18 



Art. 7. — K. Terazawa 



zr 



_ _ /7 ?>zr{z-\-a) 



2r (,.H(^ + rt)T' 



rd = 0, fz = 0. 



If we proceed to the limit a -> 0, we have the same result as 



that due to the pressure of point concentration. But this limiting 



process is, in general, not permissible. A little examination of 



the value of -y-' shows tliat tlie quantity a has a lower limit, 



such that 



27^, _ /7(2; + 3«)^ 



a- 



(45) 



A^ixX + iif ' 



in order to avoid the impossible state of affairs near the 2;-axis. 

 At a distance from the origin great compared with «, these solutions 

 reduce, in a first approximation, to those in Ex. I., so that the 

 solution which follows from the assumption of point concentration 

 >of given pressure may be valid at a great distance from tlie origin, 

 though only approximately. 



^16. It is desirable here also to see how the displacement 

 varies with the depth. On the same hypothesis as before, that 

 A = //, the variation of Uz is shown in the attached diagram, in 

 which the upper curve represents the distribution of applied pressure 

 (38) and the lower ones represent uz on a proper scale, a is put 

 equal to unity for the sake of simplicity. 



^17. At the surface, the expressions for displacement and 

 stress become 



I ^ r{r- + a-)' f 

 1 



47r(>^ + /^) 



(46) 



,-~ n J a fz r I _ a -]\ 



mR\ - -AU /^ r ^ ^ 1 + ^^ «^ 



^ ^' " 27: \x + fx L r' rXr' + aT' J >^ + /^ ' {r' + aT' 



n 



)(^T) 



^''^' ~ 2- • (r'^ + a'O"'-^ ' 



(zrX = 0, 



