the Earth's Crust. 



349 



to the weight of the deficiency of matter in the space OQSsjO, 

 and the cohesion of the crust at the two joints : and we must 



Fio;. 2. 



take their moments about as a fulcrum, as the tendency is for 

 the crust to open at u and S, and to turn about 0. 



The weight of each portion of the ocean tends downwards 

 towards the centre of the earth ; and the buoyancy arising from 

 the deficiency of that weight equals the diff"erence between the 

 weights of the same bulk of rock and sea- water, and tends up- 

 wards towards the zenith of the place. As sea-water is about 

 half the density of rock (in fact it is less), this diflPerence will 

 equal the weight of a mass of rock, of which the volume is half 

 that of the ocean under consideration. The moment of this 

 force about is the force multiplied by the perpendicular from 

 O upon its vertical direction. Suppose the resultant of all these 

 forces of buoyancy (each of which passes through the earth's 

 centre) passes through the point Q, and that u is half the area of 

 OQ,'&sqO, and k the length of the perpendicular Op. Then, 

 the units being chosen as before, « . A: is the moment of the up- 

 ward forces arising from the deficiency of matter in the ocean. 

 Let t and i' be the thickness of the crust at S and 0, then C . t 

 and C . t' are the forces of cohesion acting at w and x, and their 

 moments about are C .t .V x and C . <'. ^ <', P being perpen- 

 dicular to S V. 



Vx = Y^ — ^s — sx — a\tv?,6 — h—^t, 



where h is the depth of the ocean at S, 9 the angle of which OS 

 is the arc, and a the radius of the earth. Hence the equation 

 of moments is 



ct.k = C.t{avtv^e-h-lt)+C.l! .y ; 

 2otk 



t'^ -t^ + 2{a vers d-h)t = 



C ' 



10. I will now apply this to the case before us numerically. 

 I shall suppose that the bottom of the sea shelves down gradu- 

 ally by equal steps ; so that if h is the depth at the angular 



