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
Q = 4πR^2KT,
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,
X . (4/3)πR^3 = 4πR^2KT,
or X = 3KT/R.
Substituting the values of these constants,
X = 7 × 10^{-15} gram-calories per second
= 2·2 × 10^{-7} gram-calories per year.
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, Strutt[1] 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 Geitel[2] filled a dish of