the Solid Crust of the Earth. 283 



Moment about axis of z of forces parallel to x acting on the 

 sun-side of the plane yz 



= -2fip§$$dz dy dx . xy= -fip$$dz rfY3*(Y-2EFe*) 



8 

 =:—$ At/oDEa 5 e after all reductions. 



There will be an equal moment, and in the same direction, on 

 the opposite side. Hence 



ifi 

 Moment about axis of z of forces parallel to #= j^ 7T/x./3DEa 5 e. 



Similarly we obtain by integration, 



ifi 

 Moment about axis of y of forces parallel to#= — ^7r/*pDFtf 5 e, 



X 



a 



}} 



y=-^7rwE¥a 5 €, 



z 



a 



f} 



y=+^n-HpD 1 E i a b €, 



X 



a 



ii 



z= + ^7rfip'E¥a% 



y 



3) 



a 



Q 



z=—^7r^pDYa 5 e 



Compounding these, 



Moment of all the forces about axis of x= 0, 



g 

 „ „ „ y=—g7rtipT)~Fa 5 €, 



„ „ „ z= + j7TfjLpD]&a 5 e. 



6. If the earth's mass be regarded as heterogeneous, as it is, 

 and arranged in layers of small ellipticity increasing from the 

 centre towards the surface, it is easy to see that these expressions 

 are true of each of these layers — which equals the difference be- 

 tween two homogeneous spheroids, if pd(a 5 e) be put for pa b e. 

 Hence for the whole earth, 



Force which tends to separate the parts divided by the plane yz 

 1 C d.a 4 , 



Moment of the forces about #= 0, 



„ „ z=+jTrfiDh\p~^- -da. 



Substituting for D, E, F, these two moments are, by mecha- 



