Having determined densities for the matter composing the earth at 2, 4½, and 9 miles below the surface, that is, to where the mean diameter comes to be 7900 miles, if we divide that diameter into layers of 25 miles each in thickness, compute the volume of each layer or shell, increase the density of each layer as we descend in direct proportion from 3—the density we have fixed for 9 miles deep—to 13·734 times the density of water, at the centre, and multiply the volume of each layer from the surface downwards by its respective average density, we shall find a mass nearly equal to the mass of the earth at the density of water—always taking its mean diameter at 7918 miles, and mean density at 5·66 times that of water, as already premised. These calculations have been carefully carried out, and are represented in detail inTable IV. for future reference. They terminate in a deficiency of over 70,000,000 of cubic miles, a deficiency which would be more than made up by making the central density 13·736 instead of 13·734. Thus we see that if the density of the earth increases regularly from the surface to the centre, and if the densities we have given to the layers between the surface and 9 miles in depth are not greater than those adopted, the central density must be exceedingly near 13¾ times that of water. Of course, if the three surface densities are in realitylessthan those we have adopted, the central density must be greater than 13¾ times that of water. The whole being a result to our calculations which leads us to speculate on what kind of matter there is at the centre of the earth.
We are acquainted with various kinds of rocks, stones and other solid matter that have densities (specific gravities) of 2½ to 3 times that of water, and we have to conceive that a cubic foot of one of these would have to be compressed into a height of 2¾ or 2¼ inches in order to have the density of 13¾ required at the centre, a result which presents us with a substance which it is difficult to imagine or to believe to exist. It may be that the centre of the earth is occupied by the heaviest metals we know, arranged in layers proportioned in thickness to the masses required of them, and that they are laid oneover the other according to their densities, or mixed together until a distance from the centre is attained, at which ordinary rocks compressed as highly as their nature would admit of, may exist; but we do not derive much knowledge or satisfaction from such a supposition. An examination of our table of calculations will show that 500 miles in diameter of the central part might be filled up with platinum, the few other rarer and heavier metals, and gold amalgamated with mercury in due proportions. Then there might be a mixture of mercury and lead to 1800 miles in diameter, followed by a mixture of lead and silver to 2400 miles. After that might come a compound of silver, copper, tin, and zinc to 4900 miles, and some compounds of iron might finish the filling process up to 6000 miles in diameter, or thereby; where the known rocks, compressed to half their volume at first, but gradually allowed to expand, might complete the whole mass of the earth. It will be seen, also, that by the time compressed rocks could be used for this filling process, more than 43 per cent. of the whole volume of the earth would be occupied exclusively by pure metals mixed by rule and measure.
It would appear then that the "sorting-out theory"—about which a good deal has been written—whereby, in suns and planets, the metals on account of being heavier fall more rapidly to the centre, and the lighter metalloids remain near the surface—a theory probably got up to get over the difficulty we are in—is not a very happy one, as too much metal would be required for the process, at least for the earth. No doubt it might be applied differently to what we have done by mixing metals with rocks, stones, earth, etc., forming metallic ores—very rich they would doubtless have to be—from the centre outwards; but however disposed it would seem that very much the same quantity would be required to furnish the desired densities up to 6000 miles in diameter, where we have supposed compressed granites, etc., might come into play. Besides, such an arrangement would do away with the whole beauty of the theory; there would be no law to invoke; it would be all pick-and-shovel work.
The sorting-out theory is one of these notions that occur to humanity and are accepted at once, without consideration of what the consequences may be. If it is made to account for the four inferior planets being so much more dense, and of coming so much sooner to maturity—so to speak—than the four superior ones, it is hard to understand why the sun up to the present day almost ranks in low density with the large planets. If that theory holds good, it would be most natural to suppose that the mean density of the sun should be very much greater than that of Mercury. But it appears to be only carried as far as it suits the theorist, and to be there dropped, or rather ignored.
