Part 8

The views which I have put forward in the Paper I have referred to, read to the Royal Society, recapitulated in skeleton, so to say, are as follows. Omitting those portions which treat of our globe from the period of the first liquefaction out of a nebulous condition, and of the earliest stages of the cooling by radiation into space, when the crust was extremely thin, and of the deformation of the spheroid as one of the first effects of its contraction, and through that the general shaping out of continents and ocean beds; I have endeavoured to show that the rate of contraction of the crust, while very thin, exceeded that of the large fluid nucleus supporting it, and so gave rise to tangential tensions in the crust, and fracturing it into segments; next, that as the crust thickened, these tensions were gradually converted into tangential pressures, the contraction of the nucleus now beginning to exceed (for equal losses of heat) that of the crust through which it cooled. At this stage these tangential pressures gave rise to the chief elevations of mountain chains--not by liquid matter by any process being injected from beneath vertically, but by such pressures, mutually reacting along certain lines, being resolved into the vertical, and forcing upwards more or less of the crust itself. The great outlines of the mountain ranges and the greater elevation of the land were designated and formed during the long periods that elapsed in which the continually increasing thickness of crust remained such that it was still, as a whole, flexible enough, or opposed sufficiently little resistance to crushing, to admit of this uprise of mountain chains by resolved tangential pressures. I have shown that the simple mechanism of such tangential pressures is competent to account for all the complex phenomena both of the elevations and of the depressions that we now see on the earth's surface (other than continents and ocean beds), including the production of gaping fissures (in directions generally orthogonal to those of tangential pressure). And as our earth is still a cooling body, and the crust, however now thicker and more rigid, is still incapable of sustaining the tangential pressures to which it is now exposed, so I by no means infer that slow and small (relatively) movements of elevation and depression may not be still and now going on upon the earth's surface; in fact all the phenomena of elevation and depression, rending, etc., which at a much remoter epoch acted upon a much grander and more effective scale. So that, for aught my views say to the contrary, all the mountain chains in the world may be possibly increasing in stature year by year, or at times; but in any case at a rate almost infinitesimally small in its totality over the whole earth to that with which their ridges were originally upreared.

But the thickness of the earth's crust--thus constantly added to, by accretion of solidifying matter from the still liquid or pasty nucleus, as the whole mass has cooled--has now assumed such a thickness as to be able to offer a too considerable resistance to the tangential pressures, to admit of its giving way to any large extent by resolution upwards; yet the cooling of the whole mass is going on, and contraction, though unequal, both of thick crust and of hotter nucleus beneath also, whether the latter be now liquid or not. Were the contraction, lineal or cubical, for equal decrements or losses of heat, or in equal times--equal both in the material of the solidified crust and in that of the hotter nucleus--there could be no such tangential pressures as are here referred to, at any epoch of the earth's cooling. But in accordance with the facts of experimental physics, we know that the co-efficient of contraction for all bodies is greater as their actual temperature is higher, and this both in their solid and liquid states.

Hence for equal decrements of heat, or by the cooling in equal times, the hotter nucleus contracts more than does its envelope of solid matter.

The result is now, as at all periods since the signs changed of the tangential forces thus brought into play--i.e., since they became tangential pressures--that the nucleus tends to shrink away as it were from beneath the crust, and to leave the latter, unsupported or but partially supported, as a spheroidal dome above it.

Now what happens? If the hollow spheroidal shell were strong enough to sustain, as a spheric dome, the tangential thrust of its own weight and the attraction of the nucleus, the shell would be left behind altogether by the nucleus, and the latter might be conceived as an independent globe revolving, centrally or excentrically, within a shell outside of it. This, however, is not what happens.

