TREMORS OVER THE SURFACE OF AN ELASTIC SOLID. 15 



where 



F(K) 



a numerical quantity depending only on the ratio X : ^. 

 To examine the value of v we take the integral 



__ , / 69 x 



* _ p )2 _ 4 ^(2 _ AS) ^^ _ * 



round the same contour. Integrating along the axis of g we find 



_ 



T 



and thence by addition, since the terms due to the infinitely distant parts of the 

 contour vanish as before, 



it* fit 



cos K - ^ 



f = IfZnf-it 



2f J-,, 

 J* * f 



'( 



~r 2Ar ~T^//-\ r/TA \'W> 



JA 



where 



Hence if to the principal values of the expressions in (52) we add the system of 

 free Rayleigh waves, 



u i^R sin KX, v = i ^ K cos KX (72), 



p. p 



