In the case of the inner half we have now to consider that the attraction of the outer half alone would be the effective agent, and that the superincumbent pressure—that is, of course, the pressure acting from the centre outwards—would be interfered with, or perturbed, by the attraction of the mass on the other side of the hollow interior, so that it would not exert its full power in thatdirection. But that does not mean that the density would be in any way diminished. The attractions of the planets for each other perturb them in their revolutions around the sun, accelerating or retarding each other, but do not increase or diminish their density or mass; only it will lead us to expect that the same depth of 817 miles will not produce the same amount of pressure outwards at the meeting of the two halves as it does inwards, and that to obtain an equal pressure a greater depth will be required. We believe that an expert mathematician, taking as bases two opposite pyramids in a sphere, similar to those we have used in a former part of our work, could point out, with very approximate accuracy, what ought to be the distance of the inner surface of the shell from the centre—provided a maximum density were determined for the earth—but that goes beyond our powers, and we shall limit ourselves to the use of our own implements; which will cause us to depart from the statement we have made, that the density of the inner half must decrease from the place of meeting of the two halves, at the same rate as the outer half had increased. It must decrease much more rapidly than the other increased. All this premised, and having established a density of 3 for the interior surface, we may proceed to calculate where that surface ought to be, so as to give for the interior half of the earth a mass equal to 735,584,493,738 cubic miles of water.
If we begin our operations with a density of 8·8 times that of water at the meeting of the two halves of the shell, and diminish it for any considerable distance at the same rate as it increased when we were finding the mass of the outer half, that is 0·1812 for each layer, we soon find that before we could make up the whole mass of the inner half of the shell, the density would be decreased to at least that of water, which cannot be, as there can be no liquid or solid matter of any kind of so low density anywhere in the interior half of the shell. Furthermore, if we decrease it at the same rate as the volumes of the different layers of the earth decrease as they approach the centre, it involves a mass of calculation that serves no useful purpose, as such calculationsbring no contingent of satisfaction with them; because all the densities with which we are dealing have to be brought to a rational form before we can frame a proper approximate idea of what the interior construction of the earth is, as will be seen hereafter; and because it takes no account of the perturbation—above alluded to—produced by the attraction of the matter on the opposite side of the hollow. But, in order to get such a result as we can with our limited powers, if we begin with a density of 8·8 at the diameter of 6284·5 miles and fix the density of 3—which we have adopted above—at the diameter of 3200 miles, we shall get a mass somewhat less than one-half of the earth; and with a density of 2·91 at 3150 miles diameter we get a mass of 735,713,884,116 cubic miles of water, which is rather greater than one-half of the mass required (see operations ofTable V.). This density of 2·91 reduced to 2·5, as we mentioned, might be done when we were fixing the number 3, would make very little difference on the resulting mass, compared with what we have been in quest of.
Here we may state that we found that, had the calculations been made with documents of density proportioned to the decrease of the volumes of the layers of the earth as they approached the centre, the density would have been reduced to 2·25 at 3150 miles in diameter; which tends to show that should that process be considered to be more accurate, it would not have made any great difference on the result.
With all, we may consider that it has been demonstrated, that the greatest density of the earth is not necessarily greater at any part of its interior than 8·8 times that of water.
TABLE VI.—Calculations of the Volumes and Densities of the Inner Half of the Earth, on the same Data as those for the Outer Half.
Itmay be well to revert here to the experiment we made of putting a cubic foot of rock, of specific gravity 13·734 in the scale of a balance at the centre of the earth, where we saw that it could not depress the scale one hair-breadth, and make the same experiment by placing a cubic foot of rock of 8·8 specific gravity in the same scale, at what we have called the region of greatest density of the earth, that is, at 817 miles from its surface. Here, also, we shall find that the scale is not depressed for the very same reason as in the former case, that is because it had nowhere to be depressed to; and it might be argued that for the same reasons advanced formerly there can be no matter at that place, but the cases are entirely different. In the first case, there is nearly the whole mass of the earth drawing the matter away from the centre were it at liberty to move; whereas, in the second case, the meeting of the two halves of the shell, at the region where there is the greatest mass of matter, is also the meeting place of the action ofattraction in its greatest force; the place to which matter is attracted from all sides, remains stationary, and it is held there both by attraction and weight of superincumbent matter or gravitation. The attraction of the whole earth acts as if it were concentrated at its centre, but that is for external bodies. That kind of attraction on the inner half of the shell would be far inferior to that outwards of the outer half, owing to its greater distance and conflicting nature, and would perturb, as we have said, but not do away with it. The same could not occur at the centre, because it is not the centre of the mass, that is, it is not the place where the greatest quantity of matter existed originally, or is now to be found, and consequently never was, nor can now ever be, the actual centre of interior attraction.
It has been said when treating of the earth as being solid to the centre, that it is not easy to comprehend what may be the nature of the rocks we are acquainted with, when compressed to one-fourth or one-fifth of their volume, and we do not find ourselves much better off when we contemplate them as reduced to one-third or one-fourth of their bulk, that is, when a cube of one foot is reduced to three or four inches in height, as would be the case with it at a maximum density of 8·8 times that of water when placed at a depth of 817 miles from the surface of the earth. We find, therefore, the idea thrust upon us that there may be a limit to density, perhaps not an absolute limit, but a practical one; in which case, the greatest density of the earth may not greatly exceed 5·66 times that of water. For, if we conceive that it increases to its maximum at 100 miles from the surface, and continues nearly uniform thereafter, a little calculation will show that the greatest density of the outer half of the shell need not much exceed 6 times that of water; and, of course, the same will be the case with the inner half should its density be almost uniform till 100 miles from the inner surface is reached. It might even so happen that at a depth of 25 to 30 miles the practical limit might be reached; for a column of granite of one foot square and 25 miles high would weigh, and exert a pressure upon its base of 10,000 tons, a pressure equal to nearly fifteen times what would be sufficient to crush it into powder; in whichcase the greatest density of the earth might not much exceed the 5·66 that we are accustomed to think of—without thinking.
