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Note on Sir William Thomson's Arguments for the Age of the Earth

SIR WILLIAM THOMSON has endeavored to prove the recent age of the earth by three well-known arguments of a purely physical nature: The first is based on the age of the sun's heat; the second, on tidal retardation of the earth's rotation; and the third, on the secular cooling of the earth. Argument from the Age of the Bun's Heat.—It will be obvious that, if what has already been advanced in regard to the origin of the sun's heat be correct, it will follow that the argument for the recent age of the earth, based upon the assumption that the sun could have derived its store of heat only from the condensation of its mass, must be wholly abandoned, and that, ill so far as this argument is concerned, there is no known limit to the amount of heat which the sun may have possessed, or to the time during which it may have illuminated the earth. Argument from T,dal Retardation.—It is well known that, owing to tidal retardation, the rate of the earth's rotation is slowly diminishing; and it is therefore evident that, if we go back for many millions of years, we reach a period when the earth must have been rotating much faster than now. Sir William's argument is,* that had the earth solidified several hundred millions of years ago, the flattening at the poles, and the bulging at the equator, would have been much greater than we find them to be. Therefore, because the earth is so little flattened, it must have been rotating, when it became solid, at very nearly the same rate as at present. And as the rate of rotation is becoming slower and slower, it cannot be so many millions of years back since solidification took place. A few years ago I ventured to point out t what appeared to be a very obvious objection to this argument, viz., that the influence of subaerial denudation in altering the form of the earth had been entirely overlooked. It has been proved, as we have seen, that the rocky surface of our globe is being lowered, on an average, by subaerial denudation, at the rote of about one foot in 6,000 years. It follows, as a consequence, from the loss of centrifugal force resulting from the retardation of the earth's rotation occasioned by the friction of the tidal wave, that the sea- level must be slowly sinking at the equator, and rising at the poles. This, of course, tends to protect the polar regions and expose equatorial regions to subaerial denudation. Now, it is perfectly obvious that, unless the sea level at the equator has, in consequence of tidal retardation, been sinking during past ages at a greater rate than one foot in 6,000 years, it is physically impossible the form of our globe could have been very much different from what it is at present, whatever may have been its form when it consolidated, because subaerial denudation would have lowered the equator as rapidly as the sea sank. But in equatorial regions the rate of denudation-is, no doubt, much greater than one foot in 6,000 years. because there the rainfall is greater than in the temperate regions. It has been shown that the rate at which a country is being lowered by subaerial denudation is mainly determined not so much by the character of its rocks as by i the sediment-carrying power of its river-systems. Consequently, other things being equal, the greater the rainfall the greater will be the rate of denudation. We know that the basin of the Ganges, for example, is being lowered by denudation at the rate of about one foot in 2,300 years; and this is probably not very far from the average rate at which the equatorial regions are being denuded. It is therefore evident that sub-aerial denudation is lowering the equator as rapidly as the sea-level is sinking from loss of rotation, and that consequently we cannot infer from the present form of our globe what was its form when it solidified. In as far as tidal retardation can show to the contrary, its form, when solidification took place, may have been as oblate as that of the planet Jupiter. There is another circumstance which must be taken into account. The lowering of the equator, by the transference of materials from the equator to the higher latitudes, must tend to increase the rate of rotation, or, more properly, it must tend to lessen the rate of tidal retardation. The argument may be shown to be inconclusive from another consideration. The question as to whether the earth's axis of rotation could ever have changed to such an extent as to have affected the climate of the poles, is at present exciting a good deal of attention. The subject has recently been investigated with great care by Prof. Houghton,:!: Mr. George Darwin,§ the Rev. J. F. Twisden,1 and others, and the general result arrived at may be expressed in the words ef Mr. G. Darwin: “If the earth be quite rigid, no redistribution of matter in new continents could ever have caused the deviation of the pole from its present position to exceed the limit of about 3 deg." Mr. Darwin has shown that, in order to produce a displacement of the pole to the extent of only 1 deg. 46', an area equal to one twentieth of the entire surface of the flobe would liave to be elevated to the height of two miles. 'he entire continent of Europe elevated two miles would not deflect the pole much over half a degree. Assuming the mean elevation of the continents of Europe and Asia to be 1,000 fe t, Prof. Houghton calculates that their removal would displace the pole only 199 4 miles. It may now be admitted as settled that if the earth be perfectly rigid the climate of our globe could never possibly have been affected by any change in the axis of rotation. But it is maintained that if the earth can yield as a whole, so as to adapt its form to a new axis of rotation, the effects may be cumulative, and that a displacement of the pole as much as 10 deg. or 15 deg. is possible. But then if the earth be able to adapt its form to a change * '. Transactions of the Geolocal Society of Glasgow,” vol. iii.. p. 1. t August 21. 1872; .' Climate and Time,” p. 335. "Proceedings of the Royal Society,” vol xxvi , p. 51. “Proceedings of the Royal Society.” vol. xxv.. p. 228. Paper read before the U4IOlolPcal Society, tebrruary 21, 1877. in the axis of rotation, there is no reason why it may not be able to adapt its form to a change in the rate of rotation, and if so, the flattening at the poles and the bulging at the equator would diminish as the rate of rotation diminished, even supposing there were no denudation going on. * Argmterd from the Secular Gouling of the Earth.—The earth, like the sun, is a body in the process of cooling, and it is evident that if we go back sufficiently far we shall reach a period when it was in a molten condition. Calculating by means of Fourier's mathematical theory of the conductivity of heat, Sir William Thomson has endeavored to determine how many years must have elapsed since solid ification of the earth's crust may have taken place. This argument is undoubtedly the most reliable of the three. Nevertheless, the data on the subject are yet very imperfect, so tbat no definite and trustworthy result can be arrived at by this means as to the actual age of the earth. In fact, this is obvious from the very wide limits assigned by him within which solidification probably took place. ” We must,” quoting Sir William's own words on the subject, “allow very wide limits on such an estimate as I have attempted to make, but I think we may, with much probability, say that the consolidation cannot have taken place less than 20,000,000 years ago, or we should have more underground heat than we actually have—nor more than 400,000,000 years ago, or we should not have so much as the least observed underground increment of temperature. That is to say, I conclude that Leibnitz's epoch of ' emergence' of the ' consistentur status' was probably within these dates. “t—Quarterly Journal of Science.

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