Results of the Contraction of a Solid Globe. 17 



dh ' b 



dh _ b / 6 a*\ 



a.» a \ 2 ?' / 



a \ 2 2 ?- / 



, « 2 3 - 2 

 \ — A 



To obtain the mean height of the total elevations which can 



be formed out of all the portion of the crust which has been 



subjected to compression up to the present time, the integral 



3 o? 

 must be taken from to K — • 

 2 r 



Therefore, finally, 



^imr-mr) 



b9o? 

 6 a 4 r 2 ' 



In order to fix upon a value for e, the coefficient of con- 

 traction for 1° F., I have reduced the results of some 

 experiments by Mallet upon large masses of slag run from 

 the furnace. They give e = 00000071*. The mean of six 

 results obtained for the contraction of rocks at much lower 

 temperatures by Mr. Adie was -000005 7 f, and Mr. Mellard 

 Eeade's experiments lead to a like result^. We may there- 

 fore accept 0*000007 with tolerable confidence as being at 



any rate large enough. - is the temperature-gradient at 



present, which may be taken at ^ F. per foot. The 

 value of a, corresponding to 7000° F. as the temperature 

 of solidification, is 402832 feet, and r the radius is 20900800 

 feet. With these numbers our result gives, for the mean 

 height of all the elevations which would be formed upon a 

 solid earth by cooling, 



19 feet. 



The smallness of this result renders it impossible to attribute 

 the inequalities of the earth's surface to this cause, even if we 

 confine our attention to the height of the land above the sea, 

 for that alone has been reckoned at 900 feet§. It is also to be 

 observed that, if the level of no strain does not conform to 

 the varying level of the surface, which it probably does, it 

 would not pass beneath the floor of the deeper oceans. 



Another very important fact is that the temperature of the 



* ' Physics of the Earth's Crust,' by the Author, p. 68. 

 f Trans. Roy. Soc. Edinb. vol. xiii. p. 370. 

 X ' Origin of Mountain-Ranges,' p. 112. 

 § Nature, vol. v. p. 479. : 



Phil Mag. S. 5. Vol. 25. No. 152. Jan. 1888c C 



