204 T. Mellard Reade — A Cooling and Shrinking Globe, 



The Earth considered as a Homogeneous Cooling Solid. 



Adopting Lord Kelvin's view as stated in Thomson and Tait's 

 Natural Philosophy (1867, pp. 711-727), that since the beginning 

 of Geological Time the Earth has been a highly heated solid body 

 cooling into space by being kept at a constant lower temperature 

 at the surface, we will try and trace out the physical consequences 

 that must follow.^ We will, for the purposes of investigation, first 

 assume that the globe is homogeneous throughout and that the 

 cooling and outward flow of heat is equable on all radii, or otherwise 

 symmetrical. Lord Kelvin assumes that at the time of first solidifi- 

 cation the augmentation of tempei'ature downwards, or the temperature 

 gradient, was 1° Fahr. in 10 feet, which has gradually decreased to 

 1° in 50 feet, this being taken as the average at the present time. 



The time that has elapsed between these two conditions hardly 

 forms an element in our present considerations ; but Lord Kelvin, in 

 the paper referred to, worked it out to 96,000,000 years. On p. 719 

 is a diagram, one curve on which shows the excess of temperature 

 above that of the surface; the other shows the rate of augmentation 

 of temperature downwards that has taken place in 100 million years of 

 cooling. Lord Kelvin says : " Thus the rate of increase of tempera- 

 tiare from the surface downwards would be sensibly irr of a degree 

 per foot for the first 100,000 or so ; below that depth the rate of 

 increase per foot would begin to diminish sensibly. At 400,000 feet 

 it would have diminished to about xir of a degree per foot ; at 

 800,000 feet it would have diminished to less than sV of its initial 

 value, that is to say to less than -o-sVo^ of a degree per foot ; and so 

 on, rapidly diminishing as shown in the curve. Such is on the 

 w^hole the most probable representation of the earth's present 

 temperature at depths of from 100 feet, where the annual variations 

 cease to be sensible, to 100 miles, below which the whole mass, or 

 all except a nucleus cool from the beginning, is (whether liquid or 

 solid) probably at or very nearly at the proper melting temperature 

 for the pressure at such depth." 



Level-of -No- Strain. 



If these conclusions be just it is very obvious that not much more 

 than a superficial shell of the earth has been affected by cooling. 

 A hundred miles is but ^V part of the earth's radius. Let us see 

 how this affects the distribution of stresses and strains in a solid 

 homogeneous globe. 



It vs^ill need a little consideration to see that there are two 

 elements involved — radial contraction and circumferential con- 

 traction. Both radial and circumfei'ential contraction are, as we 

 see, practically confined to a shell 150 miles thick (800,000 feet). 

 Commencing very gradually from zero at the surface the contraction 

 increases in intensity until it attains a maximum at about 50 miles, 

 it then finally graduates into a practical zero at 150 miles deep. 



1 See also Sir W. Thomson, Erit. Assoc. Eeport, 1876, and Dr. C. H. Darwin, 

 Phil. Trans. 1879, part i. It is considered that the earth is as rigid as steel, or at 

 least fflass, from the surface to the centre. 



