On Theories of the Origin of Microseisms 115 



a compressional wave travelling in the liquid in 

 the direction y is described by 



u = ~ — , w = — — , <t> = A e 



dx dz 



J /x sin y + Z cos y \ 

 Xp \ iv l c "I 



where v = the frequency, c = the velocity of At the bottom z = h three other waves are 

 sound in water, and y is an angle of incidence excited: 

 measured from the vertical. 



the reflected wave 4 t = HA exp < ivl 1 1 _t 



{/x sin 

 ivl 



and two refracted waves: 



d* d* 



the longitudinal one: u - — , w = — , with the potential 



dx dy 



, | /x sin a + 2 cos a h cos y n cos a \l 



<P = D l Aex P | iv \ i + c^ 5 tjl ; 



3u/ 3 1)/ 



and the transverse wave : u = , w - 



9z 3x 



with the vector-potential xp in the y-direction: 



f /x sin p + 

 D t Aexp ^ivl - 



Z cos p h cos y h cos p \1 



a and b are the velocities of longitudinal and tion (R and D) are determined by the condition 



transverse waves in the solid. The quantities that the tensions T Z7 , T zx and the vertical 



a and P are angles of refraction for compres- motion w have to be continuous across the 



sional and sheer waves in the solid respectively. plane z = h ; 



The coefficients of reflection and refrac- 



cos y cos y cos a cos B 

 w: R = Dj + D t 



