THE STRENGTH OF THE EARTH'S CRUST 737 . 



stressed by a continuous load, greatest at the center in accordance 

 with the harmonic curve and acting in the reverse direction from 

 the adjacent spans. This is a very simple Hmiting case. The maxi- 

 mum bending moment would be on the cross-section at the crest 

 of each downward and upward arch. For a given height of load 

 the bending moment would increase with the square of the span 

 or wave-length. The maximum bending stresses would be hori- 

 zontal, acting as tensile and compressive stresses at the top and 

 bottom of the lithosphere. In the middle of the lithosphere there 

 would exist a neutral surface suffering neither tension nor com- 

 pression, but subjected to horizontal shear. The theory of beams 

 shows that the strength is limited by the marginal tensions and 

 compressions, not by the internal shear. As the lithosphere is, 

 however, weakest on the upper and lower margins, its material is 

 poorly arranged to resist the bending stresses. The greatest 

 resistance to bending in a certain plane is given by the form of an 

 I-beam, but the crust is analogous to a beam in which a single flange 

 should intersect its middle, giving a cross-shaped section. The 

 earth's crust is consequently a peculiarly weak structure to resist 

 harmonic loads of great wave-length, and as the strength varies 

 inversely with the bending moment it varies inversely with the 

 square of the wave-length. It is seen then that wave-lengths of 

 continental breadth are very poorly supported by the strength of 

 the crust, but if they reach notable amplitude must rest chiefly 

 upon the asthenosphere. The consideration of the stress diagram 

 given by a wave-length of 200 km. showed why very pronounced 

 departures from isostasy can occur in one direction over areas up 

 to at least 100 km. across and why marked regional compensation 

 extends commonly to limits of 100-200 km. radius. The stress 

 effects produced by harmonic loads a thousand kilometers or more 

 in a wave-length show, on the other hand, why regional compensa- 

 tion of the same vertical magnitude cannot extend effectively across 

 a whole continent. It explains why the United States as a whole 

 is in nearly perfect isostatic equilibrium with respect to the ocean 

 basins. 



Nature of stresses imposed by internal loads. — Take the case of 

 harmonic loads distributed on a plane S-S, Fig. 17, within an 



