before and after the Sinking of a Bore-hole. 793 



where p\ and p& are the pressures at the depths in question 

 in the vertical and horizontal directions respectively. 



Assuming p — Cz everywhere positive, the stresses are all 

 numerically greatest over the base z = ; also 



$ 2 =o=gph-p (24) 



§ 8. Hollow, vertical, circular cylinder of density p acted 

 on by gravity, the outer cylindrical surface r = a being- 

 exposed to normal pressure^— Gz, where p and C are constants, 

 the inner cylindrical surface r = a' and the upper plane sur- 

 face z = h being free from force. 



The solution is obtainable from one on p. 550 of the Phil. 

 Mag. for November 1901 by suitably altering the notation. 

 It is, in cylindrical coordinates, 



t ii?\ T it. \ n ,a 2 (p — Cz)"] a 2 a' 2 (p-Cz) 



10 



(;/E) [-gph + *££] + i ^ (z> + **) y (25 



Here rj is a constant which can be determined so that w has 

 any assigned value at any given point. 

 For the stresses we have 



•~ — ^»( i -?)(>- '} 



(26) 



25 = — gp(h—z). 



Assuming p, C, and p — Ch positive, the stresses are all 

 negative and numerically greatest at the base of the cylinder, 

 where z vanishes; and the greatest value of the maximum 

 stress difference — which is met with over the inner surface — 

 is the greater of the two quantities : — 



8 X = 2jpa 9 /(a«. 



>S 2 



gph. 



«'%) 



(27) 



"When a ja is very small, then very approximately 



&i = '2p (28) 



§9. Right prism exposed to uniform pressures P and p 

 over its flat ends and prismatic surface respectively. The 



