THE STRENGTH OF THE EARTH'S CRUST 663 



density distribution which results. With only these three limiting 

 assumptions, the number of unknown quantities remains larger 

 than the number of equations, and the results are, strictly speaking, 

 indeterminate; but by making various reasonable further assump- 

 tions definite solutions in accordance with these may be obtained. 

 The elimination of stress-differences at the base of the lithosphere, 

 taken as equivalent here to the zone of compensation, requires, 

 however, that there shall be a peculiar relation of densities. To 

 compensate an elevation it must be offset by matter below of less 

 density than the mean for that depth, but in order to quench the 

 stress-differences at the base of the lithosphere there must be 

 between the light matter and this base a layer of more than mean 

 density for that depth. Thus the light layer must perform a two- 

 fold function, compensating not only the elevation above but the 

 heavy layer below. For depressions in the crust there must be a 

 reverse arrangement, matter of more than mean density existing 

 immediately below the surface. But above the base of the litho- 

 sphere there must be a layer of less than mean density for that 

 depth. The artificialities of this scheme would be sufiicient to 

 form a disproof of the initial assumption which determined it, but 

 it also seems to be directly disproved by the evidence brought 

 forward in the earlier parts of the present article. Nevertheless, 

 the exact mathematical solution of this difficult problem is of great 

 value as giving the results of the assumptions of extreme isostasy. 



For the largest inequality of the crust, regarded as a zonal 

 harmonic of the first order, that represented by the land and water 

 hemispheres. Love shows that the lateral stress-differences under 

 this hypothesis of isostasy reach a maximum at a depth equal to 

 one- third of the zone of compensation and are equal to only o . 006 

 of the weight of a column of rock of height equal to the maximum 

 height of the inequality. For harmonics of the second and third 

 orders, representing the continents, the fractions are 0.0134 and 

 0.0208. These results, Love states, are extremely favorable to the 

 hypothesis of isostasy, since the inequalities could be supported by 

 any reasonably strong material. 



There are two criticisms, however, to be noted while citing this 

 conclusion. First, it is known that the crust is vastly stronger than 