Having been defeated in our attempt to build up or construct an earth solid to the centre by appealing to the metals to make up the weight or density required for the foundation layers, and that even to somewhere about three-fourths of the diameter of the whole structure, we are forced to fall back upon our known rocks, earths, etc., in order to compound out of them the dense material we require, and of course we feel that we have in hand a more hopeless task than we had with the metals. How are we to compress the everlasting hills into one-fourth or one-fifth of their volume? Some solution of the difficulty, or mystery, must be found somewhere; but at the same time the mountains of gold, silver, and less precious metals required have shown us how absurd, even laughable, it is to appeal to them.
Let us suppose that we have a cubic foot of matter of any kind of 13¾ times the density of water, and that we place it in one of the scales of a balance at the centre of the earth; we shall find that it does not depress the scale one hair-breadth, for the very good reason that it has nowhere to depress it to; it would be already at what may be called the end of gravitation or tendency to fall lower. As it could not get any lower it would have a tendency to fly off anywhere—provided it was free to do so—and drag the scale and balance along with it, in obedience to its own attractive power and the attraction of all the matter of the earth surrounding it, except that the attraction might be so equally distributed all around it that it would not move in any direction. It would, however, be in astate of very unstable equilibrium, and if by some means the attraction were increased a little on one side more than the others, and it were at liberty to do so, it would abandon the centre and fly off in that direction never to return. Now, this being the case, we are forced to consider how a cubic foot of matter, such as the one we are dealing with, could ever have found its way to the centre of the earth; and the law of gravitation, or rather of attraction, does not in any way help us out of the difficulty. We know that we put our cubic foot of extremely dense matter there for an experiment, but we do not know of any process of nature that could place there any equal mass of matter of that density.
Gravitation and attraction are generally used as synonymous terms, more especially gravitation—somewhat after the manner of the likeness between the two negroes, Cæsar and Pompey, the latter being most especial in the likeness—but there is a very appreciable distinction between them, if we want to use each of them in its proper and strict sense. Gravitation implies the conception of a weight of some kind falling to a fixed centre, while attraction gives the idea of two weights, or masses, drawing each other to a common centre, which when properly looked at is a different thing; because the centre may be anywhere between the two, depending entirely on the difference, if any, in the weights of the masses. The confounding of the two, or rather the almost universal adoption of the less correct term, name, expression—whichever it may be called—has been the cause of wrong conceptions being formed of the construction of almost all—probably all—celestial bodies, and of that most absurd expression,attraction of gravitation, used by all our most eminent physicists. Thegravitationofattractionmight be excused, but putting cause for effect is hardly scientific. A name is nothing as long as what is meant by it is understood and taken into consideration, but that is not always the case, as we shall proceed to show.
The term gravitation may be applied with almost, but not absolutely, perfect strictness to the attraction between the sun and the planets, because the common centres of their attractions and the centre of the sun are so near each other thatthey may be looked upon as one and the same thing, or point; but it is not so with the attractions of the planets for each other where there is no common fixed centre, or if there is something approaching to it in a far off way, it is constantly varying, so that the term gravitation cannot be strictly applied to them, nor even to the sun, to speak truly. Planets sometimesgravitate awayfrom each other and from the sun, otherwise Adams and Leverrier could not have discovered Neptune from the perturbations of Uranus. Neither can it be properly applied to the different masses of matter in the sun or in the earth—although it was no doubt notions connected with the earth that gave rise to the term, from all ponderable matter falling upon it—becauseper sethey could have no tendency to fall to the centre, forat the centrethere is no sufficient attractive force to draw them towards it. Gravitation was a known term long before the days of Newton, who had the glory of enlightening the world by showing that attraction was the cause of it; and, perhaps unfortunately, the name was continued to represent what it in reality does not.
