the Earth's Crust. 347 



nent is the upper surface, presses down on the lava beneath it, 

 which communicates the pressui'e to the under surface r n of the 

 mass under consideration. This is counterbalanced by the 

 downward pressure of the portion A.mnr k. lying below A m, the 

 level of the continent. Thus the weight of the mass AmnrA 

 is exactly supported by the lava below r n. 



5. And this will be true whatever be the form of the line rn 

 joining r and n. Thus suppose the upper line I have drawn is 

 the true boundary between the crust and the lava. The differ- 

 ence between the two cases is, that the matter, I, between the two 

 lines is in one case solid, in the other fluid. But as the solid is 

 formed out of the fluid, their densities are very much alike, and 

 the difference, one way or the other, will have but slight influ- 

 ence upon the equilibrium. The thickness of the crust at the 

 assumed joints A r and an is of importance ; because the greater 

 it is, the greater the sustaining force arising from cohesion^ as 

 we shall see. 



6. The forces, then, which we have to consider are the down- 

 ward pressure of the redundant mass AmabA, and the adhesive 

 force of the materials at the joints a n and A r. 



Let C be the average cohesive force of the materials, or the 

 length of rock of a unit section the weight of which equals the 

 cohesive force on a unit of surface of the joints. Mr. Airy has 

 stated (Phil. Trans. 1855, p. 102) that the crust could not exert 

 such a cohesive force as to make C so much even as one-fifth of 

 a mile. I shall take this as the limiting value of C. 



Let a be the area of the section Amab A; then, the unit of 

 mass being chosen equal to the mass of which the transverse 

 section is a unit of area, the mass of the redundant matter =a. 

 Suppose its centre of gravity lies in the vertical through G, and 

 AG = k; 



.', moment of mass Amab A about fulcrum r = a. . k. 



If g and / be the mid-points of the two joints an and Ar, and 

 i-p be perpendicular to an (produced if necessary), and t and t' 

 be the lengths of the joints or the thickness of crust at a and A, 

 then the moments of the force of cohesion about r are 



Qi .t .gp and C . t' .rl. 

 Now 



pg=pm! — m'g = rA — ag + am -\- mm' = t' — ^t + h + a vers 6, 



where h = height of plateau above Dehra; a = radius of the 



earth, 4000 miles ; and the angle of whicli Am is the arc, viz. 



3° 40*. llcncc the equation of moments about r is 



u.k = C.t{t'-^t + h-\-averse) + C.t'.y', 



... /'2 ^ 2tt'-t^ +{h + a vers 6)1= ^^. 



