MECHANICS OF FORMA TION OF ARCUA TE MOUNTAINS 1 75 



the entire arch a figure is obtained represented by the area 

 AGOHB, which for convenience we may refer to as the "cosine 

 area." To this there is probably to be added for the crown region 



particularly some part of 

 the tangent-normal com- 

 ponent of the load which 

 is spent in internal strain 

 within the arch; but since 

 any extensive settling of 

 the crown would bear upon 

 the subjacent formation 

 and transmit this burden 

 to them, the additional 

 amount from this source is 

 probably so small as to be 

 negligible in our discussion. 

 For the different stages 

 which we have selected in 

 the evolution of an anti- 

 cline, these cosine areas 

 may be derived by graphi- 

 cal methods, and through 

 dividing each by the total load, the percentage which is Hfted by 

 the competent member may in each case be roughly estimated. 



Relative competence of a member in successive stages of anticline 

 evolution. — The cosine areas for each of the successive stages of a 

 developing anticline which are represented in our series afford the 

 figures of the following table: 



TABLE I 



Fig. 14. — ^Diagram to show the proportion 

 of total load which is lifted from underlying 

 formations by an anticline here assumed for 

 convenience to be the arc of a circle. AOB, 

 anticline; CDEF, area proportional to the entire 

 load; AGOHB, cosine area proportional to the 

 load lifted from interior formation beneath the 

 arch. 