It may be deemed absurd to think that there is even a practical limit to the density of matter, but on the other hand it is much more absurd to suppose that there is not an absolute limit to it. We cannot conceive of density being other than the result of compression, and we cannot believe that matter can be compressed more and more continually for ever. There must be some end to compression. Perhaps it was the difficulty in conceiving of rock being compressed to so small a fraction of its volume as would enable it to take its place at the centre of the earth—where it has been said that, "it must weigh like lead"—that originated the idea of its centre being occupied by the metals, arranged as they would be in a rack in a store, the heaviest pieces at the bottom of the rack, and the lighter ones higher up.
When fairly looked at, density would really seem to have a limit, except in so far as it may be combined with heat. We know that water is compressed 0·00005 part of its volume for every atmosphere of pressure to which it is subjected. But 0·00005 for round numbers, is in fractional numbers 1/20,000; therefore a pressure of 20,000 atmospheres would compress a cubic foot of water into 1/20,000 of a foot in height, or practically into nothing. We know, also, that as a column of water 33·92 feet high balances one atmosphere, one mile in height will be equal to 155·66 atmospheres, and 20,000 atmospheres will produce a pressure equal to a column of water 128 miles high; therefore, a cubic foot of water, subjected to such a pressure, would be compressed into virtually nothing. Again, supposing that we have a column of liquid rock, of 2½ times the density of water, of the same height of 128 miles, we should have a pressure of 2½ times that of the column of water; and as we have no reason to believe that granite in a liquid state has to obey a different law of compression to the one obeyed by liquid ice; then a column of granite 51 miles high would be sufficient to squeeze its own base, not only off the face of the earth but out of the bowels thereof. It will be seen, therefore, that at 100 milesdeep from the surface, the density of the earth might well be equal to not only 5·66 times the density of water but to a great deal more; and that our estimate of 3 times the density of water, at 9 miles deep, was far within the mark.
The authors of text-books on the strength of materials tell us that "the Modulus of Elasticity of any material, is the force that would lengthen a bar of that material of 1 inch square to double its length, or compress it till its length became zero; supposing it possible to stretch or compress the bar to this extent before breaking." This is neither more nor less than a counterpart of the law of gases, upon which the air thermometer is constructed, applied to solid matter, and may be used in the same manner. But we can never produce a perfect vacuum, and so annihilate a gas and temperature; neither can we annihilate matter, nor easily reduce it to one half of its volume. Now, we have seen, a little way back, that a column of granite 25 miles high would exert a pressure at its base 15 times as great as would crush it to pieces; so that a column of 25÷15, or 1·66 miles high would destroy the elasticity of the material, because, when crushing takes place, all elasticity is gone. We cannot, therefore, get much satisfaction out of any calculations made upon the theory of the strength of materials; still, by them, we can make more plain the absurdity of any notion of the indefinite compressibility of matter. But if, in the face of contravening its conditions, we follow the reasoning used for the formation of the theory, and take the modulus of elasticity for granite as 2,360,000 feet, then the same modulus would compress a bar of granite of 1 inch square in section till its height became zero. And as that length is equal to 447 miles, at that depth from the surface of the earth, granite or any other rock or stone of a similar nature would be compressed out of existence by the weight of the superincumbent matter.
Thus we have arrived at two measures of force which would compress to zero the rocks that are known upon the earth. One where rocks are looked upon as in a molten, liquid state, and analogous to water, where the force is equal to that exerted by a column of the material 51 miles high;and the other where the column requires to be 447 miles high. In either case the same method of calculation will show that columns one-half of these heights, will compress the material into at least one-half of its volume—that is half-way between what it is at the surface and would be at the specified depths—and consequently into double its density. So we find in the one case that the density of the earth ought to be about 5·66 times that of water at a depth of 25½ miles; and, in the other, at somewhere less than 225 miles deep. But, before proceeding to use and reason upon these depths, we must recall to mind that the calculations from which we have derived them, in the second case, have been made in violation of the theory that was adduced for the purpose, and that in consequence the latter depth must be excessive. For, were we to erect a structure of any kind, calculating the stresses it would have to bear, under the same violation of the theory, we should inevitably find that the structure would give way under the strains that would be brought upon it; that is the columns 25½ and 225 miles high would compress the same kind of matter composing them into very far below one-half of its volume.