The question then arises, Can the solid shell support the tangential thrust to which it would be thus exposed? By the application to this problem of an elegant theorem of Lagrange, I have proved that it cannot possibly do so, no matter what may be its thickness nor what its material, even were we to assume the latter not merely of the hardest and most resistant rocks we know anything of, but even were it of tempered cast-steel, the most resistant substance (unless possibly iridio-osmium exceed it) that we know anything about. Lagrange has shown that if P be the normal pressure upon any flexible plate curved in both directions, the radii of these principal curvatures being r' and r'', and T the tangential thrust at the point of application and due to the force P, then:

P = T (1/r' + 1/r'')

When the surface is spherical, or may be viewed as such, r' = r'' and

P = 2T/r or, T = P × r/2

In the present case P is for a unit square (taken relatively small and so assumed as plane) of the shell, suppose a square mile, equal to the effect of gravity upon that unit, r being the earth's radius, and if we assume the unit square be also a unit in thickness, P is then the weight of a cubic mile of its material; and if we take (roughly) the earth's radius as 4,000 miles, the tangential pressure, T, is, on each face of the cubic mile, equal to

(4000/2) P,

or equal to the pressure of a column of the same material of 2,000 times its weight.

If the cubic mile that we have thus supposed cut out of the earth's crust at the surface were of the hardest known granite or porphyry, it would be exposed to a crushing tangential pressure equal to between 400 and 500 times what it could withstand, and so must crush, even though only left unsupported by the nucleus beneath, to the extent of 1/400 or 1/500 of its entire weight. And what is true here of a mile taken at the surface, is true (neglecting some minute corrections for difference in the co-efficient of gravity, etc.) if taken at any other depth within the thick crust.

The crust of our earth, then, as it now is, must crush, to follow down after the shrinking nucleus--if so be that the globe be still cooling, and constituted as it is; even to the limited extent to which we know anything of its nature--it must crush unequally, both regarded superficially and as to depth; generally the crushing lines being confined to the planes or places of greatest weakness; and the crushing will not be absolutely constant and uniform anywhere, or at any time, or at any of those places of weakness to which it will be principally confined, but will be more or less irregular, quasi-periodic, or paroxysmal: as is, indeed, the way in which all known material substances (more or less rigid) give way to a slow and constantly increasing, steady pressure.

We have now to ask, How much of this crushing is going on at present year by year? And the answer to this depends upon what amount of heat our world is losing into space year by year.

Geologists who have taken on trust the statement, that La Place has proved that the world has lost no sensible amount of heat for the last 10,000 years seem generally to suppose that to be a fact; but in reality La Place has proved nothing of the sort, as those geological teachers who have echoed the conclusion should have known, had they deciphered the mathematical argument upon which it has been supposed to rest.

By application of Fourier's theorem (or definition) to the observed rate of increment of heat in descending from the geothermal couche of invariable temperature, and the co-efficients of conductivity of the rocks of our earth's crust, as given by the long-continued observations made beneath the Observatories of Paris and of Edinburgh, it results that the annual loss of heat into space of our globe at present is equal to that which would liquefy into water, at 32° Fahr., about 777 cubic miles of ice; and this is the measuring unit for the amount of contraction of our globe now going on. The figures are not probably exact, for the data are not on a basis sufficiently full or exactly established as yet; but they are not very widely wrong, and their precise exactness is not material here. Now, how is this annual loss of heat (great or small, as we may please to view it) from the interior of our globe disposed of?

What does it do in the interior? We have already seen that it is primarily disposed of by conversion into work; into the work of diminishing the earth's volume as a whole, and in so doing crushing portions of the solid surrounding shell.

But does the transformation of lost heat into the work of vertical descent, and of the crush as it follows down after the shrinking nucleus, end the cycle? No. A very large portion of the mechanical work thus produced, and resolved, as we have seen, into tangential crushing pressure, is retransformed into heat again in the very act of crushing the solid material of the shell. If we see a cartload of granite paving-stones shot out in the dark, we see fire and light produced by their collision; if we rub two pieces of quartz together, and crush thus their surfaces against each other, we find we heat the pieces and evolve light.

The machinery used for crushing by steam-power, hard rocks into road metal, gets so hot that the surfaces cannot be touched.

These are familiar instances of one result of what is now taking place by the crushing of the rocky masses of our cooling and descending earth's crust, every hour beneath our feet, only upon a vastly greater scale. It is in this local transformation of work into heat that I find the true origin of volcanic heat within our globe. But if we are to test this, so as in the only way possible to decide is it a true solution of this great problem, we must again ask the question, How much? and to answer this, we must determine experimentally how much heat can be developed by the crushing of a given volume, say a cubic mile, of such rocky materials as we know must constitute the crust of our globe down to the bottom of the known sedimentary strata, and extending to such crystalloid rocks as we may presume underlie these. We must also obtain at least approximately what are the co-efficients of total contraction between fusion and atmospheric temperature of such melted rocks, basic and acid silicates, as may be deemed representative of that co-efficient for the range of volcanic fused products, basalts, trachytes, etc., which probably sufficiently nearly coincide with that of the whole non-metallic mass of our globe.

