its secular cooling from a molten mass, is given by Lord Kelvin in Appendix D of Thomson and Tait’s Natural Philosophy. He has there shown that about 100 million years after the earth was a molten mass, the gradual cooling due to radiation from its surface would account for the average temperature gradient of ¹⁄₅₀° F. per foot, observed to-day near the earth’s surface.
Some considerations will now be discussed which point to the probability that the present temperature gradient observed in the earth cannot be used as a guide to estimate the length of time that has elapsed since the earth has been at a temperature capable of supporting animal and vegetable life; for it will be shown that probably there is sufficient radio-active matter on the earth to supply as much heat to the earth as is lost by radiation from its surface. Taking the average conductivity K of the materials of the earth as ·004 (C.G.S. units) and the temperature gradient T near the surface as ·00037° C. per cm., the heat Q in gram-calories conducted to the surface of the earth per second is given by
where R is the radius of the earth.
Let X be the average amount of heat liberated per second per cubic centimetre of the earth’s volume owing to the presence of radio-active matter. If the heat Q radiated from the earth is equal to the heat supplied by the radio-active matter in the earth,
Substituting the values of these constants,
Since 1 gram of radium emits 876,000 gram-calories per year, the presence of 2·6 × 10-13 grams of radium per unit volume, or 4·6 × 10-14 grams per unit mass, would compensate for the heat lost from the earth by conduction.
Now it will be shown in the following chapter that radio-active matter seems to be distributed fairly uniformly through the earth and atmosphere. In addition, it has been found that all substances are radio-active to a feeble degree, although it is not yet settled whether this radio-activity may not be due mainly to the presence of a radio-element as an impurity. For example, Strutt50 observed that a platinum plate was about ¹⁄₃₀₀₀ as active as a crystal of uranium nitrate, or about 2 × 10-10 as active as radium. This corresponds to a far greater activity than is necessary to compensate for the loss of heat of the earth. A more accurate deduction, however, can be made from data of the radio-activity exhibited by matter dug out of the earth. Elster and Geitel51 filled a dish of volume 3·3 × 103 c.c. with clay dug up from the garden, and placed it in a vessel of 30 litres capacity in which was placed an electroscope to determine the conductivity of the enclosed gas. After standing for several days, they found that the conductivity of the air reached a constant maximum value, corresponding to three times the normal. It will be shown later (section 284) that the normal conductivity observed in sealed vessels corresponds to the production of about 30 ions per c.c. per second. The number of ions produced per second in the vessel by the radio-active earth was thus about 2 × 106. This would give a saturation current through the gas of 2·2 × 10-14 electromagnetic units. Now the emanation from 1 gram of radium stored in a metal cylinder gives a saturation current of about 3·2 × 10-5 electromagnetic units. Elster and Geitel considered that most of the conductivity observed in the gas was due to a radio-active emanation, which gradually diffused from the clay into the air in the vessel. The increased conductivity in the gas observed