Quite recently the renowned physical chemist Rutherford has expounded a most original method of estimating the age of minerals. Uranium and thorium are supposed to produce helium by their slow dissociation, and we know how much helium is produced from a certain quantity of uranium or thorium in a year. Now Ramsay has determined the percentage of helium in the uranium mineral fergusonite and in thorianite. Rutherford then calculates the time which would have passed since the formation of these minerals. He demands at least four hundred million years, "for very probably some helium has escaped from the minerals during that time." Although this estimate is very uncertain, it is interesting to find that it leads to an age for the solid earth-crust of the same order of magnitude as the other methods.
During this whole epoch of almost inconceivable length of between one hundred million and two thousand million years, organisms have existed on the surface of the earth and in the sea which do not differ so very much from those now alive. The temperature of the surface may have been higher than it is at present; but the difference cannot be very great, and will amount to 20° Cent. (36° F.) at the highest. The actual mean temperature of the surface of the earth is 16° Cent. (61° F.). It varies from about -20° Cent. (-4° F.) at the North Pole, and -10° Cent. (+14° F.) at the South Pole to 26° Cent. (79° F.) in the tropical zone. The main difference between the temperatures of the earth’s surface in the most remote period from which fossils are extant and the actual state rather seems to be that the different zones of the earth are now characterized by unequal temperatures, while in the remote epochs the heat was almost uniformly distributed over the whole earth.
The condition for this prolonged, almost stationary state was that the gain of heat of the earth’s surface by radiation from the sun and the loss of heat by radiation into space nearly balanced each other. That the replenishing supply by radiation from an intensely hot body—in our case the sun—is indispensable for the existence of life will be evident to everybody. Not everybody may, however, have considered that the loss of heat into cold space or into colder surroundings is just as indispensable. To some people, indeed, the assumption that the earth as well as the sun should waste the largest portions of their vital heat as radiation into cold space appears so unsatisfactory that they prefer to believe radiation to be confined to radiation between celestial bodies; there is no radiation into space, in their opinion. All the solar heat would thus benefit the planets and the moons in the solar system, and only a vanishing portion of it would fall upon the fixed stars, because their visual angles are so small. If that were really correct, the temperature of the planets would rise at a rapid rate until it became almost equal to that of the sun, and all life would become impossible. We are therefore constrained to admit that "things are best as they are," although the great waste of solar heat certainly weakens the solar energy.
The opinion that all the solar heat radiated into infinite space is wasted, starts moreover from a hypothesis which is not proved, and which is highly improbable—namely, that only an extremely small portion of the sky is covered with celestial bodies. That might certainly be correct if we assumed, as has formerly been done, that the majority of the celestial bodies must be luminous. We do not possess, however, any reliable knowledge of the number and size of the dark celestial bodies. In order to account for the observed movements of different stars, it has been thought that there must be in the neighborhood of some of them dark stars of enormous size whose masses would surpass the mass of our sun, or, at least, be equal to it. But the largest number of the dark celestial bodies which hide the rays from the stars behind them probably consist of smaller particles, such as we observe in meteors and in comets, and to a large extent of so-called cosmical dust. The observations of later years, by the aid of most powerful instruments, have shown that so-called nebulæ and nebulous stars abound throughout the heavens. In their interior we should probably find accumulations of dark masses.
The light intensity of most of the nebulæ is, moreover, far too weak to permit of their being perceived. We have, therefore, to imagine that there are bodies all through infinite space, and about as numerous as they are in the immediate neighborhood of our solar system. Thus every ray from the sun, of whatever direction, would finally hit upon some celestial body, and nothing would be lost of the solar radiation, nor of the stellar radiation.
As regards the radiation-heat exchange, the earth might be likened to a steam-engine. In order that the steam-engine shall perform useful work, it is necessary not only that the engine be supplied with heat of high temperature from a furnace and a boiler, but also that the engine be able to give its heat up again to a heat reservoir of lower temperature—a condenser or cooler. It is only by transferring heat from a body of higher temperature to another body of lower temperature that the engine can do work. In a similar way no work can be done on the earth, and no life can exist, unless heat be conferred by the intermediation of the earth from a hot body, the sun, to the colder surroundings of universal space—i.e., to the cold celestial bodies in it.
To a certain extent the temperature of the earth’s surface, as we shall presently see, is conditional by the properties of the atmosphere surrounding it, and particularly by the permeability of the latter for the rays of heat.
If the earth did not possess an atmosphere, or if this atmosphere were perfectly diathermal—i.e., pervious to heat radiations—we should be able to calculate the mean temperature of the earth’s surface, given the intensity of the solar radiation, from Stefan’s law of the dependence of heat radiation on its temperature. Starting from the not improbable assumption that, at a mean distance of the earth from the sun, the solar rays would send 2.5 gramme-calories per minute to a body of cross section of 1 sq. centimetre at right angles to the rays of the sun, Christiansen has calculated the mean temperatures of the surfaces of the various planets. The following table gives his figures, and also the mean distances of the planets from the sun, in units of the mean distance of the earth from the sun, 149.5 million km. (nearly 93 million miles):
| Planet | Radius | Mass | Mean distance | Mean temperature | Density according to See |
|---|---|---|---|---|---|
| According to See | |||||
| Mercury | 0.341 | 0.0224 | 0.39 | + 178°(332°) | 0.564 |
| Venus | 0.955 | 0.815 | 0.72 | +65° | 0.936 |
| Earth | 1 | 1 | 1 | +6.5° | 1 |
| Moon | 0.273 | 0.01228 | 1 | +6.5°(105°) | 0.604 |
| Mars | 0.53 | 0.1077 | 1.52 | -37° | 0.729 |
| Jupiter | 11.13 | 317.7 | 5.2 | -147° | 0.230 |
| Saturn | 9.35 | 95.1 | 9.55 | -180° | 0.116 |
| Uranus | 3.35 | 14.6 | 19.22 | -207° | 0.388 |
| Neptune | 3.43 | 17.2 | 30.12 | -221° | 0.429 |
| Sun | 109.1 | 332,750 | 0 | +6200° | 0.256 |
In the case of Mercury, I have added another figure, 332°. Mercury always turns the same side to the sun, and the hottest point of this side would reach a temperature of 397°; its mean temperature, according to my calculation, is 332°, while the other side, turned away from the sun, cannot be at a temperature much above absolute zero, -273°. I have made a similar calculation for the moon, which turns so slowly about its axis (once in twenty-seven days) that the temperature on the side illuminated by the sun remains almost as high (106°) as if the moon were always turning the same face to the sun. The hottest point of this surface would attain a temperature of 150°, while the poles of the moon and that part of the other side which remains longest without illumination can, again, not be much above absolute zero temperature. This estimate is in fair agreement with the measurements made of the lunar radiation and the temperature estimate based upon it. The first measurement of this kind was made by the Earl of Rosse. He ascertained that the moon disk as illuminated by the sun—that is to say, the full moon—would radiate as much heat as a black body of the temperature 110° Cent. (230° F.). A later measurement by the American Very seems to indicate that the hottest point of the moon is at about 180°, which would be 30° higher than my estimate. In the cases of the moon and of Mercury, which do not possess any atmosphere to speak of, this calculation may very fairly agree with the actual state of affairs.