The first I have determined experimentally by two different methods, but principally by the direct one of the work expended in crushing prisms of sixteen representative classes of rock; the specific gravities and specific heats of which I have also determined.

If H be the height of a prism of rock crushed to powder by a pressure, P, applied to two opposite faces, which, when the prism has been reduced to its volume in powder, has acted through a range of H - t, then

P × (H - t) / 772

is the heat corresponding to the work expended in the crushing, expressed in British units of heat. The following were the rocks experimented upon: Caen stone, Portland (both oolites), magnesian limestone, sandstones of various sorts, carboniferous limestones (marbles), the older slates (Cambrian and Silurian), basalts, various granites and porphyries, thus ranging from the newest and least resistant to the oldest and most resistant rocks. The results have been tabulated, and are given in detail in my Paper, now in possession of the Royal Society. The minimum obtained is 331 and the maximum 7,867 British units of heat developed, by transformation of the work of crushing one cubic foot of rock. If we apply the results to a thickness of solid crust of 100 miles (British), of which the upper twenty-one miles consist of neozoic, newer palæozoic, older palæozoic and azoic rocks in nearly equal proportion as to thickness, and the remaining eighty miles of crystalloid rocks (acid and basic magmas of Durocher) of physical properties which we may assume not very different from those of our known granites and porphyries--and which, in so far as they may differ, would give a still higher co-efficient of work transformed into heat than I have attributed to them by ranging them as only equal to the granites, etc.--then we obtain a mean co-efficient for the entire thickness of crust of 100 miles of 6,472 British units of heat, developable from each cubic foot of its material, if crushed to powder. It results from this that each cubic mile of the mean material of such a crust, when crushed to powder, developes sufficient heat to melt 0·876 cubic miles of ice into water at 32°, or to raise 7·600 cubic miles of water from 32° to 212° Fahr., or to boil off 1·124 cubic miles of water at 32° into steam of one atmosphere, or, taking the average melting point of rocky mixtures at 2,000° Fahr., to melt nearly three and a-half cubic miles of such rock, if of the same specific heat.

Of the heat annually lost by our globe and dissipated into space, represented by 777 cubic miles of ice melted, as before stated, the chief part is derived from the actual hypogeal source of a hotter though not necessarily fused nucleus, and nearly, if not wholly, is quite independent of the heat of Vulcanicity, which is developed as a consequence of its loss or dissipation. But were we to take the extreme case, and suppose it possible that all the heat the globe loses annually resulted from the transformation of the work of internal crushing of its shell, we shall find that the total volume of rock needed to be crushed in order to produce the required amount of lost heat is perfectly insignificant as compared with the volume of the globe itself, or that of its shell. For, as 1·270 cubic miles of crushed rock developes heat equivalent to that required to melt one cubic mile of ice to water at 32°, and if we assume the volume of our globe's solid crust to equal one-fourth of the total volume of the entire globe, 987 cubic miles of rock crushed annually would supply the whole of the heat dissipated in that time. But that is less than the one sixty-five millionth of the volume of the crust only.

But a very small portion of the total heat annually lost by our globe is sufficient to account for the whole of the volcanic energy of every sort, including thermal waters, manifested annually upon our earth. In the absence of complete data, we can only approximately calculate what is the annual amount of present volcanic energy of our planet. This energy shows itself to us in three ways: 1. The heating or fusing of the ejected solid matters at volcanic vents. 2. The evolution of steam and other heated elastic fluids by which these are carried. 3. The work of raising through a certain height all the materials ejected. To which we must add a large allowance for waste, or thermal mechanical and chemical energy ineffectually dissipated in and above the vents. All these are measurable into units of heat.

I have applied this method of calculation to test the adequacy of the source I have assigned for volcanic heat, in two ways, viz.: 1. To the phenomena presented during the last two thousand years by Vesuvius, the best known Volcano in the world; and 2. To the whole of the four hundred and odd volcanic cones observed so far upon our globe, of which not more than one-half have ever been known in activity.