252 P. W. Bridgman — Failure of Cavities in Crystals 



eter equal 5-5) using the values of the constants found by 

 Voigt (see Love's Elasticity, page 157), the displace- 

 ments, stresses and strains at the inner surface under an 

 external pressure of 12,000 kg. are as follows : radial dis- 

 placement 2-9/c of the original radius, circumferential 

 pressure 25,000 kg/cm 2 , axial shearing stress 5700 kg., 

 radial elongation 0-5%, circumferential compression 

 2-9%, shearing strain between radius and axis 0-97%. 

 The inapplicability of the ordinary criteria of rupture is 

 obvious. Under ordinary conditions of tests in one- 

 sided compression, the crushing strength of quartz is 

 about 1200 kg/cm 2 . A stress 20 times as great, with cor- 

 responding larger values of shearing stresses and 

 strains, was supported by the crystal above, and then 

 rupture took place in a manner different from that to be 

 expected. 



The measurements of the change in internal dimen- 

 sions already mentioned were not in conflict with what is 

 to be expected from the mathematical analysis. Thei 

 measurements were only rough, giving the order of the 

 effect. Those on the second cylinder were much more 

 consistent than those on the first, and gave a radial dis- 

 placement of 2-7% under 12,000 kg. against 2-9 % calcu- 

 lated above. The agreement is much better than could be 

 expected. The accuracy of the measurements was of 

 course not great enough to permit detection of the small 

 oscillating effect superposed on the average radial dis- 

 placement. The measurements of radial displacement 

 furthermore showed that the relation between displace- 

 ment and stress remains linear up to the point of com- 

 plete rupture, thus justifying the use of the ordinary 

 mathematical analysis of elasticity. This is of course 

 only what is to be expected from a substance of such 

 small viscosity as to show no flow under these very high 

 stresses. 



Tourmaline.- — Both specimens were of approximately 

 the dimensions of the second quartz specimen. They 

 were cut perpendicularly to the axis. The first specimen 

 was colored, ranging from light green through purple to 

 dark brown, but was sufficiently transparent so that all 

 the inner defects could be seen. The crystal was full of 

 small strisB parallel to the axis, and also contained many 

 surfaces of internal reflection, which were probably 

 minute cracks. These were scattered at random through- 



