THE STRENGTH OF THE EARTH'S CRUST 435 



Now the modulus of rigidity is related to the modulus of com- 

 pressibility by means of a formula involving Poisson's ratio/ 

 This ratio varies for each substance, but for rocks, for iron and 

 steel, and probably for ice, it lies between 0.2 and 0.3 in value, so 

 that in general the rigidity of these substances can be judged roughly 

 by their degree of incompressibility. Consequently it is seen that 

 glacier ice at temperatures such as those which prevail in the body 

 of the moving glacier possesses a degree of incompressibility and 

 rigidity which, if these elastic constants were measures of its 

 strength, would make it wholly incapable of motion on such 

 gradients as are observed. This can be made more obvious by 

 some quantitative statements. Granite and similar rocks, for 

 example, can stand permanently in steep cliffs to heights of thou- 

 sands of feet. They constitute mountain ranges whose height 

 and steepness are limited entirely by the forces of erosion on the 

 one hand and the strength of the asthenosphere on the other. The 

 cliffs could be very much higher and the mountains much more 

 lofty before glacier-like flow at the base of the mountain mass would 

 occur. In fact, with a compressive strength of 25,000 pounds per 

 square inch, a rectangular block of granite could stand as a vertical 

 wall 22,000 feet high, and of indefinite breadth, without yielding 

 of the base. With a sloping face and supported by spurs such as 

 occur in nature, the height of the granite mass could become con- 

 siderably greater. For parallel mountain ranges of harmonic form 

 and gentle slopes resting upon a foundation whose compressive 

 strength to indefinite depths was 25,000 pounds per square inch, the 

 mountain crests could stand eleven miles above the valley bottoms 

 before the maximum stress-difference would reach this limit. 

 Even then, if the slopes were as low as those of a continental ice 

 sheet, the failure would not take place by flowage of the mountains 

 laterally into the valleys, but by a vertical settling of the mountains 

 and a vertical upwarping of the valleys. The lateral, plastic flow 

 would be at some depth in the earth. If the asthenosphere were 

 indefinitely rigid, granite mountains of sufficiently gentle slope 



'Let P = Poisson's ratio; C, the modulus of rigidity; D, the modulus of com- 

 pressibility. ThenC=- ^^ £> . 

 2 i+F 



