802 Stresses in the Earth's Crust. 



whose density equals that of the crust, at a depth equal to 

 that of the projected boring ; the latter may be as large as 

 the former or have any smaller value. Under the conditions 

 supposed by Mr. Martin the pressures, in tons weight on the 

 square inch, would be 



3 6" 8 on the flat ends, 

 from to 36*8 on the curved surface. 



§ 19. Near the bottom of the hole the conditions are com- 

 plicated. An approximate idea of the conditions immediately 

 below the hole may be derived from § 13. At the centre of 

 the bottom of the hole the tendency to rupture according to 

 (43) is actually less than before the hole was bored, unless 

 the material be incompressible when it vanishes in either 

 case. This diminution is almost certainly confined to the 

 central part of the base of the hole. When a core is hollowed 

 out of a cylinder exposed to uniform pressure p the stress- 

 difference — as shown in § 10 — rises to 2p. Under the same 

 circumstances, when a core is taken out of a sphere the stress- 

 difference — as shown in (36) — becomes 3p/2. The conditions 

 at the edge of the base of the hole seem more likely to 

 approach the conditions in the sphere than those in the 

 cylinder. Thus while uncertainty prevails as to the condi- 

 tions in the base — a good deal depending in practice on the 

 borer — this seems on the whole not so weak a spot as the 

 walls of the boring a few diameters of the bore above the 

 base. 



The above considerations unite in indicating that the 

 largest value to be anticipated for the maximum stress- 

 difference anywhere over the surface of the bore-hole is 2p, 

 where p is the hydrostatic pressure that would exist at the 

 bottom of the hole if filled with a liquid whose density equals 

 the mean density of the core extracted. 



§ 20. There are, however, two contingencies to be borne in 

 mind. Whilst large horizontal pressures of the order of 

 hundreds of tons weight on the square inch may be regarded 

 as practically impossible near the surface, it is quite con- 

 ceivable that smaller but still large horizontal pressures may 

 exist in strata which differ notably from adjacent material. 

 If a bore-hole should pierce such a stratum a nipping action 

 may well ensue. Again, whilst no one is likely to select the 

 immediate neighbourhood of an active volcano as a site for 

 a boring, it might be well in any case to be prepared for the 

 possibility of piercing material in so unstable a condition 

 that sudden relief of pressure may lead to semi-volcanic 

 action. 



