260 B. WILLIS DISCOIDAL STRUCTURE OF THE LITHOSPHERE 



approximately correct. The prolongation of the curve gives a probable 

 value of 25.8 miles for the average internal friction and of 9.2 miles for 

 the added friction or resistance. The point K corresponds in position to 

 these figures. 



The values of 25.8 miles and 9.2 miles ma}' be plotted as in plate 8 to 

 fix the point P, which is a point on the curve of internal resistance of 

 granite to flow when confined by the corresponding load. The position 

 of P may be changed by a slight variation of curvature in the diagram 

 from which its ordinates are derived. It is^ therefore, not of high value. 

 But based as it is on what seem the more reasonable assumptions, it 

 indicates a probability that the curve LMN"P will continue to bend down- 

 ward and may be extended, approaching a straight, in such manner as to 

 intersect the diagonal of 45 degrees at the point C, at a depth of 40 miles 

 below the surface. 



This result may be interpreted to mean that, at approximately 40 miles 

 below the surface, the column of rock of specific gravity 2.8 would equal 

 in weight the crushing strength or internal friction of granite at surface 

 temperature. Below 40 miles the curve which represents the increase of 

 internal friction under the above stated conditions may be extended, as 

 shown on the diagram, to D, but its form is hypothetical. 



The preceding inference is to be qualified by the effect of heat, which 

 is discussed in a subsequent paragraph. 



To pursue the inquiry a little further, we may consider the relation 

 of the strength of the granite at any depth to the superincumbent load 

 and, using a familiar engineering term, may call the ratio of strength to 

 load the factor of safety. Thus, where the load is 4.2 miles and the 

 strength of granite is known by experiment to be 21.6 miles, the factor 

 of safety is 5.1. Similarly, at 5.8 miles it is 4, and, by estimate, at 40 

 miles it is 1. (See the curve EST, plate 8.) 



Below the level at which it becomes 1 the factor of safety is a fraction — 

 that is, an excess of stress, which is a corresponding fractional part of 

 the overlying load, will cause the granite to flow. But, even though that 

 be so, the absolute strength of the granite at surface temperatures, as 

 shown by the abscissas of the curve of internal friction, continues to 

 increase with depth. 



The relative strength of the granite, expressed by the factor of safety 

 or the ratio of strength to load, can become zero only if the numerator 

 becomes zero. This latter would be equivalent to assuming that the 

 internal friction of the granite becomes zero, or that the granite is a 

 fluid — that is, is molten. But the normal increase of temperature with 

 depth is not sufficient to overcome the pressure and melt the granite. 



