642 LOUIS VESSOT KING 



the interior radius of the nickel-steel jacket, and by c the exterior 

 radius of the nickel-steel jacket. If P is the pressure per unit area 

 applied to the end of the test specimen, we have zz=—P. The 

 principal shearing stresses are one-half the algebraic difference of 

 the principal stresses and are at once obtained by writing a = o in 

 the equations (13) of the writer's paper mentioned above. We then 

 obtain 



-20", /3 



(i) \ I rr — zz I =h 

 (ii) %\fr-dd\=o 

 (hi) \ I $-S| = $ — P 



1 + /8 



where 



^I^Vi I+ H^?l *^A 2 (2) 



The radial displacement £7 at the outer surface of the rock specimen 

 is given by 



U P <r (3 



b 2p 1 + " 1 + /? 



(3) 



Each of the principal shearing stresses (i) , (ii) , (hi) , is associated 

 with a family of surfaces along which the material will crack or 

 flow. These are illustrated in Fig. 1, reproduced from the writer's 

 paper already mentioned. It is important to notice in the present 

 connection that the principal shearing stresses in the interior of 

 the rock, as given by (i) and (iii), are independent of the radius r 

 and remain equal throughout the elastic regime. It thus follows 

 from Tresca's theory that the rock, when stressed under these ideal 

 conditions, will commence to break down or flow simultaneously 

 throughout its entire volume. The surfaces of shear which will be 

 associated with the elastic breakdown may either be the system 

 of cones (i) of semivertical angle 45 or the system of helicoidal 

 surfaces (iii) of 45 pitch giving rise to the well-known Luder's lines 

 on the curved surface of the specimen. The particular surfaces of 

 shear which will be observed in any particular test will depend on 

 accidental circumstances, as either system is equally likely to occur. 



