On the Cooling of a Radioactive Sphere

Abstract

By means of the Laplace transformation, any physical problem characterized by a partial differential equation, the solution of which must satisfy prescribed initial and boundary conditions, can formally be transformed into a boundary problem for an ordinary differential equation. From the solution of the latter problem, that of the original problem may be obtained by the inversion of the Laplace transformation. The method is applied to the problem of the cooling of a radioactive sphere and the solution of this problem is applied to a discussion of the thermal history of the earth.