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.
It is impossible here to refer to the details of the method or steps of these calculations. The result however is, that making large allowances for presumably defective data, less than one-fourth of the total telluric heat annually dissipated (as already stated in amount) is sufficient to account for the annual volcanic energy at present expended by our globe.
It is thus represented by the transformation into heat of the work of crushing about 247 cubic miles of (mean) rock, a quantity so perfectly insignificant, as compared with the volume of the globe itself, as to be absolutely inappreciable in any way but by calculation; and as its mechanical result is only the vertical transposition transitorily of material within or upon our globe, the proportion of the mass of which to the whole is equally insignificant, so not likely in any way to produce changes recognisable by the astronomer.