264 Willis and Hayes — Conditions of 



petent layer will carry up the immediately overlying incompe- 

 tent layer and the total weight raised in the anticline upon its 

 numerous competent arches will be distributed through their 

 limbs to many points of support. But if the stratified series 

 consists of one massive competent stratum overlaid by a great 

 thickness of relatively incompetent strata, then the total 

 weight raised on the anticline will be transferred by the mas- 

 sive competent stratum to those parts of the curve which are 

 concave upward, that is to the adjacent synclines. Applying 

 these general conclusions to the special case of an original 

 Appalachian stepfold we may represent (tig. 5) the competent 



Fig. 5.— Development of original competent anticline A. 



stratum by a single heavy black line. If the weight raised by 

 the competent anticline A be W, then the limbs of the arch 

 w T ill transmit the weights w f and w" whose sum will be equal 

 to W and whose ratio will depend on the relative dips of the 

 two limbs. As the limb A S becomes steeper w' will increase 

 in proportion to w" and its effect will be concentrated at the 

 foot of AS. If the arch A be eroded such part of the sedi- 

 ment as falls in the syncline S will also concentrate in a narrow 

 zone, while that which falls on the other limb w T ill be distribu- 

 ted on its gentle slope. The downward pressure thus pro- 

 duced beneath the original syncline S, is directly related to W ; 

 it is an indeterminate weight which may be designated x 



(% 6). 



i > 



Fig. 6.— Development of consequent competent anticline A'. 



The weight x tends to depress the limb SA r and if it causes 

 depression at S it must displace the subjacent support, which 

 will move toward A, the region of relief; the limb S A' of 

 the competent stratum will then sink downward in a long 

 gentle curve, x must be greater than the weight required to 

 displace the support at S and the excess will be exerted in 

 bending S A' ; being effective at a point A' so far distant 



