148 Contraction during Cooling of a Solid Earth. 



surface, which, taken at 1° Fahr. per 51 feet, gives 



L = 2Y 



51 a i^^t' 



If we follow Thomson in assuming 7000° Fahr. for the tem- 

 perature of solidification (a very high value) this gives 



a =420832 feet, 



and at twice this depth, 6=Y x 0*00468; below which the 

 cooling will be small. Let us then separate the integral into 

 two portions at the point A, at the depth 2a ; and 





-1MK 



dz 



the second integral being the contribution to the surface- 

 corrugations from matter below A. 



Setting this aside, since z = r—%, .*. dz=—dx ; and, sup- 

 posing 6 now expressed in terms of x as above, reversing the 

 order of the limits, 



dh 



dx 



wherefore 



P2a 



A= 1 ( 1— '-]( l 6dx\dx-\- const. 



The integral begins at A, where x=2a and h=0 ; 



gives the mean height of the corrugations formed out of the 

 compression of the matter down to the depth 2a, which, with 

 the assumed constants, will be about 160 miles. 



If we substitute for 6 the value given above, expand the 

 exponential and integrate between the limits (see i Physics ' 

 &c. p. 63 et seq.), putting E = 0'0000215*, r=20902500 

 feet, the above gives 



7i = 933 feet. 



The effect of the contraction below A need not be considered, 

 being at most not two feet. 



The value obtained for k implies that, if all the elevations 

 which would have been produced by compression, through 

 the contraction of the earth cooling as a solid, were levelled 



* This is the coefficient of contraction obtained from Mallet's experi- 

 ments on slag. See ' Physics ' &c. p. 68. 



