730 JOSEPH BARRELL 



upon the outer part of the crust, the maintenance or restoration of 

 the isostatic condition through geologic time in spite of the opposing 

 geologic activities implied the existence of an undertow below the 

 zone of compensation. The existence of this regional isostasy 

 for continental interiors as well as for ocean basins suggests, fur- 

 thermore, that this zone of undertow is both thick and relatively 

 very weak to resist shearing stresses. But if such a zone exists 

 it must have important bearings on other branches of terrestrial 

 dynamics besides that of isostasy. Its importance gives it a right 

 to a distinct name, and it has been called here the zone of weakness — - 

 the asthenosphere. It is desirable to test its reality and its char- 

 acter by other lines of evidence, and such another line forms the 

 basis of this part. 



George H. Darwin has investigated the problem of the stress- 

 dififerences imposed on the earth by the weights of continents and 

 mountains. In his work the earth was assumed to possess com- 

 petent elasticity throughout and the topography to be without 

 isostatic compensation. Love has more recently treated the 

 contrary problem of the isostatic support of continents and moun- 

 tains, assuming as governing conditions that isostatic compensa- 

 tion was perfect within a depth of one-fiftieth of the earth's radius, 

 127 km., and that all shearing stresses due to topography and 

 compensation disappeared at that depth. Below there is assumed 

 to exist only hydrostatic pressures. In other words, Darwin pos- 

 tulates no 'sostasy and no asthenosphere; Love postulates perfect 

 isostasy and a perfect asthenosphere. As there is known to be no 

 truly fluid universal shell within the earth, and as isostasy for 

 limited regions is far from perfect, the truth must lie between these 

 two extremes. The asthenosphere must have some degree of 

 strength and a measure of its strength is derived in this part by a 

 study of the nature of the departures from isostasy. 



For this purpose is discussed the nature of the stresses as worked 

 out by Darwin. Then the departures from isostasy are analyzed 

 into harmonic series. Those of long wave-length are seen to be 

 of low amplitude, those of short wave-length of high amplitude. 

 Now the departures from isostasy are according to their very na- 

 ture without compensation and their stress effects will therefore 