This premised, let us go back to our layers of 25 miles thick with their respective volumes. Nine of them counted from the diameter of 7900 miles inwards, will be equal to 225 miles and will bring us to 234 miles deep, which at the same time that it leaves us the same volume and mass that we have always retained for the first 9 miles in depth, will facilitate our calculations considerably without making any appreciable difference in them. We shall then have to find for the 9 layers 9 corresponding densities increasing from 3 to 5·66, and if we multiply these together respectively, and add the numbers of the volumes and masses of the outer 9 miles in depth, we shall get, at the diameter of 7450 miles, a simple volume of 43,418,587,327 cubic miles, and mass volume of 195,312,523,450 cubic miles. Deducting this latter sum from 735,584,493,738 cubic miles, which represents the half mass of the earth at the density of water, we have a remainder of 540,271,970,288 cubic miles. On the other hand we find thatthe simple volume of the earth comprehended between the diameters of 7450 and 6284·5 miles is 86,543,337,361 cubic miles; so that if we divide 540,272,970,288 by this sum, we find that a density of 6·24 times that of water over the whole intervening space—between the two diameters just cited—will make up the whole half-volume, at the density of water, from the surface of the earth to the diameter of 6284·5 miles. Then, for the inner half-mass:—If we multiply the simple volume between the diameters of 6284·5 miles, and 3150 miles, which is 113,596,348,539 cubic miles by 6·24, we get 708,841,214,870 cubic miles at density of water; and if from there we run down the density to 3 at 2700 miles in diameter we get 27,400,652,354 cubic miles, which added to the last mentioned amount gives 736,241,867,224 cubic miles, somewhat in excess of the inner half-mass of the earth at density of water. Thus we see that in order that the average density of the earth of 5·66 may be made up, there is no necessity for appealing to matter of any kind with a density of more than 6·24 times of water. And there is still something else of importance to be taken into consideration before we can bind ourselves to a density even so great as that.
We have said, a few pages back, that there can now be no undeposited cosmic matter in the interior of the hollow earth, and that as far as such matter is concerned the hollow part may be a perfect vacuum. This is not absolutely true, for gases may be cosmic matter, just the same as any others of the elements out of which the earth is formed, but what is generally meant by cosmic matter is solid—at least, we have always looked upon it in that light—and all solid matter must have been deposited upon the interior surface at an immeasurably long period of time before the nebula forming the earth came to have even the density of water; certainly before it came to be in a molten liquid state; and we did not want to introduce any posterior evolutions in order not to complicate our calculations, and also to obtain some tangible bases to which the consequences of these evolutions might be applied. But as we have now both form and density to work upon we may take them into account, and it will be foundthat neither of these two bases will be very materially altered by them.
When the earth was in a molten liquid state, it is believed—as we have said on a former occasion—to have been surrounded by a dense atmosphere, composed of gases and vapours of metals, metalloids, and water, and we have no reason to doubt that the hollow of the sphere was filled with a similar atmosphere, only the vapour of water would, most probably, be dissociated into its elements of oxygen and hydrogen. Also we have every reason to believe that even at the present day gases are being produced in the interior, one part of which find their way to the surface and are dissipated into the atmosphere in the same manner as the gases from the chimney of a furnace; and another part into the interior, where they could not escape but would be stored up in the hollow. Thus at the present day there may be an atmosphere there, composed near the surface of vapours of the elements with gases above them, so to speak, at a very high degree of pressure. These gases could not have gone on accumulating always, but must have found an exit in some particular place, or places, when the pressure exceeded the resistance, or when this was diminished by some convulsion such as an earthquake; but we do not want to define too much, or make more suppositions on this point than what present themselves to us in a reasonable way. All that we need say is, that the resisting power of some thousands of miles of solid, or even viscous, matter must be enormous, and the pressure necessary to force its way through it must have been equal to many thousands of atmospheres. We know that a pressure of 773·4 atmospheres condenses air to the density of water, and it must be the same with any similar gas; so we have only to suppose that the pressure is 4827 atmospheres—which is equal to 773·4 multiplied by 6·24—in order to bring the whole of the gases, and vapours of elements, in the hollow to the same density of 6·24 times that of water, which we have shown need not be exceeded in any part of the earth. And such being the case, we can place the division between solid and gasiform matter in any point of the radius that may seem tous reasonable, only we must always have as much solid matter in the inner as in the outer half-mass of the earth.
Following nearly the result we have obtained in another way, by placing the division of the hollow part at 3000 miles in diameter, the volume of which is 14,137,200,000 cubic miles, and multiplying this by 6·24, we get a mass equal to 88,216,128,000 cubic miles at density of water, composed of vaporous and gaseous matter in the hollow centre, and consequently much greater than is required to make up the total mass of the earth at the density of water; which shows that the density of the mass between the diameters of 7450 and 3000 miles must be less than 6·24 times that of water. How much less is very easily found, by dividing the surplus of 88,216,128,000 cubic miles over the whole volume between 7450 miles in diameter and the centre, because in this way we shall include the whole mass arising from both solid and gasiform matter. This whole volume—that of a globe 7450 miles in diameter—is 216,505,262,050 cubic miles, which, divided by the surplus gives the amount 0·407 as the density to be deducted from 6·24 on its account, and therefore the greatest density of any part of the earth need not be over 5·833 times that of water.
This result derived from our operations will be acknowledged, we doubt not, to be much more satisfactory, we might say, more comprehensible, than to have to believe that our known rocks and stones could be compressed till they were 13·734 or even 8·8 times heavier than water.
