130 LOUIS VESSOT KING 
§ 5. ON THE CONDITIONS OF RUPTURE IN CYCLINDRICAL ROCK SPECI- 
MENS UNDER CONDITIONS OF EXTREME PRESSURE 
An examination of equations (13) shows that the stress- 
differences (i) and (iii) take their maximum values at r=a, and 
that (iii) takes its maximum value at r=b. We thus obtain for 
the maximum values of the stress-differences 
(i) r7—33=P 
oC 2 
Oe aes arene Ge) 
(iii) 66—22=P } eae tal +8) 
We note that (i) > (ii) provided B>237—". Also (i)> (iii) in all 
am 
cases except when 8= © (6=c) in which case (i) = (iii). 
Thus if 
p>— (i) > (ii) and (i) > (ii) (21) 
so that the specimens will develop the system of surfaces of shear 
shown in (i) Fig. 1. 
If B<°"—* we have (ii) > (i) > (iii) (22) 
In this case the system of surfaces of shear described in (ii), Fig. 1, 
will make their appearance. 
In applying the criterion 
2a (23) 
it is necessary to employ instantaneous values of the elastic con- 
stants, since from the previous section these are seen to depend 
Bh i+o 
on the load. If from (11) we write approximately Ree z 
qe 
Ccor- 
responding to c=, and a=o, the criterion (23) may be written — 
[ao mee 
p/p! = =e 
As long as « <# the first of these criteria given in (21) is always 
satisfied. We have seen, however, that the rigidity » tends to 
