ELASTIC YIELDING OF EARTH's CRUST 307 



E€^=Ps — (T {P^+ Po)- i 



In these equations E and a have the meanings previously given; p^, 

 P2 and Ps denote the stresses (positive for tension, negative for com- 

 pression) per nnit area in three mntnally perpendicular directions; e^^ 

 Co and eg denote the relative changes of length (positive for elongation, 

 negative for contraction) in the same respective directions. Let — e^ = e 

 and — Pi = P be the relative change of length and the pressure in the 

 vertical direction. By hypothesis €3 = 62 = 0, since there is no lateral 

 yielding. The second and third of equations (A) then give 



— o- p 









V-i — V2 — 



1 



— (T 



which, 



substituted 



in 



the first of (A), 



gives 









E\ 



2 

 1- 











S p 



~~ 6E' 







(3) 



since o" = %. 



The 10,000 feet of sediment exert a pressure of 6.88 X 10^ dynes per 

 square centimeter. The value of e found from formulas (1), (2), and 

 (3) are to be multiplied by the assumed thickness of the crust in order 

 to obtain the yielding in linear units. The numerical results are then 



Depression of 100-kilometer Crust hij Sediments 10,000 Feet thick 



Case (1) Case (2) Case (3) 



Formula (1) Formula (2) Formula (3) 



115 meters 76 meters 61 meters 



376 feet 251 feet 209 feet 



These results are based on the assumption that the elastic moduli remain 

 constant. The velocities of earthquake waves indicate that the moduli in- 

 crease,^^ and that at a dejDth of 100 kilometers we have k equal to 9 X 10^^, 

 or 10 X 10^^ C. G. S. units, with the other moduli in proportion. The 

 figures given above for the depression of the crust should, therefore, be 

 diminished, perhaps, 20 per cent. 



Furthermore, these formulas suppose the section of crust considered to 



" C. G. Knott : The propagation of earthquake waves through the earth, and connected 

 problems. Proceedings Royal Society of Edinburgh, vol. 39, pt. ii (191S-10), p. 169. 