At first sight 4827, say 5000, atmospheres or 75,000 lb. on the square inch, appears to be an enormous pressure, but it is nearly almost as nothing compared to the pressures we have been dealing with. A column of granite 1 mile high would exert a pressure upon its base of 6050 lb. per square inch, and one of 25 miles high of 151,200 lb., or double the number of atmospheres we have applied to the gases in the hollow of the earth. If we take a column 225 miles high, such as we considered to be the least that would be necessary to compress granite into one-half of its volume, we get 1,360,860 lb. per square inch, or over 90,000 atmospheres ofpressure; and if we go into thinking of columns of 447 and 817 miles—this last being the depth from the surface of the division of the matter of the earth into two equal portions—we could have gases compressed to 174,600 and 326,700 atmospheres or, dividing the numbers by 773·4, 222 and 422 times the density of water; so there is no cause to stumble over high pressure. With even 10,000 atmospheres, more than double the number assumed, we should have gases as heavy as the material we found at the centre of the earth, when we were looking upon it as solid to the centre—which was 13·734 times the density of water—and so get rid of burying the precious metals where they would be "matter in the wrong place," and according to D'Israeli's definition, justly entitled to the epithet applied to them, sometimes, by people who have never been blessed with a superabundant supply of them. At the same time, we find out what we knew before, viz. that we may have gases heavier than the heaviest metals and as rigid as steel, if we can only find a vessel strong enough to compress them in, along with the means of doing it; and also that the thousands of miles of highly compressed matter, between the hollow centre and the surface of the earth, are far more than sufficient to imprison gases of far, very far, greater elasticity than our modest measure of 5000 atmospheres. And we hope to be able to show presently good reason for believing that the gases compressed in the hollow, at what may really be considered as very high pressures, have had, and may probably still have, a very important part to play in the evolution of the earth.
We have just seen that the pressure produced by a column of granite 1 mile high would be 6050 lb. per square inch, consequently one of double the height, or 2 miles, would exert a pressure of 12,100 lb. per square inch at its base, equal to the crushing strain of the very strongest granite we know, while at the same time that strain would not amount to one-sixth of 4827 atmospheres; so that if the gases in the hollow of the earth were at a pressure of only 800 atmospheres, their pressures would be able to crush granite of that class to pieces, and therefore the estimate of specific gravityof 3 for the density of the interior surface—which we made at the beginning of our calculations for the hollow sphere—cannot be looked upon as by any means exaggerated.
We might now reform our calculations of the two halves of the interior of the earth, giving a more rational and curve-like form to the densities, under the supposition that at much less distance than 234 miles from the surface, matter might be compressed to its utmost limit; but as, according to our demonstration, the solid matter of the earth must have been divided into two equal parts at the place where the greatest mass was, long before it could have been condensed into a state to compress gases; and as the total mass of solid matter must, in order to make up the total mass of the earth, depend to some extent on the mass of imprisoned gases; we are unable to make any reform much different to what our calculations show. Besides, as the difference between average densities of 5·66 and 5·67 makes a difference of 2,600,000,000 cubic miles on the mass of the earth reduced to the density of water, very approximate accuracy cannot be attained in any calculations.
What is meant by a limit to density except in so far as it is combined with heat, is that whatever density may be given to matter by compression when it is in a heated state, a greater density will be found in it when it is deprived of that heat; that whatever may be the density of any part of the interior of the earth in its present state, that density will be increased when the earth becomes cooled down to the temperature derived from the heat of the sun, or to absolute zero of temperature, if such there be, on account of shrinking in cooling; and that therefore there can be no absolute limit to density as long as there is any heat in matter.
It may not be unnecessary for us to recognise now that the weight of a column of granite would decrease as the depth increased, for the force of gravitation would be diminished by having a part of the attraction of the earth above instead of below it; but at 100 miles in depth the diminution would be only about one-eighth—if distance is taken into account—of the 817 miles down to the plane of greatest density, and1/2200th part if the mass left above is considered; differences that would make extremely little alteration on our calculations.
It will not be out of place either to take a look at what may be the temperature of the interior of the shell, and of the gases shut up in the hollow part of the earth; and we have not much to say on the subject, because we shall not depart from the system we have followed up till now, with considerable strictness, of not theorising or speculating on what may be; but will restrict our observations to theories that have been very generally adopted by astronomers, geologists, and scientists in general. The air thermometer will be of no use to us, for whatever may have been the temperature when the earth was in the process of formation, it must have diminished very greatly during the cooling process it has undergone since, and we know that gases heated in a closed vessel in such manner that pressure and temperature will agree to the theory on which the air thermometer is constructed, may be cooled down afterwards to almost any degree required, and the relation between temperature and pressure destroyed thereby. At one time it was thought that the earth had only a solid crust, and that, under it, the whole of the interior was in a molten liquid state. Then some physicists thought that, through pressure of superincumbent matter, solidification must have begun at the centre; others that it began almost simultaneously at the surface and centre, and that there may still be a liquid mass between the two solidifications—this is repeating what we have said before, but it is done only to bring it to mind. We, at present at least, do not want to have anything to do with any of these theories, only we believe that we have shown in an indisputable manner that there could be no solidification at the centre, because there could be no matter there capable of being solidified—gases could not be solidified under such pressure, and at all events heat, as there must have been there. We believe at the same time that no one will deny that the heat of the earth increases as the centre is approached, and that the temperature of the interior may be very great. The crust of the earth was atone time supposed to be only 25 to 30 miles thick, because the increase of heat at that depth would be sufficient to melt any of the substances we are acquainted with on the surface—repetition again; but for many years past it has been deemed necessary to increase the thickness to even hundreds of miles, for reasons some of which will be alluded to in due time; and if, even at these depths, the increase of heat were only sufficient to fuse all the substances we know, it is very certain that at the interior surface of the shell it must be very much greater, as heat from there could only beconductedoutwards, and the difference required to cause conduction, of any considerable degree of activity, through more than 2000 miles must be enormous, according to the experiments made by various physicists upon metals, which have a very much higher conducting power than rocks, and especially strata, of any kind. Therefore there can be no doubt, we think, that the inner surface of the shell must be at a very much higher temperature than what would preserve it in its liquid state, and that the matter composing it is liquid to a depth where it might be solidified by the pressure of superincumbent matter. We do not see how convection currents could be instituted, much less kept up, in melted matter, under the viscosity, and, at least quasi-solidity, sure to be produced by pressure of tens of thousands of pounds on the square inch, and therefore we do not take them into account. Any way, whatever may be the temperature of the interior surface of the shell, the same must be that of the imprisoned gases, because there convection currents could and must exist—were they even only created by the rotation of the earth and attraction of the moon—and cannot fail to keep the whole of the hollow part at the same temperature. It would be absurd to suppose that these gases could be at a lower temperature than the upper layers, counted from the region of greatest density, of the interior surface of the shell.
