46 MODERN SEISMOLOGY 
£=(8475 e~* - 114679 e-*) cos (pt + fx) 
where y= 8475f s= 39337 
and DIf=V ='9194 Vz, 
Thus at the surface 
&,= 4227 sin (f¢+ fx) 
f= — 6204 cos (pt + fxr) 
so that the vertical motion is 1°47 times the horizontal motion 
and the apparent velocity of propagation is less than the 
velocity V,. Similar waves are possible at any plane boundary 
of two media. 
It has been sought to identify these waves with the long 
waves that make their appearance in a sesimogram after the 
second phase S. We shall postpone the discussion to the next 
chapter, but meanwhile it is important to observe that we 
must not regard Rayleigh waves as propagated in the same 
sense as the longitudinal and transversal types in the medium. 
We do not know the conditions that determine a surface 
separating an undisturbed portion of the medium from a por- 
tion influenced by these waves, and since the equations require 
the whole medium to be in motion it is difficult to specify the 
manner in which they can be originated. 
We have so far regarded the focus as being situated at a 
‘ point on the earth’s surface. But the focus of a large tectonic 
earthquake is probably situated at 
some depth of the order of to km. 
Indeed it would seem to be the 
case that if the focus is very near 
the surface the effects are stifled 
within a very short distance, and 
that it requires a fair depth of the 
focus in order that the earth may 
be given, so to speak, a good shake 
which will be experienced at re- 
Ee mote points. 
Pesan A most important influence of 
a finite depth of focus is the manner in which it modifies the 
so-called angle of emergence eat the station. If =the depth 
of the focus we get | 
