New Theories in Astronomy

by William Stirling

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.