The Age of the Earth

THE AGE OF THE EARTH The only theory of the origin of the earth that has hitherto survived quantitative test is the tidal theory. (See COSMOGONY.) This implies that the earth condensed from a filament, newly ejected from the sun under the gravitational attraction of a large star passing close to the sun's surface. The primitive earth would liquefy partly through loss of heat by radiation from the outside and partly by adiabatic expansion. The latter leads to the forma tion of liquid drops as in a liquid air machine, and the drops would gradually collect towards the centre. The formation of a liquid earth, probably with an atmosphere of some of its more volatile constituents, would be a matter of centuries. Further cooling would lead to solidification; the time needed for this would be longer on account of the reduced temperature and dis tension, but in a few thousand years at most the earth would have a thick solid shell on the outside. The further time taken for the outer surface to cool down, till its temperature was maintained al most wholly by the sun's radiation, would be only a few years. The temperature would then be near the present temperature, since the sun was in nearly its present state. The moon, if it originated in the same way as most of the other satellites, was formed a few years after the earth ; if it was formed according to Sir G. H. Darwin's resonance theory, it still separated while the earth was liquid. Thus the intervals that have elapsed since the earth sepa rated from the sun, since the moon was formed, or since the earth's outer surface became approximately as cool as it is now, do not differ by more than a few thousand years.

Denudation.

As soon as the outer surface became cool, an ocean could form—though possibly only a small one at first— and rain and rivers, denudation and sedimentary rocks came into existence. Several methods are available for estimating the age of the earth, but they are not all of equal accuracy, or reliability. The simplest, apparently, is that based on denudation. If we know the total mass of sedimentary rocks over the earth's sur face, and the annual amount of sediments carried to the sea by rivers, a simple division gives an estimate of how long the process has been going on. The transport of sodium to the sea in rivers, together with the present total amount of salt in the sea, gives another estimate. Both methods suggest ages of about Soo mil lion years. But it is important to notice that many factors can vitiate both. In particular, purely geological evidence makes it clear that the present rate of denudation is considerably in excess of the average of the past, owing to the existence of many high and comparatively new mountain ranges and the large amount of easily denuded matter left by the last glacial period. These methods can, therefore, at most suggest an order of magnitude.

Kelvin's Arguments.

Two methods were given by Lord Kelvin, one based on the rate of supply of energy from the sun, and the other on the cooling df the earth's crust by conduction. In the former he supposed, following Helmholtz, that the sun's energy was maintained by contraction, and found that the whole energy liberated by the sun, in contracting from an infinite dis tension to its present size, would maintain radiation, at the present rate, for only about 20 million years. In the latter he considered the cooling of the earth from the state just after solidification, and found how the rate of increase of temperature with depth in the crust depended on the time the earth has been cooling. This increase of temperature with depth is known by observation. The method, with modern data, gives about 27 million years for the age of the earth.

There is now an overwhelming amount of evidence that the earth and the sun are both very much older than Kelvin's numer ical results would indicate. Yet the value of his attempts has not disappeared, though some current references might lead one to suppose that it had. Numerous astronomical sources of informa tion have shown that the sun has been radiating as vigorously as now for hundreds of thousands of millions of years, and not merely for tens of millions, and we must infer that stars can draw on some source of energy much more provident than contraction under gravity. But Kelvin's argument will not be completely answered until this source can be definitely located and we can say under what conditions, and how fast, it gives up its energy; and although astrophysicists are making progress in studying it, its nature still remains largely a matter of speculation. At present we can only assert its existence.

Radioactivity.

The argument from the earth's thermal state was shown to require modification by the discovery of radioac tivity. It was found that all surface rocks contained minute quantities of radioactive elements, but they were enough to indi cate the probability that a large fraction of the heat being con ducted out of the earth is of radioactive origin and does not arise from the original heat. But if so the original heat accounts for a smaller rate of increase of temperature with depth than was pre viously thought ; in other words, cooling has proceeded to a greater depth and the time taken has been longer than Kelvin's theory in dicates. Nevertheless, his theory is not done with. The earth is not so old that original heat has ceased to be important, and Kelvin's work shows how to estimate its importance. Its geo physical interest will not disappear till after the hot central core freezes.

Radioactivity not only showed the need of supplementing the old theory, but provided a new means of determining geological time ; and this method is the best that is known. Radioactivity consists in the breaking up of elements with high atomic weights; in all known cases the disruption takes place by the loss of an a-particle, which is a charged helium atom, or by the loss of a /3 particle, which is a free electron. In each case a certain amount of radiative energy is also liberated. The atomic weight of nium is 238, that of helium is 4, and that of an electron, on the same scale, would be • Thus when an a-particle is lost the atomic weight decreases by 4 ; when a /3-particle is lost it de creases by an insignificant amount. The products of the decay of uranium have therefore atomic weights of 234, 23o, 226, 222, 218, 214, 210 and 206 ; but several may have nearly the same atomic weight owing to loss of /-particles. The most interesting of the products, for our purpose, are those with atomic weights 226 and 206, namely, radium and lead. Radium breaks up at a known rate ; in a given sample of radium i part in 2,280 breaks up every year. But in spite of its short life, radium is present in all uranium minerals, in a constant proportion corresponding to 36 atoms of radium per hundred million of uranium. The explana tion is that uranium itself breaks up at such a rate as to replenish the radium as fast as this in its turn breaks up. For this to be possibl,; one atom of uranium in 6,400 million must break up every year.

