MECHANICAL STATE OF THE ISOSTATIC SHELL 255 



iiig to the resistance of the jacket and 21.6 miles representing the internal 

 friction of the granite. 



Similarly, the same rock confined in a jacket 0.33 centimeter thick 

 flowed under a total pressure per square inch equivalent to a column 

 29.1 miles high, consisting of 5.8 miles for the resistance of the steel and 

 23.3 for the internal friction of the rock. 



This same granite has at the surface a crushing strength sufficient to 

 support a column of rock only about 5 miles high. Between the surface 

 and a depth of 5.8 miles there is, accordingly, as demonstrated by experi- 

 ment, a very rapid increase in internal friction or resistance to deforma- 

 tion by crushing or flow. 



To visualize this increase, let us plot an arbitrary curve (plate 8) 

 whose vertical ordinates shall be 0, 4.2, and 5.8 miles, corresponding to 

 the load under which the granite exhibits a resistance to flow equivalent 

 to 5, 21.6, and 23.3 miles, and let these values be the abscissas of the 

 curve. We thus obtain the curve LMN. 



In the absence of experimental data with which to prolong the curve 

 below 5.8 miles, we may speculate as follows : 



The increase in internal friction under increasing pressure may reason- 

 ably be attributed to the compression of the rock, whose particles and 

 molecules are thereby brought into closer proximity. The cubic com- 

 pressibility of rock follows Hooke's law of a direct ratio of increase per 

 unit of increment of load within the elastic limit; but in approaching 

 that limit there is a tendency toward a decrease in the rate of compres- 

 sion, as may be seen in the results of Adams^ work on compressibility.^^ 

 Lunn's curves for pressure density and temperature within the earth 

 demonstrate the same change, but in a higher degree. ^^ Accordingly, 

 any increase of internal friction which, by postulate, is a function of com- 

 pression should show a similar decrease in rate with greater loads. Now, 

 if the increase in internal friction were to proceed at a constant rate 

 below the depth of 5.8 miles, the curve would assume the slope of the 

 straight line MNF, making an angle 43 degrees with the horizontal. By 

 the above reasoning that line represents an improbable maximum of in- 

 crease of strength with depth, and the true curve falls within it. 



If the curve of increasing internal friction bends downward, as seems 

 probable, at such a rate that its abscissas grow at a less rate than its 

 ordinates, it will somewliere intersect the diagonal of 45 degrees at which 



" F. D. Adams and E. G. Coker : An investigation into the elastic constants of rocks, 

 more especially with reference to cubic compressibility. Carnegie Institution of Wash- 

 ington, Publication 4G, 1906. 



" Chamberlin and Salisbury : Geology, vol. i, p. 566. 



