134 - Mr. G. Davison on the Straining of the 



supposition that the coefficient of dilatation increases with the 

 temperature, being e + e'v, where v is the temperature. In 

 assuming this law to hold true up to a temperature as high as 

 7000° F., it is evident that the numerical results here obtained 

 cannot be regarded as reliable. They are given for their 

 qualitative rather than for their quantitative value. 



Let r be the internal radius of a thin spherical shell con- 

 centric with the earth *, its thickness Br, density p, and 

 coefficient of linear dilatation e. In any given time, let the 

 temperature of this shell be increased by ; then, if the 

 shell were isolated, r would be increased by red. But, in 

 consequence of the expansion of the mass inside it, let the 

 internal radius be further increased by rk, so that r becomes 

 r(l + «), where <x=k + e0. Also, p becomes p(l—3e0) and 

 Br becomes 



Since the mass of the shell remains unchanged, we have there- 

 fore 



d 



2a+ ~(r*)-3e0=0 



which may be written 



dr 



~(r**) = de0r 2 , 



The amount (kr) by which the radius is increased by stretch- 

 ing in the given time is therefore 



"tf r 



'&&& (!) 



Let c be the radius of the earth and x the depth of the 

 surface of radius r, v the excess of temperature at this depth 

 above that at the surface of the earth, and 6 the increase of 

 temperature in unit time, so that 0=dv/dt ; also let e be the 



* The method of proof adopted is similar to that given by Prof. G H. 

 Darwin in his paper in the Phil. Trans, 1887 A, pp. 242-249. 



