J?. S. Woodward — Mathematical Theories of the Earth. 349 



medium which instantly dissipates all heat brought by conduc- 

 tion to its surface, thus keeping the surface at a constant tem- 

 perature. Suppose we have given the initial excess of the 

 sphere's temperature over that of the medium. Suppose also 

 that the capacity of the mass of the sphere for the diffusion of 

 heat is known and known to remain invariable during the pro- 

 cess of cooling. This capacity is called diifusivity and is a 

 constant which can be observed. Then from these data the 

 distribution of temperature at an} 7 future time can be assigned, 

 and hence also the rate of temperature increase, or the temper- 

 ature gradient, from the surface toward the center of the 

 sphere can be computed. It is tolerably certain that the heat 

 conducted from the interior to the surface of the earth does 

 not set up any reaction which in any sensible degree retards 

 the process of cooling. It escapes so freely that, for practical 

 purposes, we may say it is instantly dissipated. Hence, if we 

 can assume that the earth had a specified uniform temperature 

 at the initial epoch, and can assume its diffusivity to lemain 

 constant, the whole history of cooling is known as soon as we de- 

 termine the diffusivity and the temperature gradient at any point. 

 Now Sir William Thomson determined a value for the diffu- 

 sivity from measurements of the seasonal variations of under- 

 ground temperatures, and numerous observations of the in- 

 crease of temperature with depth below the earth's surface 

 gave an average value for the temperature gradient. From 

 these elements and from an assumed initial temperature of 

 7000° Fahr., he infers that geologic time is limited to some- 

 thing between 20,000,000 and 400,000,000 years. He says : 

 " We must allow very wide limits in such an estimate as I 

 have attempted to make, but I think we may with much prob- 

 ability say that the consolidation cannot have taken place less 

 than 20,000,000 years ago, or we should have more under- 

 ground heat than we actually have, nor more than 400,000,000 

 years ago, or we should not have so much as the least observed 

 underground increment of temperature. That is to say, I con- 

 clude that Leibnitz's epoch of emergence of the consistentior 

 status was probably between those dates." These conclusions 

 were announced twenty-seven years ago and were republished 

 without modification in 1883. Recently, also, Professor Tait, 

 reasoning from the same basis, has insisted with equal confi- 

 dence on cutting down the upper limit of geologic time to 

 some such figures as 10,000,000 or 15,000,000 years* As 

 mathematicians and astronomers we must all confess to a deep 

 interest in these conclusions and the hypothesis from which 

 they flow. They are very important if true. But what are 

 the probabilities? Having been at some pains to look into 



* Recent Advances in Physical Science, London, 1876. 



