On Theories of the Origin of Microseisms 117 



and in the same way the reflected wave system 0. is 



exp 

 *. = RA 



J /x sin y - Z cos y + 2h cos y \ 1 

 | iv ^ _ tjj 



1 + R exp (2iq) 



similar expressions for the refracted waves are easily obtained. 



From these potential-functions we derive the movement of the ocean's bottom: 



u = w tan a (cos 2(3-2 —cos a cos p) and 



w = 2i v A 



Pi 



p cos a exp <iv(— sin y-tl> 



A jexp (-iq) + R exp (iq)£ 

 which after some reduction can be written as 



u = w sin(3 < cos 2pM — - sin?pl ' - 2 cos|3 I and 



ivpA ( fx \\ 



= exp < i v(— sin 3-tl > 



b Pl N \ U // ' 



where 



f /b 2 \-Vi 1 P / b 2 \-'/2 



N =^ cos 2 2pl— - sin 2 p) + 4 sin 2 p cos|3 >cos q - 2i — I sinspl 



(2) 



sin q 



and 



= (t)£-H* (3) 



The primary wave qp n which excites this sure T Z2 of the secondary waves <f>i cancel out at 

 whole wave system, causes a pressure 1„. at z = o. Supposing 4> v to be generated by a 

 the free surface z = o equal to — pv 2 <#>„ ; the pres- pressure 



P = p exp < i 



v(l sin y - t)| 



