582 



GEOLOGY, 



the supporting power will not be materially changed unless the cen- 

 tral elevation is a considerable fraction of the radius of the dome. 

 Assuming a central elevation of two miles — to represent the protru- 

 sion of the continental segments — the results for domes of different 

 horizontal extent are as follows : ' 



THEORETICAL STRENGTH OF IDEAL DOMES ARCHED TWO MILES ABOVE 

 THE AVERAGE SURFACE OF THE SPHERE. 



Diameter of given 



Multiplier of 1/525 

 i.e. the supporting 



Proportion of its own 



dome arched 



weight sustained by- 



2 miles above 



proportion of a 



given dome arched 



sphere. 



spherical dome. 



2 miles above sphere. 



3,000 mtles 



1.006 



1/522 



400 " 



1.396 



1/376 



240 " 



2.11 



1/249 



160 " 



3.49 



1/150 



80 " 



10.97 



1/48 



From this table it Avill be seen that for domes of continental dimen- 

 sions the supporting strength equals only a very small fraction of the 

 dome^s own weight. Increasing the thickness of the shell increases its 

 actual supporting powder, but the proportion is somewhat less when 

 the whole sphere is concerned. The problem has not been worked out 

 for domes of limited extent. For rough estimates, where the dimen- 

 sions of the dome are of continental magnitude, each mile of thick- 

 ness may be taken as supporting a layer of about 10 feet of its own 

 material. If the hypothetical level of no stress be placed at 8 miles 

 depth, the shell above this, by reason of its domed shape, could relieve 

 its own pressure on that below to an amount equal only to the weight 

 of about 80 feet of rock over its surface, even if its form and structure 

 were ideal. If the shell were thick enough (817 miles) to embrace one- 

 half the volume of the earth, its supporting power would be a little 

 more than the weight of one and one- half miles of rock. As the radius 

 of the earth is less than 4000 miles, the extreme supporting power 

 reckoned on this basis would be only about 8 miles of rock- depth. It 

 is interesting, if not significant, to observe that this depth barely reaches 

 the minimum shrinkage that will serve, according to current estimates, 



* It is assumed that the direction of the supporting thrust at the periphery of the 

 dome is at every point parallel to the tangent to the domed surface. This is jusUfied by 

 symmetry in the case of a shell conforming to the sphericity of the earth, and in the other 

 cases it would seem to be as favorable an assumption in the direction of high supporting 

 capacity as can reasonably be made. 