Let us suppose that we have an empty earth to fill up; if we place one mass of matter at London and another at Calcutta, they could have no tendency of themselves to fall to the centre, but if left alone would go for each other in a straight line and meet half-way between the two, provided they were equal in mass, and attraction, not gravitation, would be the proper term to apply to them. But supposing that two equal masses were placed at their antipodes and the four were left to themselves, they would gravitate towards and meet at the centre in the usual meaning of the word, but the force that drew them there would be really that of attraction. We could, however, place four similar and equal masses at the centre, and give the outer ones just and good reason for gravitating or falling down to it, because those at the centre being equally attracted in the four directions might remain stationary there, but would be in a state of unstable equilibrium. We may now suppose that when the masses had just left London and Calcutta to meet the others, a goodly number of other equal masses were added to those at these two placesand began to attract the two bound towards the centre, they would prevent the two from proceeding, or at least retard them on their journey inwards. Moreover, the larger numbers at these two places would attract the four masses at the centre with more force than would the two at the antipodes, and would draw the whole of the four away from the centre and outwards towards themselves; but we might also suppose that at the same moment an equal number of equal masses were added to those at the antipodes, which would again equalize the attractions at the four outer posts, and things would continue as they were at the first; with this difference, that the four at the centre would not be able to balance the attractions at the four outer posts, and the consequence would be—seeing that the forces at the four outer stations were equal to each other, and far superior to the four at the centre—that each one of the four at the centre would be drawn away from it towards one of the outer stations—provided the law of attraction acted impartially—and so the centre would be left without any of the masses at it, that is empty. No doubt when the four outgoing masses met the larger ones coming in, they would all then move towards the centre; but the four places where they met would be immensely nearer the places occupied at first by the outer masses than half-way between them and the centre—proportioned, in exact conformance with the law of attraction, to the excess of the numbers of the masses at the outer stations over those at the centre—and they would be moving, all of them together, to a remote and void space. We may now increase the four outer stations to thousands or millions, with the security that the mode of proceeding would be the same with the whole of them; that is, that the first tendency of the masses at each one of the millions of stations would be to draw away the filling we were pouring into the hollow earth—provided we did it equally and impartially all over the hollow—from the centre, and to leave a void there.
We are accustomed to look upon the earth as a solid body in which there are no acting and counteracting forces, no movements of matter from one place to another, similar tothose we have been calling into play, and as if there was only one force acting upon its whole mass and driving it to the centre; we have, in our ideas, got the whole mass so compressed and wedged in that it cannot move, and never has been able to move in any direction except towards the centre, and this is no doubt the case at the present day. We never stop to think with sufficient care how this compression and wedging-in were brought about, and we only accept what we have been accustomed to believe to be facts, and trouble ourselves no more about it; but there must have been a time, according to any cosmogony we may choose to adopt—even to the vague one that the solar system was somehow made out of a nebula of some kind—when the matter of the earth was neither compressed nor wedged in, nor prevented from moving in any direction towards which it was most powerfully attracted—before superincumbent matter came, so to speak, to have any wedging-in force—and we must go back to that period and study it deeply, if we want to acquire an accurate knowledge of the construction of the earth.
TABLE IV.—Calculations of the Volumes and Densitiesof the Earth between the Diameter specified,reduced to the Density of Water.
When, according to the nebular hypothesis, the ring for the formation of the earth and moon had been thrown off by the nebula, and had broken up and formed itself into one isolated mass—rotating or not on an axis, as the case may have been—it must have been in a gasiform state. What was its density, more or less, may be so far deduced fromTable III., where it will be seen that when it had condensed to about one-half of its volume, it must have had a density of only 1/9000th part of our atmosphere, and in which each grain of matter would have for its habitat 16 cubic feet of space, or a cube of 2·52 feet to the side. So that, with an average distance from its neighbours of 2½ feet, a grain of matter could not be looked upon as wedged-in in any way, and would be free to move anywhere. Now, supposing this earth-moon nebula to have been in the form of even an almost shapeless mass, and that it was nearly homogeneous—as it could hardly be otherwise after the tumbling about it had in condensing from a flatring—its molecules would attract each other in all directions, and as the mass—without having arrived perhaps at the stage of having any well defined centre—would have an exterior as well as an interior, the individual molecules at the exterior would draw those of the interior out towards them, just as much as those at the interior would attract those of the exterior in towards them; but as the number of those at the exterior would—owing to the much greater space there, being able to contain an immensely greater number—be almost infinitely greater than of those nearer to the central part, the latter would be more effectually attracted, or drawn, outwards than the former would be inwards, and there would be none left at the interior after condensation had fairly begun. The mass would speedily become a hollow body, the hollow part gradually increasing in diameter. But let us go deeper into the matter.
