x] RADIO-ACTIVE PROCESSES 345 
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 
O) dlp, JiCg Jl 
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 @ radiated from the earth is 
equal to the heat supplied by the radio-active matter on the 
earth, 
X Anh =4r eK T 
or ie ae fe 
Substituting the values of these constants, 
X =7 x 10-® gram-calorie per second 
= 2:2 x 107 gram-calorie per year. 
Since 1 gram of radium emits 864,000 gram-calories per year, 
the presence of 26x 10-" gram of radium per unit volume or 
46 x 10 gram 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? observed 
that a platinum plate was about 1/3000 as active as a crystal of 
uranium nitrate, or about 2 x 10—° as active as radium. This cor- 
responds 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 from the earth. Elster and Geitel? filled a dish of 
volume 3°3 x 10’ c.c. with clay dug up from the garden, and placed 
it in a vessel of 30 litres capacity in which was placed an electro- 
1 Strutt, Phil. Mag. June, 1903. 
2 Elster and Geitel, Phys. Zeit. 4, No. 19, p. 522, 1903. Chem. News, July 17, 
p- 30, 1903. 
