798 Dr. Chree on the Stresses in the Earth's Crust 



however, that the stresses due to centrifugal force in a homo- 

 geneous Earth are at least in large measure neutralized by the 

 compensating action of the spheroidal form on the gravi- 

 tational stresses. In our ignorance of the distribution of 

 density and elasticity throughout the Earth, there is neces- 

 sarily uncertainty as to the extent of this compensating 

 action. The compensation may be less exact than according 

 to (21), but it is at least as likely to be more exact. Further, 

 whilst the pure centrifugal stresses are very considerable at 

 the surface, their rate of variation with the depth is small. 

 There is thus every reason to believe that whatever may be the 

 combined effect of rotation and ellipticity, it will not produce 

 throughout a bore-hole only ten or twelve miles deep effects 

 differing in any essential respect from those observed in 

 ordinary mines. Owing to centrifugal forces there may be 

 a slightly greater tendency for a bore-hole to collapse in a 

 north-south than in an east-west direction. Rotation may 

 slightly facilitate collapse ; but everything points to the con- 

 clusion that its effects, whether direct or indirect, are only of 

 secondary importance. 



§ 15. A more serious source of uncertainty arises in con- 

 nexion with the value (5) of the horizontal stress 06 in a 

 homogeneous gravitating sphere. If, for example, we suppose 

 7] equal 0'25, which is approximately true of glass or iron, 



the value of — -66 is (2/l5)gpa ; this means a pressure 

 answering to the weight of a column of density p some 500 

 miles high. Near the Earth's surface this enormous hori- 

 zontal pressure would exist in company with only a relatively 

 small vertical pressure ; and under such conditions no known 

 material would continue an elastic solid. There is further 

 the observed fact that near the Earth's surface large horizontal 

 stresses are normally at least non-existent. If they occurred, 

 mines could not be constructed. No theory, in short, of the 

 Earth's condition can well be entertained which is incom- 

 patible with horizontal stresses remaining small at moderate 

 depths. 



The most obvious way out of the difficulty is to assume the 

 homogeneous "lEarth " incompressible. We then, as appears 

 from (6) and (7), have the horizontal stresses vanishing at 

 the surface equally with the vertical stresses. To this hypo- 

 thesis there is, however, the objection that no known material 

 is incompressible, and that the materials of which the Earth's 

 crust is composed do not, so far as is known, show any close 

 approach to such a condition. 



The hypothesis § 5, which limits the incompressibility to 



