Page:Lectures on Ten British Physicists of the Nineteenth Century.djvu/70

No doubt there still are people who think that the Earth is an infinite slab; but if the investigation has any application, it is to a solid globe, originally at one uniform temperature, exposed to a cooling agent at the surface. But the case of the Earth is reduced to the simple case of the slab by the following considerations. It had been ascertained by the observations of Forbes on underground temperature that change of temperature due to day and night, or summer and winter, disappears at about 24 feet below the surface; and observations in coalpits and borings show that the temperature thereafter increases at the rate of about one degree Fahrenheit per 50 feet of descent; but Fourier's results show that this rate will practically vanish at a small depth compared with the distance to the Earth's centre. Hence a spherical plate of the Earth if such thickness may be treated as a plate of the kind specified. The best value of $k$ then known was 400; hence for the case of the Earth,

${\frac {\;dv}{\;dx}}={\frac {V}{35.4{\sqrt {t}}}}e^{-x^{2}/1600kt}$

When $t$ is very large and $x$ small, the exponential factor is negligible; and we know that then is; hence and

${\frac {1}{50}}=V{\frac {1}{35.4{\sqrt {t}}}}$,

Suppose V, the original temperature of the Earth, when it had just solidified, to be 7000° F., the temperature of melting rock, then $t$ = 98,000,000 years.

Prof. Thomson concluded that the age of the Earth as a possible abode for life must lie between 400,000,000 years and 20,000,000 years. These results came like a bolt from the blue sky on the geologists and biologists of the day. The former supposed that