THE STRENGTH OF THE EARTH'S CRUST 733 



of zonal harmonics arranged on the surface of a sphere. The 

 harmonic series of the second order corresponds to oblateness of a 

 spheroid and also serves as a basis for computing the tidal strains. 

 The zonal harmonics of the fourth order correspond to an equatorial 

 continent and two polar continents, the eighth order adds to these 

 two annular continents in about latitude 45°, and so on. The 

 higher orders, above thirty, correspond to a succession of anti- 

 clinoria and synclinoria, or mountains and valleys. For all above 

 the second harmonic the depth of maximum stress lies within the 

 outer half of the earth's radius. 



Darwin's solutions were made on the assumption that there are 

 no differences of density beneath continents and oceans and that 

 all the relief of the earth is upheld by its rigidity. He reached 

 the conclusion that continents such as Africa and America gave 

 a maximum stress-difference of about four tons per square inch 

 at a depth of about 1,100 miles. The later demonstration of the 

 existence of regional isostasy nullifies this conclusion except for the 

 amount by which the topography of large areas is not completely 

 compensated. Even this part can to some extent be regarded as 

 sustained by a rigid crust floating upon a deeper zone which acts 

 dynamically nearly as a fluid. There are reasons for believing, 

 however, that this latter conception is extreme in the other direction 

 and not justified by the evidence. It is thought that by the col- 

 lective support of the arguments brought out in this part the 

 assumption will be finally justified — that for the outstanding loads 

 not in isostatic equilibrium the work of Darwin continues to apply. 



In the mathematical analysis, the loads which represent the 

 areas and heights of the regional departures from isostasy are 

 regarded as members of an infinite harmonic series of ridges and 

 furrows disposed on a plane. One wave-length is the distance 

 from crest to crest, or mid-furrow to mid-furrow. Darwin showed, 

 as illustrated in Figs. 15 and 16, that the magnitude of the stress- 

 dift'erence at any point within the crust due to a surficial harmonic 

 load depended upon the depth below the mean horizontal surface 

 measured in terms of the wave-length and not at all on the position 

 of the point considered with reference to the ridges and furrows. 

 Further in regard to the direction of the stress-difference, it is 



