Arthur Holmes—Radio-activity. 267 
more perfect isostatic equilibrium than are most areas of the earth’s 
surface, and the evidence it affords of the strength of the earth’s crust 
is therefore insufficient and inconclusive. Barrell justly concludes 
that ‘‘Isostasy . . . is nearly perfect, or is very imperfect, or even 
non-existent, according to the size and relief of the area considered ”’. 
For the continents and oceans the degree of adjustment is high ; 
within areas of 250 km. in diameter the departure from equilibrium 
may be high; while individual peaks and even small ranges may be 
wholly supported by the rigidity of the underlying rocks. 
16. THe AstHENOSPHERE. 
Barrell has shown that the greater departures from isostasy impose 
very considerable stress differences on the zone of compensation, and 
he has applied this fact to a deduction of the strength of the litho- 
sphere at various depths. If a series of wave-like curves represent 
the profile of uncompensated hills and valleys, or of oceanic islands 
and troughs, then the maximum stress difference is imposed at a depth 
of 1/27 of the wave length. In various parts of the world such wave 
lengths can be approximately measured. For example, in the ridges 
and troughs of the Pacific the wave lengths are from 300 to 500 km. 
Even if the strains set up by these loads were entirely unmitigated 
by compensation, the maximum stresses would not be applied at 
depths greater than 80 km. That is to say, the existing inequalities 
which lack complete compensation are responsible for loads that are 
almost wholly borne by the zone of compensation as defined by 
Hayford. Greater inequalities of topography would, if uncompensated, 
throw stress differences to correspondingly greater depths, and the 
-fact that such inequalities do not exist unless they are largely or 
wholly compensated implies that the rocks below the zone of 
‘compensation are too weak to support them. Otherwise, if the rocks 
were rigid enough to support great mountain ranges, why should 
_the latter be compensated at all? It is a natural conclusion that 
the lithosphere (limited at its base by the bottom of the zone of 
compensation) is strong, especially in its upper half, compared with 
the underlying zone. For the latter Barrell proposes the name 
asthenosphere—sphere of weakness. The evidence he brings forward 
leads him to suggest the following approximate figures, to illustrate 
the variation of strength with depth (op. cit., 1915, p. 44) :— 
Depth in Strength in 
kilometres. percentage. 
0 100+ 
20 400 
Lithosphere é 5 ae 
50 25 
100 ele 
200 8 
Asthenosphere 300 5 
400 4 
The relative weakness and plasticity of the asthenosphere is capable 
of a second proof based on the implications of isostasy. Denudation 
1 At the surface strong limestone or granite can sustain a stress difference of 
25,000 pounds per square inch (1,750 kg. per sq. cm.). 
