338 A. C. LAWSON ISOSTATIG COMPENSATION CAUSE OF THRUSTING 



tributed in the cross-section of the prism, then the limiting length of the 

 prism which may be moved is determinable ; since, when the stress neces- 

 sary to overcome the frictional resistance becomes greater than the 

 strength of the material of the prism, a new rupture will be inaugurated. 

 Let ABC be a wedge-shaped prism of the earth's crust, AB being the 

 surface of the earth, and BC a fracture plane which has been established 

 at the initiation of a thrust. 



W = weight of prism. 

 w = weight of cubic foot of rock. 

 / = coefficient of friction. 

 P = component of W normal to BC. 

 G = component of W parallel to BC. 

 Q 1 = horizontal force equal to G. 

 F = frictional resistance. 

 F x = horizontal force equal to F. 

 S = crushing strength of rock. 



AB . AC . w AB 2 . tan a . w 



AB 2 . tan a . cos a . w AB 2 sin a . w 



2 2 



Make xyz similar to BCA and xy = W 



Then P = xz = xy cos a = "W cos a 

 / . AB 2 . sin a . w 



F / . AB 2 . sin a . 10 f . AB 2 . tan a . w 



1 cos a 2 cos a 2 



AB 2 . tan a . w sin a 



G = yz = xy sin a = W . sin a = 



o 

 G AB 2 . tan a . w . sin a AB 2 . tan? a . w 



cos a 2 cos a 2 



Fi + Gj = AC . S 



/ . AB 2 . tan a . w + AB 2 tan 2 a . w . _ ^ 

 that is, r = AB . tan a . S 



AB 2S 



(/ + tan a) w ' 



As the angle a becomes larger, the expression (/ -f- tan a) w increases, 

 so that the value of AB decreases. 



That is to say, the greatest possible length of a thrust-block, measured 

 in the direction of the thrust-movement, is for the case where the thrust- 

 plane is horizontal. 



This value of AB varies with the thickness of the prism in so far as the 

 crushing strength varies with depth. But we are concerned only with 

 the minimum value of S, namely, that at the surface, since when the 