Let us suppose that the whole mass had assumed nearly the form of a sphere. We have already shown that, although the general force of attraction would cause all the component particles of the sphere to mutually draw each other in towards the centre, yet the more powerful tendency of the particles at the exterior—due to their greatly superior number—would at first be to draw the particles near the centre outwards towards them, and that there would consequently be a void at the centre, for a time at least. Of course it is to be understood that each part of the exterior surface would draw out to it the particles on its own side of the centre, just in the same manner as the four masses we placed at the centre were shown to be drawn out by those at London, Calcutta, and their antipodes. Now we must try to find out what would be the ultimate result of this action; whether it would be to form a sphere solid to the centre, or whether the void at first established there would be permanent.
In order to show how the heat of the sun is maintained by the condensation and contraction of that luminary, Lord Kelvin—in his lecture delivered at the Royal Institution, on Friday, January 21, 1887—described an ideal churn which he supposed to be placed in a pit excavated in the body of thesun, with the dimension of one metre square at the surface, and tapering inwards to nothing at the centre. In imitation of him, we shall suppose a similar pit of the same dimensions to be dug in the spherical mass, out of which we have supposed the earth to have been formed; only we shall call it a pyramid instead of a pit. This we shall suppose to be filled with cosmic matter, and try to determine what form it would assume were it condensed into solid matter, in conformity with the law of attraction. The apex of our imaginary pyramid would, mathematically speaking, have no dimension at all, but we shall assume that it had space enough to contain one molecule of the cosmic matter of which the sphere was formed. This being so arranged, we have to imagine how many similar molecules would be contained in one layer at the base of the pyramid at the surface of the sphere, and we may be sure that when brought under the influence of attraction, the great multitude of them would have far more power to draw away the solitary molecule from the apex, than the single one there would have to draw the whole of those in the layer at the base in to the centre of the sphere. A molecule of the size of a cubic millimetre would be an enormously large one, nevertheless one of that size placed at the apex of the pyramid would give us one million for the first layer at the base, and shows us what chance there would be of the solitary one maintaining its place at the apex. At the distance of one-twentieth of the radius of the sphere from the centre, the dimension of the base of the pyramid would be one-twentieth of a square metre, and the proportion of preponderance of a layer of molecules there would be as 25 to 1, so that the molecule at the centre would be drawn out almost to touch those of that layer; at one-tenth of the radius from the centre, the preponderance of a layer over the solitary central molecule would be as 10,000 to 1; and so on progressively to 1,000,000 to 1, as we have already said.
Following up this fact, if we divide the pyramid into any number of frusta, the action of attraction will be the same in each of them; the molecules in the larger end of each will have more power to draw outwards those of the small end,than they will have to draw inwards those of the larger end; and then the condensed frusta will act upon each other in the same manner as the molecules did, the greater mass of those at the larger end, or base, drawing down, or out—whichever way it may seem best to express it—a greater number of the frusta at the smaller end of the pyramid, until, in the whole of it, a point would be reached where the number of molecules in the various frusta drawn down from the apex would be equal to those drawn up from the base, leaving a part of the pyramid void at each end, because we are dealing with attraction, not gravitation, and there would be no falling to the base or apex, but concurrence to the point, just hinted at, where the outwards and inwards attractions of the masses would balance each other. This point of meeting of the two equal portions of cosmic matter may be called the plane of attraction in the pyramid. The whole pyramid would thus be reduced to the frustum of a pyramid, whose height would be as much more than double the distance from the plane of attraction to its base, as would be required to make the upper part above the plane of attraction equal in volume, or rather in number of molecules, to the lower part. It would be impossible for us to explain how, in a pyramid such as the one we have before us, the action of attraction could condense, and at the same time cram, the whole of the molecules contained in it into the apex end.
