42 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



If we suppose the mass not to become compressed, and the dis- 

 turbance not to extend beyond the vertical lines AA', BB\ it is mani- 

 fest that the lengths of the lines ACB, A C B' will be equal; and since 

 their original lengths were so, their extension Avill be the same. 



It is evident, however, that the force required to elevate the 

 mass ABBA' will be much greater than that just necessary to over- 

 come its weight, on account of the forces called into action at the ex- 

 tremities of the elevated mass, and that some degree of compression of 

 the mass will consequently exist, which will render the vertical line 



CC shorter than its original length. It is also evident that the dis- 

 turbance of the upper part of the mass will extend laterally beyond 

 the verticals through A and B, as above represented. 



The compression of CC will clearly make the curvature of A'C'B 

 less than that of ACB, and will consequently render its extension less 

 than it would otherwise be. The greater extent of lateral disturbance 

 in the upper portion will also produce the same effect. For let us 

 suppose the portion ^> of the upper curve exactly similar, and equal 

 in length to ^iC, then is it easily seen (assuming the extension of A'B' 

 to be uniform throughout) that the line joining the physical point p, 

 and its undisturbed position will be vertical, while similar lines for 

 2}„ p„ and q„ will be inclined, as in the figure. Hence it immediately 

 appears that the difference between the lengths j}„q„ and a/3 " will be 

 less in this case than if p„ and q„ were in the verticals through A and 

 B respectively. We may therefore infer that the same will hold gene- 

 rally, since the condition of the similarity of A'p and pC will be 

 approximately satisfied when the tangents at A' and C are parallel, and 

 the curvature small, as we may here assume it to be. 



