430 BECKER: MEAN DENSITY OF FRACTURED ROCKS 



ing the mass into polyhedral fragments tightly pressed together. 

 As flexure proceeds fragments will grind against one another, 

 edges and corners being comminuted. It would seem prob- 

 able that the original fragments would thus be more or less 

 rounded, the interspaces becoming packed with attrition prod- 

 ucts. In this condition the mass would somewhat resemble a 

 pile of cannon balls in close order filled in say with buckshot. 

 Now the interstitial space in closely piled spheres of the same 

 radius is 0.2595 and if this space be filled with relatively very 

 small spheres the voids would be reduced to the square of the 

 fraction just stated or to between 6 and 7 per cent. If the buck- 

 shot were mingled with fine birdshot the voids would be still 

 further reduced. 



But the amount of voids can be found much more satisfactorily 

 by experiment. If a tube of soft metal is filled with sulphur, 

 run in in a liquid state, the pipe can be bent cold without collaps- 

 ing, while, since sulphur is very brittle, the filling of the tube must 

 be reduced to powder, with an accompanying diminution of 

 density. At my request Mr. A. F. Melcher has made some trials 

 by this method which will be described in the next note. The 

 results show that the voids increase with the flexure up to a 

 limit very nearly corresponding to the forecast which appar- 

 ently represents a maximum reduction of density through rupture. 



Imagine a tabular mass of rock exposing a plane surface at 

 sea level as wide and as long as' a mountain range and extending 

 to a depth of 120 km. Suppose it either to be unf ssured or that 

 any fissures once intersecting it had been solidly filled with vein 

 minerals. Then suppose that by lateral horizontal forces the 

 mass be crushed as the Coast Ranges and other ranges have been. 

 There would be a tendency to diminish the cross sectional area, 

 but it may be imagined that the reduced width is compensated 

 by increased horizontal length. The result of the formation of 

 voids through fracture must be upheaval and, if the voids amount 

 throughout to 5 per cent, the elevation produced by these alone 

 will average 6 kms. or say 20,000 feet. 



It is thus evident that the diminution of density due to crush- 

 ing is of the order of magnitude requisite to account for the 



