THE STRENGTH OF THE EARTH'S CRUST 505 



proportionately higher. But the tidal stresses, though serving 

 as a measure of the rigidity of the earth as a whole, are so small 

 that they are ineffective as a measure of the strength of the earth 

 as a whole, or of even its weakest parts. The smallness of the 

 stresses can be appreciated by noting Darwin's numerical calcu- 

 lations. In his original paper Darwin arrived at the conclusion 

 that the tidal stress-differences at the center of the earth were 

 eight times as great as at the surface, and this result has been 

 widely quoted. In the final publication, however, a correction 

 is made showing that this is the ratio between the surface stress 

 at the poles as compared to the center. The stresses at the poles, 

 at the equator, and at the center he finds to be in the ratio of i to 3 

 to 8. The diurnal tide gives an actual stress-difference per square 

 centimeter amounting to 16 grams at the poles, 48 at the equator, 

 and 128 at the earth's center.^ The strength of granite at the 

 surface of the earth averages about 1,700,000-2,000,000 grams per 

 square centimeter. The elastic limit for steel subjected to tensile 

 or compressive stresses in one direction ranges from about 3,500,000 

 grams to 4,500,000 grams per square centimeter, according to the 

 grade of the metal. The ultimate strength is about twice as high 

 as the elastic limit. Thus the earth is stressed by the tidal forces 

 even at the center to only about one part in fifteen thousand of the 

 strength of good granite at the surface, or about one part in twenty- 

 seven to thirty-five thousand of the limits of perfect elasticity 

 which steel exhibits in the laboratory. With stresses so small 

 it is not surprising that although tides give measurements of 

 rigidity their evidence regarding viscosity is most uncertain. The 

 results of estimates of the viscosity are more or less contradictory 

 and so small as to be within the probable error of determination. 

 Nevertheless Schweydar considers that there is a suggestion of a 

 slightly plastic zone extending from a depth of about 120 to 620 km. 

 Although this has been adopted in the present article as the limit 

 of the asthenosphere, it would appear that the convincing proof for 

 the existence of such a zone, and the determination of its limits 



^ George H. Darwin, "On the Stresses Caused in the Interior of the Earth by 

 the Weight of Continents and Mountains," Collected Scientific Papers (1908), II, 

 p. 481; original publications, Phil. Trans. Roy. Soc, CLXXIII (1882), 187-223, and 

 Proc. Roy. Soc, XXXVIII (1885), 322-28. 



