118 



Symposium on Microseisms 



uniformly applied on the plane z = o, the ampli- 

 tude A of <f> u is equal to P/pv 2 . 



In actual circumstances this periodic pres- 

 sure — which is in any case necessary to obtain 

 waves of compression — is confined to a finite 

 area; in order to obtain a function which de- 

 scribes the actual conditions better than the 

 function 



we change this into 



pJ (v - sinyj exp (-ivt) 



where J„ is a Bessel function and 



p exp < iv( — siny - t) 



r = ( X 2 + y2)' 



The motion of the bottom is then given by 

 the same expressions (2), if we change the fac- 

 tor exp (ivx/c sin y) into iJ 1 (vr/c sin y) for 

 the horizontal (radially directed) component 



and into J (vr/c sin y) for the vertical one. 



Remembering the discontinuous factor of 

 Weber 



r 



J (|r) J x (5r ) d (gr ) =■ 



ifr>r 



1 ifr<r 



It will be seen that the pressure function p J„ 

 (vr/c sin y) exp (-ivt) changes into a func- 

 tion which is equal to p exp (-ivt) for r < r 

 and vanishes for r > r if we apply the oper- 

 ator 



remains constant (= Q). In the limiting case 

 r„ = the normal force Q is evidently concen- 

 trated in the point and is expressed by 



r ^ ( r ° ■ \ a ( r ° • \ 



I Ji |v — sin yl d Iv — sin yl 



oo 



|r) % d£. 



The parameter r„ is arbitrary; following 

 Lamb's procedure (1904) we diminish r,„ at the 

 same time increasing p in such a way that the 

 total force 7ipr| exerted on the plane z = 



Consequently by applying the operator 



Q j v sin y /v sin y\ 



