262 G. II. Darwin — Stresses caused in the Earth by 



the direction of the stresses does, however, depend on this lat- 

 ter consideration. 



The greatest stress-difference depends merely on the height 

 and density of the mountains, and the depth at which it is 

 reached merely on the distance from ridge to ridge, being w fo 

 of it. 



Numerical calculation shows that if we suppose a series of 

 mountains whose crests are 4,000 meters, or about 13,000 feet, 

 above the intermediate valley-bottoms, formed of rock of spe- 

 cific gravity 2 '8, then the maximum stress-difference is 2-6 tons 

 per square inch (about the tenacity of cast tin); also if the 

 mountain chains are 314 miles apart the maximum stress 

 difference is reached at 50 miles below the mean surface. 



It may be necessary to warn the geologist that this investiga- 

 tion is approximate in a certain sense, for the results do not 

 give the state of stress actually within the mountain prominen- 

 ces or near the surface in the valley bottoms. The solution 

 will, however, be very nearly accurate at some five or six miles 

 below the valley -bottoms. The solution shows that the stress- 

 difference is nil at the mean surface, but it is obvious that 

 both the mountain masses and the valley-bottoms are in some 



The mathematician will easily see that this imperfection 

 arises because the problem really treated is that of an infinite 

 elastic plane, subjected to simple harmonic tractions and 



To find. the state of stress actually within the mountain 

 masses would probably be difficult. 



The maximum stress-difference just found for the mountains 

 and valleys obviously cannot be so great as that at the base of 

 a vertical column of this rock, which has a section of a square 

 inch, and is t,000 meters high. The weight of such a column 

 is t '1 tons, and therefore the stress difference at the base would 

 be 71 tons per square inch. The maximum stress-difference 

 computed above is 2*6, which is about three-eighths of 71 tons 

 per square inch. Thus the support of the contiguous masses 

 of rock, in the case just considered, serves as a relief to the 

 rock to the extent of about five-eighths of the greatest possible 

 stress-difference. This computation also gives a rough esti- 

 mate of the stress-differences which must 'exist if the crust of 

 the earth be thin. It is shown below that there is reason to 

 suppose that the height from the crest to the bottom of the 

 depression in such large undulations as those formed bv Africa 

 and America is about 6,000 meters. The weight of a similar 

 column 6,000 meters high is nearly 11 tons. 



In § 7 I take the cases of the even zonal harmonics from the 

 second to the twelfth, but for all except the second harmonic 

 only the equatorial region of the sphere is considered. 



