OF GEOLOGICAL DYNAMICS. 123 



required to lift a body equal to f of the earth's 

 mass from the present surface to an infinite distance. 

 But observation proves the mean density of the 

 earth to be 5-6, which is about twice the average 

 surface density ; and if we use Laplace's probable 

 law of interior density, 1 we find more exhaustion 

 of energy in coalition, by about 10 per cent., than 

 if the density were uniform, the result for the 

 whole being, as nearly as may be, a mass equal to 

 f of the earth's, raised from the surface to an 

 infinite distance. This second estimate we may 

 adopt with great confidence, as probably very close 

 to the truth, considering how little it differs from 

 the first. Now, the work required to lift a mass 

 from the earth's surface to an infinite distance, 

 against the diminishing force of gravity, is the 

 same as that which would be required to lift an 

 equal mass through a space equal to the earth's 

 radius, against a force everywhere equal to the 

 actual force of gravity at the surface. Hence, as 

 the earth's radius is 6,370 kilometres, the whole 

 amount of potential energy exhausted in the 



1 Thomson and Tait, 824. 