We must not, however, forget that there are two sides to a sphere, as well as to a question, and that we must place on the opposite side to the one we are dealing with, another equal pyramid with apex at the centre and base at the surface, at a place diametrically opposite to the first one, and that the tendency of the whole of this new pyramid would be to draw the whole of the first one in towards the centre of the sphere. But in the second, the law of attraction would have the same action as in the first; the molecules of the matter contained in it near the base would far exceed, in attractive force, those near the apex, and would draw them outwards till the whole were concentrated in a frustum of a pyramid, exactly the same as the one in the first pyramid. And while the wholemasses of matter in the two pyramids were attracting each other at an average distance, say, for simplicity's sake, of one-half the diameter of the sphere, the molecules in each of them would be attracting each other from an average distance of one-quarter the diameter of the sphere; their action would consequently be four times more active, and they would concentrate into the frusta as we have shown, before the two pyramids had time to draw each other in to the centre. There would be then two frusta of pyramids attracting each othertowardsthe centre with an empty space between them. Here then we have two elements of a hollow sphere, one on each side of the centre, and if we suppose the whole sphere to have been composed of the requisite number of similar pyramids, set in pairs diametrically opposite to each other, we see that the whole mass of the matter out of which the earth was formed must have—by the mutual attractions of its molecules—formed itself into a hollow sphere.
All that has been said must apply equally well whether we consider the earth to have been in a gasiform state, or when by condensation and consequent increase of temperature it had been brought into a molten liquid condition. For up to that time it must have been a hollow sphere, and we must either consider it to be so still, or conceive that the opposite sides have continued to draw each other inwards till the hollow was closed up; in which case, the greatest density would not be at the centre, but at a distance therefrom corresponding to what has been called the plane of attraction of the pyramid. That the opposite sides have not yet met will be abundantly demonstrated by facts that will meet us, if we try to find out what is the greatest density of the earth at the region of greatest mass or attraction, wherever that may be.
Seeing that the foregoing reasoning forces us to look upon the earth as a hollow sphere, or shell, in which the whole of the matter composing it is divided into two equal parts, attracted outwards and inwards by each other to a common plane, or region of meeting, we shall divide its whole volume into two equal parts radially, that is, one comprising a half from the surface inwards, and the other a half from the centreoutwards—that is to say, each one containing one-half of the whole volume of the earth. Referring now to our calculations,Table IV., we find that the actual half volume of the earth is comprised in very nearly 817 miles from the surface, where the diameter is 6284 miles, because the total volume at 7918 miles in diameter is 259,923,849,377 cubic miles. This being the case, we cannot avoid coming to the conclusion, after what has just been demonstrated by the pyramids that if one-half of the whole volume is comprehended in that distance from the surface, so also must be one-half of the mass.
But for further substantiation of this conclusion let us return to the table of calculations. There we find that from the surface to the depth of 817 miles—where the diameter would be 6284 miles—which comprehends one-half of the volume—the mass at the density of water is shown to be only 518,596,945,467 miles instead of 735,584,493,738 cubic miles, which is the half of the whole mass of the earth reduced to the density of water. That is, the outer half of the volume gives only 70·5 per cent. of half the mass, while the inner half of the volume gives not only one-half of the mass but 29·5 per cent. more; or, to put it more clearly, the mass of the inner half-volume is 1·84 times, nearly twice as great, as the mass of the outer half-volume. On the other hand, we have to notice that the line of division of the mass into two halves falls at 1163·25 miles from the surface, where the diameter is 5591·5 miles; so that on the outer half of the earth, measured by mass, 64·74 per cent. of the whole volume of the earth contains only one-half of the mass, whereas on the inner portion, measured in the same way, 35·26 per cent. of the same whole contains the other half. All these results must be looked upon as unsatisfactory, or we must believe that two volumes of cosmic matter which at one time were not far from equal, had been so acted upon by their mutual attractions that the one has come to be not far from double the mass of the other; that the vastly greater amount of cosmic matter at the outer part of a nebula has only one-half of the attractive force of the vastly inferior quantity at the centre. This we cannot believe if the original cosmic, or nebulous, matter was homogeneous;and if it was not homogeneous we have, in order to bring about such result, to conceive that the earth was built up, like any other mound of matter, under the direction of some superintendent who pointed out where the heavier and where the lighter matter was to be placed.
We shall now proceed to find out what would be the internal form, and greatest density of the earth, under the supposition that it is a hollow sphere divided into two equal volumes and masses—exterior and interior—meeting at 817 miles from the surface; but before entering upon this subject we have something to say about the notion of the earth being solid to the centre.