This section of our work may now be brought to a close by stating the conclusions at which we have arrived, leaving the results involved by them to be discussed separately, which we shall proceed to do immediately without binding ourselvesso strictly, as we have done hitherto, to the avoidance of anything that may be looked upon as theorising or speculating. We believe we have conducted our operations in the most strict conformity to the law of attraction, and have no doubts whatever about the form of the interior of the earth resulting from them; but there may be some room for small variations in the details of the various densities, and the position of the interior surface of the shell, arising from the pressure of the gases in the hollow centre, and the weight they will, in consequence, add to the general mass of the earth. The conclusions are as follows:—
(1)That the earth is not solid to the centre, nor is it possible that it could be, according to the law of attraction, but is a hollow sphere.
(2)That its greatest density must be at the region where the greatest mass of matter is to be found—as must have been always the case from the time it was a globe revolving on its axis, whether gasiform, liquid, or solid—which is now at 817 miles deep from the surface; and that the greatest density may not be much more than the mean of 5·66 times that of water ascribed to it by astronomers.
(3)That the inner surface of the shell of the hollow globe cannot be much over or under 2000 to 2200 miles from the outer surface.
(4)That the hollow part of the globe must be filled by an atmosphere consisting possibly in part of vapours of the chemical elements, and by gases at a very high degree of pressure.
(5)That the region of greatest density, and the position of the interior surface of the shell, may be expressed with very approximate accuracy as follows:—The former must be at 0·7939 of the mean radius of the earth, and the latter at 0·5479 of the same; both counted from the centre.
(6)That if the earth is a hollow sphere, the same must be the case with all the major planets and their satellites, the sun, and all the suns, or stars, that are seen in the heavens; and that their interior proportions and form must be in much the same ratios to their radii as those we have found for the earth.
The Earth.—The idea that bodies such as those of the solar system, even of the whole universe, have their greatest density where the greatest mass is and are hollow spheres, is so natural and logical, more especially if it is supposed that they have all been formed out of some kind of nebulæ, that it seems strange it has never been brought forward prominently before. We say prominently because we know that the earth has been considered to be a hollow sphere by very eminent men, such as Kepler, Halley, Sir John Leslie, and by others of lessname long after them. In support of this last remark, we shall make a few extracts—with comment on them—from an article on the "Interior of the Earth" in "Chambers's Journal" for February 1882, which have some interest in connection with our work.
1."The great astronomer Kepler, for instance, in seeking to account for the ebb and flow of the ocean tides, depicted the earth as a living monster, theearth animal, whose whalelike mode of breathing occasioned the rise and fall of the ocean in recurring periods of sleeping and waking, dependent on solar time. He even, in his flights of fancy, attributed to the earth animal the possession of a soul having the faculties of memory and imagination."
If it could be believed that Kepler had any idea of the earth being formed out of a nebula, whether hollow, or solid to the centre, the idea of a breathing animal was almost a consequence, because the attraction—a thing he is supposed to have known nothing about—of the original nebula for the earth one, on matter so light as nebulous matter, would raise enormous tides and make the earth, in its then state, not far from like an enormous primitive bellows made out of goatskins. No one knows what dreams may have passed through his brain. The last part of his notion was altogether fanciful.
2."Halley was opposed to the idea of the globe being solid, 'regarding it as more worthy of the Creator that the earth, like a house of several storeys, should be inhabited both without and within.' For light, too, in the hollow sphere, he thought provision might in some measure be contrived." This notion appears to be altogether fanciful, the fruit of an enthusiastic, exuberant imagination, leaving no trace of scientific thought upon the subject."
3."Sir John Leslie, like Halley, conceived the nucleus of the world to be a hollow sphere, but thought it filled, not with inhabitants, but with an assumed 'imponderable matter having an enormous force of expansion.'" It would be interesting to know on what bases he formed his ideas, as the filling of the hollow with imponderable matter seems to show more method than the former cases, but we have never seenany allusion made to his theory anywhere, except in the article we are quoting from. There may have been some reasons given for such a supposition in his "Natural Philosophy," but when we began to read that work in times long past, a more modern one was recommended to us, and we lost the chance, never to return.
There are other theories referred to in the article, but we shall take notice of one more only.
