MECHANICAL STATE OF THE ISOSTATIC SHELL 259 



tiidinal pressure at the center (of the bulge) is somewhat less than that 

 of the ends by amounts which increase considerably with the harder 

 rocks.''" 



Now one might readily assume that the internal friction in a rock 

 forced to flow toward an open cavity would be lower than that developed 

 in the same rock when forced to flow and in flowing to overcome a con- 

 fining stress; but the above considerations indicate that the friction may 

 also depend upon the constriction or expansion of the cross-section. If so, 

 the two types of experiments which have been described may yield com- 

 parable results. 



I saw no way of making the comparison, however, until Professor 

 Durand made the suggestion which developed the following method. 



In the experiments wdth the yielding steel jacket the total pressure 

 applied to the end of the rock specimen overcame the internal friction of 

 flow of the rock and also the resistance of the steel jacket. In the experi- 

 ments with an unyielding steel jacket the total end pressure overcame the 

 internal friction of flow throughout the mass, plus the added friction due 

 to centripetal crowding. We have for granite three experiments, two 

 with the yielding steel jacket and one with the unyielding jacket and 

 open cavity, in all of which flow was well established. They are: (1) the 

 experiment with a steel jacket 0.25 centimeter thick, equivalent to a load 

 of 4.2 miles, which developed an internal rock strength equal to 21.6 

 miles; (2) the similar experiment with the jacket 0.33 centimeter thick, 

 equivalent to a load of 5.8 miles, which developed a rock ^^trength of 23.3 

 miles; and (3) the experiment number 358, in which granite flowed 

 toward a central cavity under a total pressure of 35 miles. The total 

 load applied to the end of the cylinder in each of these cases is: for (1), 

 4.2, 21.6, 25.8 miles; for (2), 5.8, 23.3, 29.1 miles; and for (3), 35 miles. 

 We also know that at the surface a load of about 5 miles would crush the 

 granite. 



Plotting the total end pressures 5, 25.8, 29.1, and 35 as ordinates, and 

 the known strength of the granite, 5, 21.6, and 23.3 as abscissas, we 

 obtain three points on a curve which may be prolonged to cut the abscissa 

 corresponding to 35 miles. (See plate 8.) The length of that abscissa, 

 JK, will then represent the average internal friction or strength of the 

 rock under the total end pressure of 35 miles, and the difference between 

 JK and the length corresponding to 35 miles will represent the added 

 internal friction due to centripetal movement. 



Since the values thus obtained depend upon the curvature of a line 

 whose true curve is not definitely known, the result is arbitrary, but 



" Op. cit., p. 655. 



