8 Rev. 0. Fisher on the Surface Elevations and other 



cooled as a solid, and that there has always been within the 

 crust a level of no strain, below which the elementary 

 spherical shells have tended to be extended, and above it to 

 be compressed ; and we make the probable (though not 

 certain) hypothesis that, below the level of no strain, during 

 the process of contraction, the interior sphere remains without 

 vacancies — that is, the substance settles together by what 

 Mr. Reade calls " compressive extension " and Mr. Davison 

 " stretching.''' This precludes our applying separately the 

 coefficient of contraction to the vertical and horizontal dimen- 

 sions throughout that portion ; but we may so apply it to the 

 voluminal only, which is generally applicable. 



Retaining the symbols used by Sir William Thomson, in 

 his paper on secular cooling*, let 



r=the radius of the earth at present, taken at 20,900,800 



feet, 

 i=the time elapsed since the globe solidified, 

 V = the temperature of solidification, 

 #=the distance of a spherical shell of elementary thickness 



dx from the surface at the time t, 

 z=the distance of the same shell from the centre, 

 2' = the distance of the same at the time t + dt, 

 v = the temperature of the said shell at the time r, 

 = the fall of temperature of the shell between the time 

 when it first began to be compressed and the time t, 

 <£ = the fall of temperature of the level of no strain, 

 E = the coefficient of voluminal contraction, 

 6 = the coefficient of linear contraction, 

 h = the mean height of the surface-elevations. 

 Two other quantities are involved, which are defined in Sir 

 W. Thomson's paper, wherein he shows that, at the depth .c 

 at the time t, 7 x -— 



a 



where b is a temperature such that 



and a is a length such that 

 a=2 \/kF 

 = 402832 feet at the present time, 

 k being the conductivity of the substance expressed in terms 

 of its own capacity for heat. 



* Trans. Roy. Soc. Edinb. vol. xxiii.part 1, p. 157; also Phil Ala" 

 [4] vol. xxv. ; and Thomson and Tait's ' Natural Philosophy,' p. 711. 