4."A certain Captain Symmes, who lived in the present century, was strongly convinced of the truth of Leslie's theory. He held that near the North Pole, whence the polar light emanates, was an enormous opening, through which a descent might be made into the hollow sphere, and sent frequent and pressing invitations to A. von Humboldt and Sir Humphrey Davy to undertake this subterranean expedition! But these imaginative conceptions must one and all be set aside, and the subject treated on more prosaic, though not less interesting, lines."
This conception of Captain Symmes will probably be looked upon as the most absurd of the whole lot, but to us it seems to give evidence of more thought than any one of them. One would think that he must have formed some notion of how a hollow sphere, with an opening out to the surface at each one of its two poles, could be formed. We must note that he lived in, possibly after, the time of Laplace.
We doubt whether anyone has ever studied out thoroughly how even a solid sphere could be ultimately elaborated from a nebula. It has always been a very general idea that a condensing and contracting nebula would, under the areolar law, assume the form of a lens rather than of a sphere. If this be so in reality, we may ask: How can the law of attraction produce a sphere out of a lens-shaped mass of rotating vaporous or liquid matter? It seems evident that to bring about such a result attraction must cease to act altogether in the polar directions, and only continue to draw in the matter from the equatorial directions of the lens, till the desired sphere was formed; and, How were the action and inactionof the law of attraction to be regulated meanwhile? Or, when the time came that a sphere of a pre-arranged diameter could be formed, a goodly part of the lens must have been cut off and abandoned; in which case we have again to ask: What was done with the surplus, the cuttings? No doubt they could be used up in meteor swarms, comets, or something; but Captain Symmes's theory has opened up a field for a good deal of thought, and our present knowledge of polar matters prevents us from being sure that strange discoveries may not be made as to the condition of the earth at the poles, although there may not actually be holes into the hollow interior. With regard to the last sentence of the quotation, we fully agree and are doing our best to comply with it. And in so doing, we shall have to return to the formation of globes out of nebulæ, elaborated into something more advanced than even lens-shaped discs.
There is no doubt that the reasons assigned by most, if not all, of the authors of the notions above cited are very fanciful, but one can hardly believe that the true reason—why the earth must be hollow—has not occurred to some of them; and that they did not follow it out because it involved too much work, and they did not feel inclined to undertake it, or had not time. On the other hand, modern astronomers and physicists have been so fascinated by the discoveries they have made, and in following them up, that the temptation to go on in the same course has been too great to allow them to spend time on the investigation of sublunary and subterranean affairs. Some of them have indeed studied the interior of the earth for special purposes, such as the thickness of the crust, solidity or liquidity, stability, precession of the equinoxes, the action of volcanoes, etc., etc.; but they never, apparently, examined into any of these features to the very end, otherwise, we believe, they would have come long ago to the same conclusion as we have. And withal it seems wonderful how near some of them have come to it. To most people it would appear absurd to think that any part of the earth of any great magnitude can be hollow, if in order to make up its mass its average specific gravity must be 5·66—more especially, if wetell them that the greatest specific gravity at any place need hardly exceed 5·66—forgetting that weight or mass can be taken from the interior where the volume per mile in diameter is small, and be distributed near the exterior where the volume per mile in diameter is comparatively immensely greater. But in whatever light we look upon the conclusions we have arrived at, a change in the construction of the bodies in space from solid to hollow spheres must produce changes in our ideas of them, and have consequences of great importance, too numerous to be all taken account of; we shall, therefore, only take notice of the most prominent.
Looking at the earth as a hollow sphere, we get rid of the difficulty of conceiving that matter can be compressed to three or four times less than the volume it has as known to us; and also of the misplacement of metals to the incredible degree we have shown to be necessary to make up its whole mass according to the sorting-out theory. And if we can only be bold enough to look upon gases as ponderable matter that can be compressed to great density, and so added to the weight of the whole mass, we may not be under the necessity of compressing the known matter composing it to even the half of its volume.
Somewhere in the first quarter of this century (see "Edinburgh Review," January 1870) Mr. Hopkins argued that the solid crust of the earth must be at least 800 to 1000 miles thick, in order to account for the precession of the equinoxes and nutation, but about a quarter of a century afterwards M. Delaunay demonstrated before the French Academy by actual experiment that the thickness of the crust had no bearing whatever on the problem. And about the same time Lord Kelvin inferred from the same thickness of crust that "no continuous liquid vesicle at all approaching to the dimensions of a spheroid 6000 miles in diameter could possibly exist in the earth's interior without rendering the phenomena of precession and nutation sensibly different from what they are"; and that the earth, as a whole, must be far more rigid than glass and probably more rigid than steel, "while the interior must be on the whole more rigid, probablymany times more rigid, than the upper crust." With the theory of a hollow shell, a better foundation is given for Mr. Hopkins's argument than a solid crust at about the same depth as he assumed, while at the same time the liquid vesicle of 6000 miles in diameter is removed, which Lord Kelvin showed would change the phenomena of precession and nutation. We have seen that imprisoned gases may have a high degree of density, and consequently rigidity, and may in some measure supply what was required by Lord Kelvin, who knows, also, very well that a structure with some degree of elasticity in it is stronger than one that is absolutely rigid. Moreover, the shell of the earth, composed of solid materials at a very high temperature, and consequently so far plastic, could not fail to accommodate itself to any variation of centrifugal force that could take place. Variations in rotation of the earth could only have come on extremely slowly, and even the most rigid matter we know will gradually yield to extreme pressure long continued. But this subject of the plasticity of the most solid part of the interior was discussed and, it may be said, demonstrated during the meeting of the British Association of 1886, as reported in "Nature" from July to September of that year. Any way, the possibility of plasticity is most patently shown by the hollow-sphere construction of the earth.
