Considering a globe of uniform material, and of great radius, which was initially at one temperature, and at a certain instant had its surface suddenly brought to, let us say, the temperature of melting ice, at which the surface was kept ever after, we can find, by Fourier's mathematical theory of the flow of heat, the gradient of temperature at any subsequent time for a point on the surface, or at any specified distance within it. For a point on the surface this gradient is simply proportional to the initial uniform temperature, and inversely proportional to the square root of the product of the "diffusivity" of the material (the ratio of the conductivity to the specific heat) by the interval of time which has elapsed since the cooling was started. Taking a foot as the unit of length, and a year as the unit of time, we find the diffusivity of the surface strata to be 400. If we take the initial temperature as 7000 degrees F.--which is high enough for melting rock--and take the interval of time which has elapsed as 100,000,000 years, we obtain at the surface a gradient approximately equal to that which now exists. A greater interval of time would give a lower gradient, a smaller interval would give a higher gradient than that which exists at present. A lower initial temperature would require a smaller interval of time, a higher initial temperature a longer interval for the present gradient. With the initial temperature of 7,000 degrees F., an interval of 4,000,000 years would give a surface gradient of 1° F. in 10 ft. Thus, on the assumption made, the surface gradient of temperature has diminished from 1⧸10 to 1⧸50 in about 96,000,000 years. After 10,000 years from the beginning of the cooling the gradient of temperature would be 2° F. per foot. But, as Thomson showed, such a large gradient would not lead to any sensible augmentation of the surface temperature, for "the radiation from earth and atmosphere into space would almost certainly be so rapid" as to prevent this. Hence he inferred that conducted heat, even at that early period, could not sensibly affect the general climate.