TREMORS OVER THE SURFACE OF AN ELASTIC SOLID. 17 



= f- *^* 



- Jo 2 F* - 4r 2 



+ F)* - 4r? 2 + V) 



Similarly, in the right-hand contour, 



f * //) d r = f 



~ " - T) 



We infer, by addition, 



Pf k-ae^dg > v . 



" TT7]tV = 2:rK sm ^ + 2 



*> J ? 



( 



If we multiply this hy Q/27T/X, and add in the term due to the free Rayleigh 

 waves represented by (72), we obtain, as an equivalent form of (74), 



_ 



4jQ f* F^(g 2 - /^) v/(A s -J 2 ) e^^ cf ^ 

 " " " 



, Q . w f"_ 



h Jo 2 8 



_ _ _ 



(2V 8 + F)* - 47,2 ^(/i* +.^) ,/(P + r/ 2 ) ' 



It is evident that all terms after the first diminish indefinitely as x is increased. 



* From this we can deduce, by the Scime method as in Art. 4, an expression for the mean rate W at 

 which a vertical pressure Q cospt does work in generating waves, viz., 



w = 



/i '2lTj 



12 ft 



+ ~J"t. I ^LS>_\*_ 



VOL. CCI1I. A. D 