We do not know what were M. Delaunay's proofs that the thickness of the crust has no bearing whatever on precession and nutation, but if they were complicated with the fluidity, or even viscosity, of a liquid interior beyond a depth of 800 to 1000 miles, they must be entirely changed under the notion of a hollow sphere where there could be no really liquid molten matter, except near the inner surface. One thing we may be certain of, and that is, there must be something to account for precession and nutation, and we believe that the hollow shell, with the greatest density where the mass is greatest, is a much more rational cause for these phenomena than the bulging out of the earth to the extent of 13 miles or so at the equator.
It is very difficult to find out what geologists consider to be the nature of the interior of the earth in its details, but forour purpose no particular knowledge is required. However, it is necessary to allude to the principal features of their theories in order to note and remark how far they will agree to, or be facilitated, or the reverse, when applied to a hollow sphere. It would seem that almost all geologists are agreed that the central part is solid, and possibly extremely rigid owing to the enormous pressure of superincumbent matter; that it has a solid crust of several hundreds of miles in thickness; and that under this there is a sub-crust divided into two or more layers of different densities, partially liquid or at all events plastic, extending all over the solid interior matter; the chief purpose for which it is required being apparently to supply matter for volcanic action and surface movements.
Under the theory we are advocating, the place of greatest density of the interior is calculated to be at 817 miles from the surface, and its greatest approach to solidity will be there also; consequently, if geologists consider that it will have sufficient plasticity there to provide matter for volcanic eruptions, they will be at one with us so far. But should they consider that they require, for volcanoes, matter more liquid than is likely to be found at that depth, they will have to place their magma layers either much deeper or somewhere between that depth and the surface, in which case they will encroach on the requirements of astronomers, without liberating themselves from a difficulty in which they must find themselves involved under their present ideas. They say that these plastic layers exist under the solid crust all round the interior of the earth, so that if one of the duties they have to perform is to keep the various chains of volcanoes in communication with each other, their lateral movements must extend to some hundreds of miles in the cases of the enormous volumes of matter that are sometimes thrown out in even modern eruptions, and they have to provide the means for procuring that lateral motion. Shrinkage from cooling, or falling in of part of the solid crust, might bring about these enormous outbursts of lava, but they would be more likely to produce simple overflows than the explosive ejection of suchmasses as are now being recorded from time to time. We have brought into remembrance,page 148, that water cannot penetrate into the interior of the earth to a greater depth than 9 miles, more or less, as water, and that beyond that depth it can only exist in the form of steam, or dissociated into its elements of hydrogen and oxygen. As long as it continued in the form of water it could be suddenly flashed into steam, of not far from two thousand times its volume, by relief from pressure or sudden application of heat, and thus be converted into a violent explosive almost instantaneously; but when it came to have the form of a gas, it could only be heated gradually the same as any other gas. It is clear, therefore, that water cannot be looked to for producing the force, explosive or otherwise, that is required to raise even molten matter from depths of hundreds of miles to overflow from the summits or outlets of volcanoes.
A pressure of 400 atmospheres would be required to balance a column of average rock ofone milehigh. A mass of water, through shrinkage of the crust, might get introduced to the vent of a volcano, or some cavity connected with it, a few miles under the surface of the earth and cause an earthquake—it might be introduced by an earthquake—or eruption or both, abundantly formidable and destructive, no doubt, but only comparatively superficial, such as those of Naples and Charleston, where the extreme depth was calculated to be only a few miles; but it seems to us to be totally inadequate to produce those outpours that last for days and weeks, covering leagues of land, and filling up bays of the sea, with floods of lavas. It may be the principal agent or ally in producing the horrors and devastation of a grand eruption that has invaded the regions of water, but it is not to be conceived as possible that it can be the prime cause. The volumes of steam, water, and mud thrown out on such occasions, only tend to distract our attention from looking deeper for the true cause of the eruption. Geologists are therefore thrown back upon their magma layers to look for the motive power for producing these grand eruptions, and they cannot get water down deep enough to do it.
Tides produced by the sun and moon cannot be appealed to, otherwise the eruptions would be more or less uniform in their periods of occurrence. Sudden evolution of gases in the magma layers could not be accounted for in any way known to us, and accumulation of gases would involve the idea of immense cavities, to serve as reservoirs to be gradually filled till the pressure was sufficient to force a way out, and would imply a formation of the interior in compartments specially adapted for particular purposes, and altogether too fanciful to be entertained. Where could such enormous masses of matter, as those thrown out, come from at only a few miles from the surface? The great eruption at the Sandwich Islands, of about a century ago, after flowing over a distance of many miles of land, on which it left enormous quantities of lava, filled up a bay of the sea twenty miles long, and ran out a promontory of three or four miles into the sea; and we cannot conceive it to be possible that such a quantity of matter could be blown out from something less than 9 miles deep by water suddenly flashed into steam.
