FRICTION AND LIMITING STRENGTH OF ROCKS 649 



the interior to be hydrostatic. If p be the hydrostatic pressure 

 required to bulge the nickel-steel jacket to the same radius b, we 

 have instead of (18) the equation 



Ttpobl+lpo cos t dS = Trb 2 p , (19) 



where e now denotes the direction which the normal to the deformed 

 surface makes with the axis of the cylinder. It was carefully ascer- 

 tained in the experiments of Adams and Bancroft that the shape of 

 the bulged nickel-steel jacket was the same when occupied by the 

 softer rocks and such an easily flowing metal as lead, in which con- 

 ditions of pressure approach very nearly to hydrostatic conditions 

 under the very intense loads employed. As the deformation of the 

 nickel-steel jacket is due to the distribution of surface tractions p, 

 it is reasonable to assume that they are distributed in approximately 

 the same way. This is equivalent to asserting that the tangential 

 component of the surface traction between rock and nickel-steel is 

 negligible compared to the normal component, a statement which 

 seems to be reasonable in view of the fact that both rock and nickel- 

 steel are highly polished over the surface of contact. We may thus 

 write \p cos e dS = \p cos e dS in (18) and (19) and arrive at the 

 relation 



P = p (i-b 2 /b 2 )+P b 2 /b 2 , (20) 



giving the average pressure-intensity at the center of the specimen 

 to be identified with zz of equation (17). The corresponding lateral 

 pressure is given by p , which is identified with xx of (17). 



We are now in a position to test the theory of internal friction 

 expressed by (17) from the observations of Adams and Bancroft. 

 It is only necessary to plot against each other the end pressures zz 

 and the lateral pressures xx as determined above. Such specimens 

 as give straight lines may be said to possess a definite modulus of 

 plasticity, K, and coefficient of internal friction, fx. Curves obtained 

 in this way are shown in the Appendix, where they are described 

 in detail for the various specimens tested. The results show that 

 for some kinds of rock the curves approximate closely to straight 

 lines between certain limits of pressure. In the interpretation of 

 these curves it must be kept in mind that the material is not broken 



