the Solid Crust of the Earth. 287 



* f a d.ahj C^d.cPj d.a 5 e,. d.a* 



' m ' fB }J t ~sr da ' r }j t isr da=p -da- ^p-da-t 



_e( ade\€J~ zqH* 3g-gV \ 

 ~ 5 V + e da)" 5 l3*-? 2 a 2 + z I 



after reduction : e is here the ellipticity of the crust. Now by 

 the Figure of the Earth, 



f**'-*-z=l*> <? 2 a 2 =6'054, €= 2 -L; 



.-. /, for the crust, =0*00375. 



This is larger than it is for the whole earth : see above. 



11. Now I must consider the action of the sun and moon on 

 the fluid, and so on the crust by pressure. I shall suppose that 

 at the instant under consideration the fluid is, as M. Delaunay 

 supposes it to be, arranged and moving just as if it were part of 

 the solid mass of the earth, but capable of communicating pres- 

 sure. The forces acting on the fluid are the centrifugal force 

 arising from the earth's rotation, the attraction of the sun and 

 moon, and the attraction of the crust and fluid. These last and 

 the centrifugal force cannot disturb the position of the axis, 

 owing to the symmetry of the crust. Nor can any constant 

 pressure, the same on every part of the inner surface of the crust. 

 Hence I shall reject all constant terms in the expression for p 

 at the surface. The equation of equilibrium, then, taking only 

 the sun at present, is 



dp = p (2fMxdx — fjuydy — jxxdx) 



= ip fJ ,d(2x' 2 -y*-z 2 ) =ifipd$x*-r*). 



In calculating the effect of the pressure on the crust, I shall 

 neglect in p all terms depending on e, because otherwise I should 

 be introducing terms depending on the square. This is clear ; 

 for the smallness of the moment of the pressure arises from the 

 near symmetry of the figure, and therefore the near balance of 

 pressure on opposite sides of the centre. Now considering p to 

 be a function of r, we have, as x -r r is independent of r, 



p-=. ^( 1 j I pd . r 2 = -~-^ a? at the surface, 



putting G for the definite integral, and rejecting the constant 

 term. The cosine of the angle which the normal at any point 

 of the inner surface of the crust makes with the axis of x is 



x(Dx+Vy + 'Fz) 2 



