Q = 4πR2KT,

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)πR3 = 4πR2KT,

or

3KT

X = ------ .

R

Substituting the values of these constants,

X = 7 × 10-15 gram-calories per second