The critical temperature of water—that temperature at which it changes into steam under any pressure however great—being 412°, its pressure in the state of steam will be somewhere about 7150 lb. per square inch, let us say 500 atmospheres; then, if 400 atmospheres are required to balance 1 mile in depth of average rock, as we have stated above, the pressure of steam just cited would balance only 1¼ miles of rock. We can, therefore, see how inadequate it would be to force a column of lava up from even the depth of 9 miles. At that depth 3600 atmospheres of pressure are required to balance a column of lava, and there are only 500 available. It has been said that the downward pressure of steam would force up the lava through the vent of a volcano, but an arrangement of that kind would require a downcast shaft as well as the upcast one of the vent like as there are in collieries; but the downcast would have to go very deep to compress the steam—a gas now—to the required number of atmospheres. Far more likely that the steam itself would put an end to any increase of water, by driving it backthrough the channels by which it was descending; for if they are supposed to exist under a solid crust of 800 miles thick the pressure required would be 320,000 atmospheres, and with a crust of only 100 miles thick 40,000 would be required. The only way, therefore, in which volcanic eruptions can be produced in the earth, if solid or liquid, or partially solid and partially liquid, to the centre—in other words, from magma layers—is by the shrinking of the crust squeezing out the lava. With a hollow earth and shell of more or less 2200 miles in thickness, liquid to some depth on the interior surface the difficulty becomes very much less. The communication between the vents of volcanoes would be complete and simple, without any lateral forcing of the lava through magma layers made expressly for the purpose; it would be an open and natural flow from one place to another. That there are such volcano vents connected with each other has been very generally believed, and even almost proved by observation of eruptions taking place in two or more almost simultaneously, or at the least showing signs of violent agitation, the motive forces for which would be the gases which we have concluded must be imprisoned in the hollow centre. When their pressure came to be sufficient to blow or force out the liquid, or semiliquid matter, bubbling and boiling in the vents in constant activity, there would be an eruption, during and after which the gases would escape till their pressure was greatly reduced, when the volcanoes would return to their semi-active state. The gases would naturally be those of the many kinds that are found in eruptions, by reason of their being generated in the earth, mixed with steam and water in the manner we have already shown.
Let it not be supposed that the gases would require to have force enough to raise lavas from depths of over 2000 miles from the surface. According to our arguments for a hollow earth, at 817 miles from the surface the two halves—outer and inner—of the matter composing it meet and balance each other, so that all the pressure required would be what is necessary to overcome the inertia, viscosity, or cohesion of the matter in the vents. What that would be wedo not pretend to be able to calculate, but we believe that it would be very much inferior to that required to balance a column of lava of even 100 miles high. We have seen that gas compressed to 4835 atmospheres would be 6¼ times more dense than water, and of equal specific gravity to the heaviest matter required in any part of the earth to make up its average density to 5·66 that of water, and we cannot assume any greater pressure than this, without diminishing that maximum. If that, or any lesser degree of compression, would supply the necessary force, then all difficulty is removed further than pointing out the means of keeping the volcano vents open or openable; and the quality of openable may be facilitated by the contraction of the interior from cooling. If a greater pressure be necessary, we need not be afraid of greatly increasing it, for the only consequence would be to diminish the maximum density of solid matter required in any part of the earth, to make up the general average to 5·66, which means less compression of the matter. If the idea of the accumulation of gases in the hollow centre, or of the hollow centre itself, is inadmissible, then scientists in general can continue as before with their magma layers—aqueo-igneous if they like—but they must abandon the notion of lavas being expelled from them by steam pressure. We repeat that steam could never get down in the form of steam to the depths they require. The temperature there would be more than sufficient to resolve it into its elements of oxygen and hydrogen, and it would behave very much like the gases we have supposed to be in the hollow; there might be accumulation, but there could be no sudden flashing into existence like steam from water.
In support of our observation—if it needs support—that water as water cannot penetrate into the earth to a greater depth than where it meets a temperature of 412° we may refer to reports on earthquakes of comparatively recent occurrence. We learn from the "London Quarterly Review" of January 1869, that in the Neapolitan earthquake of 1857, Mr. Mallett found the greatest focal depth to have been 8-1/8 geographical, or 9·35 statute miles, which agrees very well withthe depth to which water could penetrate and be suddenly flashed into steam. (We say nothing, for the present at least, about how the water and the heat managed to meet so instantaneously.) The shock of the instantaneous generation of steam might be felt much lower, but it would tend to interrupt, not to produce, the eruption of lavas. In speaking of the pressure on the walls of the cavity, where the shock was produced, being 640,528 millions of tons, the reviewer says, "it may have been greater because the steam might be supposed to have acquired the temperature of the lava," and that is 2000°F.; but that could not well be. In order to meet lava of that temperature the steam would have to descend to from 20 to 25 miles deep; on the other hand, if the lava is assumed to have entered the cavity, it could only do so at a comparatively low velocity and would not reach more than a fraction of the steam at a time, and even for that reason there could be no flashing, as steam is only a gas, and cannot be heated otherwise than as a gas. Here the spirit of facilitating the meeting of the lava and the steam, is as apparent as in bringing about the meeting of the water and the lava noticed above. On the whole, therefore, we think that we were right in saying that steam or water cannot be the cause of volcanic eruptions, but that the invasion of the domains of water by the lavas may be the cause, in the main, of the explosive part of eruptions, and of the most disastrous effects of earthquakes. Moreover, the focus of the Neapolitan earthquake was 75 miles distant from Vesuvius, and therefore far removed from anything like direct connection with the vent of the volcano, so that water from it in any form could have no effect upon the magmas of scientists.