relation to the Constitution of the Earth's Crust. 11 



potential of the Earth at the same point. Then, supposing 

 the space occupied by R to be vacant, the potential of the 



TT /tT? 

 Earth will become ™ . Hence, when we take into account 



r D 



all the masses which contribute to form the potential, recol- 

 lecting that their sum at every point at the surface of the 

 ocean must be constant, w r e have, upon restoring R, 



pM aU /E <tR\ 

 constant = ^- + -^ + {- - ^J, 



_ P M (<r- //QR E 

 ~ D D' + r" 



At a distance from the masses where their attraction is inap- 

 preciable, r becomes c the mean radius. 



Let r=c + $c, whence $c will be the rise of the sea-level. 

 Then we have 



E 

 the constant = — ; 

 c 



E_ E _E E/ Sc\ pM (o— jx)B 



•"' c c + Sc" c A c/~ D D' ' 



or 



But 3 =# 



5* - /oM _ (cr-^)B 



If the included mass had been more dense than the enveloping 

 stratum, we should have had 



1J>M »-(r)B | 

 6c -^l¥ + D' J - 



We see, then, that the included mass R, if less dense, will 

 have the effect of depressing the sea-level, and if more dense, 

 of raising it. It may turn out, therefore, that our hypothesis 

 of hydrostatic equilibrium will be found to accord with a very 

 slight change in the sea-level. 



There will be a slight change in the value of gravity at the 

 depth occupied by the root : let its mean value be supposed 

 to occur at the middle part, and be </. Then, remembering 

 that the attraction of the spherical shell exterior to the point 