We are forced to believe that, according to the theory of a nucleus being formed at the centre as the first act, the matter collected there must have remained stationary ever since, because we cannot see what force there would be to uniform the nucleus just formed; gravitation, weight falling to a centre, would only tend to increase, condense, and wedge in the nucleus more thoroughly. Attraction, as we have shown, would not allow the matter to get to the centre at all. Convection currents, or currents of any kind, could not be established in matter that was being wedged in constantly. Moreover, when in a gasiform state, it would be colder than when condensed by gravitation to, or nearly to, a liquid or solid state, and heat would be produced in it in proportion to its condensation, that is, gradually increasing from the surface to the centre in the same manner as density, which, when the cooling stage came, would be conducted back to the surface to be radiated into space, but could not be carried—by convection currents—because the matter being heavier there than any placed above it, and being acted upon by gravitation all the time, would have no force tending to move it upwards; and above all, when solidification began at the surface, it is absurd to suppose that the first formed pieces of crust could sink down to the centre through matter more dense than themselves; unless it was that by solidification they were at once converted into matter of the specific gravity of 13·734. Even so the solid matter would not be very long in beingmade liquid again by meeting with matter not only hotter than itself, but constantly increasing in heat through continual condensation, which would act very effectively in preventing any convection current being formed to any appreciable depth, certainly never to any depth nearly approaching to the centre. If solidification began first at the centre—as some parties have thought might be the case—owing to the enormous pressure it would be subjected to there, before it began at the surface, then, without doubt, the central matter must have remained where it was placed at first, up to the present day. This would suit the sorting-out theory very well, as all the metals would find their way to the centre and there remain; but judged under a human point of view, it would be considered very bad engineering on the part of the Supreme Architect to bury all the most valuable part of His structure where they could never be availed of; or that He was not sufficiently fertile in resources to be able to construct His edifice in a way that did not involve the sacrifice of all the most precious materials in it. Man uses granite for foundations—following the good example He has actually given we believe, and are trying to show—and employs the metals in superstructures; but some people may also think that it was better to keep the root of all evil as far out of man's reach as possible. What a grand prospectus for a Joint Stock Company might be drawn up, on the basis of a sphere of a couple of thousand miles in diameter of the most precious metals, could only some inventive genius discover a way to get at them!
Returning to our pyramids. We know that the centre of gravity of a pyramid is at one-fourth of its height, or distance from the base, and if we lay one of 3959 miles long (the radius of the earth) over a fulcrum, so that 989¾ miles of its length be on one side of it and 2969¼ miles on the other, it will be in a state of equilibrium. This does not mean, however, that there are equal masses of matter on each side of the fulcrum, for we know that the mass of the base part must be considerably greater than that of the apex part, and that it must be counterbalanced by the greater leverage of the apex part, due to its greater distance from the point of support. This being so, in the case of a pyramid consisting of gasiform,liquid, or solid matter, the attractive power of the 989¾ miles of the base part would be greater than that of the 2969¼ miles of the apex part, and the plane of equal attraction of the two parts would be less than 990 miles from the base of the pyramid. This is virtually the same argument we have used before repeated, but it is placed in a simpler and more practical light, and shows that the plane of attraction in a pyramid will not be at its centre of gravity but nearer to its base, and that it must be at or near its centre of volume. Thus the plane of attraction in one of the pyramids we have been considering of 3959 miles in length, and consequently the radial distance of the region of maximum attraction of the earth, would not be at 990 miles from the base or surface, but at some lesser distance.
Now, if we take a pyramid, such as those we have been dealing with, whose base is 1 square and height 3959, its volume would be the square of the base multiplied by one-third of the height, that is 12× 3959/3 = 1319·66, the half of which is 659·83. Again, if we take the plane of division of the volume of the pyramid into two equal parts to be 0·7937 in length on each side, and consequently (from equal triangles) the distance from the plane to the apex to be 0·7937 the total height of 3959, which is 3142·258; then, as we have divided it into a frustum and a now smaller pyramid, if we multiply the square of the base of this new pyramid by one-third of the height we have 0·79372× 3142·258/3, or 0·62996 × 1047·419 = 659·83, which is equal to the half-volume of the whole pyramid as shown above. Thus we get 3959 less 3142·258 = 816·74 miles as the distance from the base of the plane of division of the pyramid into two equal parts, which naturally agrees with the division of the earth into the two equal volumes that we have extracted from the table of calculations, where we have supposed the earth to be made up of the requisite number of such pyramids. So that it would seem that we are justified in considering that the greatest density of the earth must be at the meeting of the two half-volumes, outer and inner, into which we have divided it.
