216 SEE— TEMPERATURE, SECULAR COOLING [April 20, 



By platting this equation Lord Kelvin found the curve for the rate 

 of variation of temperature in the earth, 100 million years after the 

 initial epoch, on the hypothesis that the surface temperature was 

 suddenly lowered V degrees, and kept at this figure, so as to produce 

 a steady flow of heat from within outward. 



He took V = yooo° Fahr. 

 § 9. The Age of the Earth's Consolidation Calculated by the Fourier- 



Kelvin Method. 



Considering the earth to be a sphere of the same conductivity as 

 average rock, we have for the rate of augmentation of temperature 

 downward 



d% V _^ I V _^ 



= — ^ e 4«« = — e i«i>o<, (18) 



K being 400, when the units are the foot, year, and degree Fahrenheit. 

 Solving this equation for t, and putting F=7000° Fahr., we have 



\35-4y 



101,673,000 years. (20) 



This is Lord Kelvin's method of estimating the age of the earth, or 

 the duration since the beginning of the consolidation of the crust, 

 which is supposed to have occurred very soon after the initial epoch. 

 We have already seen that the assumption of an original uniform 

 temperature for the earth is only a first approximation to the true 

 condition, not justified by a closer examination of the subject. The 

 mathematical theory of the heat distribution in a gaseous globe shows 

 that the temperature increases rapidly towards the center, and hence 

 falls off correspondingly near the surface. Relatively to the average 

 temperature of the whole mass, that of the surface is very low, and 

 that of the center quite high. This is the condition in a gaseous 

 sphere, and it seems certain that it cannot be greatly modified by the 

 surface cooling which leads to encrustation. We have seen that this 

 latter arises mainly from resisted circulation, and retarded supply of 

 heat from the under layers, as the surface density increases. Prior 

 to the beginning of surface cooling the planet passes through a stage 

 of maximum temperature, and heat is both radiated and conducted 

 through to the outer layers ; but eventually the resistance to propaga- 

 tion of heat becomes so great that a fall of temperature is inevitable. 



