664 JOSEPH BARRELL 



these requirements, so that such a perfected isostatic arrangement 

 is not demanded on the score of crustal weakness. Second, the 

 harmonic curves giving these figures are of a gently sweeping 

 character; whereas, the actual continents are in many places high 

 on their margins, and from these margins they slope with compara- 

 tive steepness to the mean depth of the ocean floors. The stresses 

 set up beneath the continental margins are accordingly a closer 

 approximation to those imposed by lofty mountain ranges. Assume 

 that compensations of the continental margins are perfect and the 

 problem becomes that which Love takes up in the following chap- 

 ter, namely, the isostatic support of mountains, except that we deal 

 with only one great slope, whereas the theory calls for a succession 

 of mountains and valleys. 



It is shown that for such a compensated series, postulating the 

 distribution of densities previously discussed, the greatest stress- 

 difference exists at the mean surface, beneath the crests, and 

 reaches a value equal to half the weight of a column of rock equal 

 to half the height of the crests above the valley bottoms. From 

 this maximum the stress-difference decreases to zero at the base of 

 the zone of compensation. The solution by G. H. Darwin for 

 uncompensated mountains and valleys gave a maximum stress- 

 difference equal to 74 per cent of half the height, this maximum 

 occurring at a depth equal to about one-sixth the distance between 

 mountain crests. Even with perfect isostatic compensation, dis- 

 tributed after the fashion assumed by Love, the stress-differences 

 for mountains and valleys are seen consequently to be two-thirds 

 in value of those produced by an uncompensated relief, and are 

 approximately one-fourth of the hydrostatic pressures. This frac- 

 tion, one-fourth, happens also to be the same as Poisson's ratio, 

 the ratio of the lateral expansion to the vertical shortening of a 

 free rock column under vertical stress. 



Now the distribution of density has been found to be more or 

 less irregular, and there is no evidence of such a reversing layer at 

 the base as Love has postulated. Stress-differences will conse- 

 quently extend below the isostatic compensation. If, however, the 

 latter is not uniformly distributed, but is concentrated somewhat 

 in the outer half of the lithosphere, the stress-differences will become 



