RADIOACTIVITY AND THE EARTH's AGE 131 



On reviewing the papers dealing with the earth as a cooling body, how- 

 ever, I must confess to finding them unsatisfactory. The assumption ol 

 uniform initial temperature made by Kelvin seems to me untenable, 

 because it leads either to earths which are tidally unstable for vast periods 

 of time or to earths so cool that there was no fusion at all and no rear- 

 rangement of terrestrial matter by density. I have therefore investigated 

 a somcM'hat more general problem,"" the cooling of an earth in which the 

 initial temperature increases directly as distance from the surface. The 

 original surface temperature is supposed to be about that of the hottest 

 recent lavas, say 1,300°, while on the basis of Mr Barus's experiments on 

 diabase, the initial temperature at 40 miles from the surface is estimated 

 at 1,600°. A discussion of the level of isostatic compensation, determined 

 by Messrs Tittmann and Hayford/^ leads to the belief that at a distance 

 of 71 miles, or 114 kilometers, from the surface the rock temperature 

 most closely approaches its melting point. Finally, the diffusivity is 

 taken as that of the Calton Hill trap investigated by Forbes and Kelvin. 

 These data lead to an earth which has been solid throughout from the 

 moment when the surface first conjealed; it is about 60 million years 

 old, and the present surface gradient should be 1° Fahrenheit in 77 feet 

 (1° centigrade in 42.3 meters). This gradient seems very low; but many 

 still lower gradients are known, and whether it is too low to be acceptable 

 is a matter for consideration.-"'- It will be observed that in this method of 

 dealing with the problem the age is not dependent, as it is in Kelvin's 

 solution, on the present surface gradient of temperature. The gradient 

 here is a deduction. Since, also, the age found is in fairly good accord 

 M'ith the ages reached by other methods, my result for gradient is avail- 

 able for an approximate estimate of the relative importance of radio- 

 activity. 



The outer part of the earth is essentially a shell of massive rock several 

 hundred miles in thickness. Eoche ^^ would make this thickness a sixth 



"" Science, vol. 27, 1908, p. 227. In this paper, by an error in copying from the 

 rough draft, the level of isostatic compensation is stated as 71 miles, or 140 kilo- 

 meters. The last figure should be 114. The proper value was used in the formulas 

 and computations. 



'''■ Report to general conference of the International Geodetic Association, Washington, 

 1906. 



''- In my solution the curvature of the earth's surface is neglected. As is well known, 

 Mr R. S. Woodward has discussed both the free and the conditioned cooling of a sphere 

 InitialLv at a uniform temperature ("Annals of mathematics," vol. 3, 1887, pp. 75 and 

 129). Excepting for ages of thousands of millions of years, his formulas applied to 

 the earth give the same results whether the cooling is free or conditioned. I have 

 compared his formula and Kelvin's for a 60 X 10" year earth initially at 1307° having 

 the difEusivity of the Calton Hill trap. The maximum difference is at a depth of 41 

 kilometers and amounts to less than 4°. The neglect of the curvature is thus of no 

 consequence. 



°' M6moire Academie de Montpellier, 1882. 