The final product is a kind of lead; that is to say, no chemical test will distinguish it from ordinary lead, but its atomic weight is 206 instead of 207.2. Lead is always found in uranium minerals, and when it was isolated it was actually found to have atomic weight 206. The different kinds of lead were the first examples discovered of isotopes, elements identical in chemical behaviour but differing in atomic weight; but numerous others are now known through the work of Aston.

Now, this lead is being produced from uranium at a known rate : for every 6,400 million atoms of uranium 1 atom of lead is produced every year, or, if we allow for the difference in atomic weights, 7,400 million parts by weight of uranium produce i part by weight of lead every year. Hence if a mineral contained no lead to begin with, and now contains x parts of lead to i of ura nium, the age of the mineral is 7,400x million years. Petrologists can recognize when original lead must have been absent, and the method is therefore applicable to the determination of the ages of minerals, and hence to the absolute measurement of geological time. The element thorium behaves somewhat similarly to ura nium, its final product being a lead of atomic weight 208. When uranium and lead are both present in a mineral the age can be calculated by the formula of Holmes and Lawson :— Age = Pb U-+o•38Th X 7,400 million years.

Holmes and Lawson give also a slightly more accurate formula, allowing for the variation of the amounts of uranium and thorium with time. The oldest known minerals to which this method is applicable have been found to have ages of about 1,500 million years. The coal measures were laid down about 250 million years ago. The former estimate is therefore a minimum estimate of the age of the earth.

The radioactive elements can be applied in another way, due to H. N. Russell, to find an upper limit to the age of the earth. The above method is based on the analysis of minerals specially rich in uranium and thorium. But these elements are present in all rocks, and the method could be applied to the earth's crust as a whole. A caution necessary is that some of the lead may have always been lead and not have been produced by radioactivity during the geological time. Consequently the method gives an upper limit. The amounts of the relevant elements, in parts by weight, shown by averages of analyses of rocks, are U, 6 parts per million ; Th, 15 parts per million; Pb, 7.5 parts per million. The quantity of lead is too small to be consistent with the ex istence of the earth for more than about 3,00o million years, according to Holmes's latest revision. Thus radioactivity leads to the conclusion that the age of the earth is between 1,500 and 3,00o million years.

Evidence from Cosmogony:

The Orbit of Mercury.—Two arguments from cosmogony also give evidence concerning the age of the earth. The first is based on the fact that planets formed by ejection from the sun would move originally in very elongated orbits, which must have been altered to their present circular form by some later influence. The only cause known that could produce such an effect is the resistance of the gaseous medium surrounding the sun, formed of the parts of the primitive filament that failed to condense into planets. The medium would mean while degenerate gradually on account of viscosity and diffusion. The time such a medium would take to reduce the eccentricity of the orbit of Mercury to its present value is inversely propor tional to its density ; the time it would take to become destroyed by viscosity and diffusion is directly proportional to its density.

These times must be somewhere near equal, because, if the me dium was not dense enough to begin with, it would have disap peared before it had produced its actual effect, while if it was too dense a large amount of it would still remain and would be visible. From a comparison of the two intervals of time it is found that the age must be of the order of magnitude of 3,00o million years. Great accuracy is not possible.

Tidal Friction.—An alternative method depends on the his tory of the earth and moon. The rotation of the earth is not abso lutely uniform; the day is becoming longer by about one second in 120,000 years. The change affects the observed times of ancient eclipses to a measurable extent, and it is from these that the amount is determined. The explanation depends on the tides pro duced by the sun and moon. The tidal currents in shallow seas are resisted by friction over the bottom, and this leads to a cer tain amount of dissipation of energy and to a reaction on the tides in mid-ocean, giving a systematic disturbance of the times of high water. If no friction took place the attraction of either the sun or the moon on the tides raised by itself would act exactly through the centre of the earth, and would have no tendency to turn it ; but the displacement of the times of high water causes the attrac tion to act along a line passing a little to one side of the centre, and consequently to alter the rotation of the earth. A reaction on the moon makes the moon go farther off, and explains how the moon can have receded to its present distance from its probable original close proximity to the earth's surface. The rate of change of the earth's speed of rotation due to lunar tidal friction varies inversely as the sixth power of the moon's distance, and must therefore have been much greater in the past. An estimate of the time needed to bring the moon to its present distance, based on the supposition that the phase lag of the oceanic tides has always been as at present, indicates an age of the order of 4,000 million years.

These two methods are much less accurate than those based on radioactivity. Their utility is that they both depend on theories that explain a large number of other facts, and that the agreement of their conclusions in order of magnitude with those drawn from radioactivity gives independent reason to believe that the latter are not vitiated by some fundamental error of principle.