792 Dr. Chree on the Stresses in the Earttis Crust 



Thus tt and <jxf> would both vanish all over the surface if 



4 a — c _ o) 2 a 



la g 



In the actual earth 



co 2 a/g = 1/290 approximately. 



BessePs value for (a—c) /a is 1/299, while Clarke's is 

 1/293*5. Taking the former value, and employing as before 

 X to denote the latitude, we find in the surface 



tt =—0'90 . . . tons weight per square inch * 



<^ = -0-90(1-3 cos 2 X) 



fe = •"* • n n ii 



►(21) 



The following particular values of j><j> (all in tons weight 

 per square inch) should be noted : — 



Equator. Lat. 35° 16'. Lat. 54° 44'. Poles. 



+ 1-8 +0'9 0-0 -0*9 



The stress in the meridian plane is always a pressure when 

 the material is incompressible ; but that perpendicular to the 

 meridian is a tension in latitudes below 54|°. The numerical 

 values of these surface stresses would be reduced by assigning 

 to the earth's compression a—c/a any value, such as Clarke's, 

 which is larger than Bessel's. 



§ 7. Right vertical prism of density p acted on by gravity, 

 the prismatic surface being exposed to normal pressure 

 p — Gz, where p and C are constants, and the upper plane 

 surface z = h being free from force. 



To give definiteness to the problem we shall suppose the 

 vertical displacement nil at the C.Gr. of the base. The shape 

 of the cross section does not matter. 



The solution is obtainable from one on p. 545 of the Phil. 

 Mag. for November 1901, by suitably altering the notation. 



Taking rectangular axes of a?, y, z, the axis of z being 

 drawn vertically upwards, and the origin being at the C.Gr. 

 of the base of the prism, the displacements a, /3 ; 7 are 

 given by 



a/«=/8/y=(l/JQ{w(A-*)-(l-*)(p-0*)}i -l r22 , 



y =-( Z /E)y P (h-iz)- V (2p-Cz)} + (l/2EXz*+f){gpv-(l-v)C}-J K " 



The principal stresses and the stress-difference are given by 



xx = yy = -(p-Qz) = -p K , j 



Tz =-gp{h-z)=-p Y , >. • • (23) 



