Inquiry into the Interior Construction of the Earth—continued.

It may 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 of attraction 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 which case 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 miles deep 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 that the 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 found that 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 to us 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 of pressure; 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 gravity of 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, and 1/2200th 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 at one 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 be conducted outwards, 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 ourselves so 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.