418 Theories of the Formation of Mountains. 



perficial extent to at least half the continent and averaging nearly 

 a mile in thickness, have been gradually thus transferred. The 

 total effect of the weight must be the same, whether accumulated 

 on the region acted upon, gradually during myriads of ages, or 

 during a single age. 



Professor Hall's theory simply adds the plication suggested by 

 Sir Charles Lyell to the subsidence theory of Sir John Herschel. 

 We think however that although a minute plication would be the 

 result of subsidence, the grand waves of the Appalachians could 

 never have been formed in that way. In proof of this we shall 

 offer a very simple mathematical demonstration. 



Fig. 2. 



Let A. B. C. represent the section of the portion of the earth's 

 crust undergoing subsidence. The straight line A. C. is the chord 

 of the arc A. B. C , and therefore it is shorter than A. B. C. 

 In the process of subsiding towards A. C. the arc A. B. C« 

 must be compressed into a shorter space than it occupied 

 before the subsidence commenced, and to accommodate 

 itself to this diminished space it must become more or less undu- 

 lated. It can be easily shewn than the greatest amount of undula- 

 tion will take place when A. B. C. sinks to the level of A. C. It 

 must there exhibit one or more undulations. Below that level 

 the undulation will become gradually less in proportion to the 

 amount of subsidence. Ihe difference between the leno^th of 

 A. C. and A. B. C. will give us the measure of the greatest wave 

 that can be produced, and provided we have the diameter of the 

 sphere and the width of the belt undergoing subsidence, that dif- 

 ference can be found. 



Let it be granted that the diameter of the earth is 41775500 

 feet ; then this sum multiplied by 3.14159265 would give 

 131241603.75007500 feet for the circumference and this again 

 divided by 360 would give 364560,01041687 feet as the arc o^ 

 one degree. 



Again multiplying 41775500 or the earth's diameter by 



