before and after the Sinking of a Bore-hole. 799 



the deep-seated material, is less open to criticism.. At great 

 depths, according to any view yet suggested, the material 

 must be exposed to very severe pressure ; and it is difficult to 

 imagine material exposed to pressure of hundreds of tons 

 weight on the square inch being anything but nearly incom- 

 pressible under variations of that pressure. The hypothesis 

 of an incompressible nucleus and compressible crust is of 

 course at best only an approximation to the truth. A theory 

 which treated the material as varying continuously with the 

 depth, or as consisting of a large number of homogeneous 

 layers, would presumably be more exact. Its complication, 

 however, would be great ; and in the absence of data the 

 simplest consistent hypothesis seems the best. 



§ 10. The above considerations indicate that in the absence 

 of a bore-hole the stresses at depths of a few miles in reason- 

 ably homogeneous strata are probably not widely different 

 from those appearing in (15). According to this equation 

 the pressure on a horizontal plane equals the weight of the 

 material between it and the surface. This pressure, in short, 

 is the same as if the superincumbent material were liquid. 

 The result implies that the superincumbent material is so 

 much dead weight, and does not act to an appreciable extent 

 as a protecting arch. In reality, some slight action of this 

 kind is likely to exist. In not a few cases, the bending 

 visible in rocks is suggestive of large horizontal thrusts. The 

 condition, however, of the material when the bending occurred 

 may have been plastic. 



An idea of the probable diminution in the vertical pressure 

 due to the horizontal thrust in superincumbent material may 

 be derived from (5). If in this case we suppose 77 equal 1/4 the 

 vertical pressure,—?'? 1 , is only 11/15 of its value when the 

 material is incompressible; but the horizontal or arching 

 pressures to which this reduction is due (/. e, the value of 



— 66 in (5)) if we suppose the density to be 5*5, amounts at 

 the surface to nearly 3000 tons weight on the square inch. 

 The natural inference is that whilst <jph is a maximum 

 <-timate for the vertical pressure on a horizontal plane, it is 

 unlikely to be many per cent, in error. 



As regards horizontal pressure, the largest value given by 



(15) for — 66 is gph, answering to 77 = 0*5. It follows from 

 our previous considerations that if shallow borings show no 

 considerable horizontal pressure, the value of this pressure at 

 depth h is unlikely to be much in excess of gph. On the 



other hand, according to (15), —66 vanishes when 77 = 0, and 

 is only gph/3 when 77 = \. It is thus by no means improbable 



3 G2 