Considering, then, that one-half of the volume and mass of the earth is contained within 817 miles in depth from the surface, this half must have an average density of 5·66 times that of water, the same as the whole is estimated to have. Also, as we have seen already, that, taking its mean diameter at 7918 miles, its mass will be equivalent to 1,471,168,987,476 cubic miles, one-half of this quantity, or 735,584,493,738 cubic miles will represent the half-volume of the earth reduced to the density of water. With these data let us find out what must be the greatest density where the two half-volumes meet, supposing the densities at the surface and for 9 miles down to remain the same as in the calculations we have already made, ending with specific gravity of 3 at 7900 miles in diameter.
Following the same system as before when treating of the earth as solid to the centre, and using the same table of calculations for the volumes of the layers: If we adopt a direct proportional increase between densities 3 at 7900 miles and 8·8 at 6284·5 miles in diameter, multiply the volumes by their respective densities, and add about 31 per cent. of the following layer, taken at the same density as the previous or last one of the number, we shall find a mass (see Table V.) of 735,483,165,215 cubic miles at the density of water, which is as near the half mass 735,584,493,738 cubic miles as is necessary for our purpose. It would thus appear that if the earth is a hollow sphere, its greatest density in any part need not be more than 8·8 times that of water, instead of 13·734 times, if we consider it to be solid to the centre.
Let us now try to find out something about the inner half-mass of the earth, and the first thing we have got to bear in mind is, that where it comes in contact with it, its density must be the same as that of the outer half-mass at the same place, and continue to be so for a considerable distance, varying much the same as the other varies in receding from that place, and diminishing at the same rate as it diminishes. This being the case—and we cannot see how it can be otherwise—if we attempt to distribute the inner half-mass over the whole of the inner half-volume, and suppose that its density decreases from its contact with the outer half—where it wasfound to be 8·8 times that of water—to zero at the centre, in direct proportion to the distance; then, it is clear that at half the distance between that place and the centre, the density must be just 4·4 times that of water. Now, if we divide the outer moiety of the inner half-mass of the earth—that is, the distance between the diameters of 6284·5 miles and 3142·25 miles—into layers of 25 miles thick each, take their volumes fromTable IV., and multiply each of them by a corresponding density, decreasing from 8·8 to 4·4, we shall obtain a mass far in excess of the whole mass corresponding to the inner half of the earth. This shows that a region of no density would not be at the centre but would begin at a distance very considerably removed from it. It is another notice to us that the earth must be a hollow sphere. But why should there be a zero point or place of no density? And what would a zero of no density be? It would represent something less than the density of the nebulous matter out of which the earth was formed; and all that we have contended for, as yet, is that there is a space at the centre where there is no greater density than that corresponding to the earth nebula; but we must now go farther.
If the earth is a hollow sphere, it must have an internal as well as an external surface. But how are we to find out what is the distance between these two surfaces? Let us, to begin, take a look at the hollow part of the sphere. From the time of Arago it began to be supposed that there is a continual deposit of cosmic matter upon the earth going on, and since then it has been proved that there is a constant and enormous shower of meteors and meteorites falling upon it. But although this is the case on the exterior surface, it may be safely asserted that on the interior surface, where the supply of cosmic matter must have been limited from the beginning, there can be no continual deposit of such matter going on now; nor can there have been from, at least, the time when the earth changed from the form of vapour to a liquid state. We may, therefore, be sure that there is no undepositedcosmicmatter of any kind in the hollow of the sphere, and that, as far as it is concerned, there is an absolute vacuum.
TABLE V.—Calculations of the Volumes and Densities of the Outer Half of the Earth—taken as a Hollow Sphere—at the Diameters specified, and reduced to the Density of Water.With mean diameter of 7918 miles. Diameter of half-volume at 6284·5 miles, and density there of 8·8 times that of water.