relation to the Constitution of the Earth's Crust. 13 



every elementary pyramid, having its vertex at the Earth's 

 centre. 



The root being contained within the same verticals, taking 

 w as the chord of the semiarc at the middle of it, we have 



-('+!) 



and, the crust being independently in equilibrium, we must 

 have for the support of the mountain by the root, 



i k+ 1) 



__ = 1 9 approximately, 



u? 



u 



And since g' = g(l—a), 



'* + ' 



pA=(<r-,*)(l-«)( : l-2-^)<, 



k + l 



where a has the value already found ; substituting which 



/ t , t 

 ph=(<r-,.){l- X -^ (Jp + fcrJ + i—J-a—J *)t, 



= (G-—fi)(l — r)t; suppose. 



This is a quadratic to determine t. 



As a first approximation, ph= (<r—fi)t (of course). 



To find the rise of the sea-level under the supposed con- 

 ditions. Pratt says that, " for problems of this kind, the 

 Himalayas may be considered as a vast tableland about three 

 miles high."* The spherical cap already described as form- 

 ing the basis of the calculations in that case will become a 

 cylinder. 



First, then, suppose a cylinder of radius n, and small height, 

 standing upon the surface of the mean sphere. 



* Page 213. 



