the Earth's Crust. 353 



it by putting its resultant weight in the direction 

 AE=A.^.Dcos«. 

 Hence the force acting outwards 



2'ir IP 

 = -o- -2DM(1 — cos^a)— A./«.Dcos«=F suppose. 



17. This is the force which tends to separate the portion of 

 the crust DCC'D' from the rest. It is resisted by the cohesion 

 of the surfaces in contact. This cohesion, for the measure of 

 which I shall take C as before, must be such that 



C IS not < r. -J ^- 



area of surfaces in contact' 



the part F cos^S if F is resisted by friction. 



Let u and v be the distances of D and C from EA. Then the 

 surface of the frustum of the cone generated by the revolution 



of CD about EA= ^ . „ -\ Also C = wei2;ht of ith mile 

 sm ;a o 



length of the materials of the crust (section unity) 

 ___«_, _ «D E _ 3DM 

 ~ 20,000 ^ ~ 207000 ■ «2 - 800« ' . 



Hence the above condition of equilibrium becomes 



„2_^.2 1 / ty 800A/ieos« 

 —^-~-, not < tttAI — cos"* «) I 1 ) — —^r^ . 



18. First. Sii])pose that CD coincides with Cc, or /3 = a. 

 Then A = 0; also u--v"-=(:2at-t'^)^m^ u; 



2t /2 \-co^^u(. ty 



.•. a mvist not be < -77 1 1 ) . 



a a^ 20 \ a/ 



The second side is greatest when a = 90°j in this case t—.-^-Qa 

 = 100 miles. This shows that if the crust be not as much as 100 

 miles thick, the pressure of the lava upwards towards the moon 

 will be cajjuble of cracking the crust all round, at a great circle 

 of which the plane is at right angles to the direction of the moon. 

 Since no such fracture takes place, as this great circle travels 

 over the earth following the moon^s motion, we must conclude 

 that the thickness is at least 100 miles. The same may be said 

 of the sun ; and therefore, as I have already stated, the thickness 

 cannot be less than 140 miles. 



19. Secondly. If CD does not concide with Cc, the thickness 

 need not be so great if it lie above it ; but if it lie below it, the 

 thickness must be greater, because then the term in A will change 

 sign. The limiting case is when /S = and u = v; the part of 

 the crust acted on by the pressure will become cylindrical instead 



Phil. May. S. 4. Vol. 18. No. 121. Nov. 1859. 2 A 



