THEORY OF A SOLID ISOTROPIC EARTH 45 
motion of the ground is zero, and only horizontal motion in 
the plane of incidence remains. On the other hand when 
é= 45° the horizontal motion is zero and only vertical motion 
remains. Further when e=o the motion of the ground is zero 
whatever A may be, and thus transversal disturbance in which 
the displacement is perpendicular to the ground cannot be 
propagated parallel to the surface. 
Our discussion, which has proceeded on elementary lines, 
is particularly useful in showing how difficulty arises in de- 
tecting S at considerable distances owing to interference with 
other maxima, or it may be the actual vanishing of the hori- 
zontal movement. It has indeed sometimes been asserted that 
S never reaches beyond a certain distance, and to explain this 
an impenetrable core of the earth has been assumed. We see 
that no such hypothesis is at all necessary to explain the ob- 
servations. 
A complete discussion which shall take account of the 
magnitude of the diffracted effects as well as of their time of 
arrival even for a simple type of initial disturbance would, I 
believe, be a valuable contribution to seismological theory, and 
in particular I should hope that it would throw some light on 
the origin of a class of waves we have still to consider. 
We have observed that it is impossible to. propagate along 
a plane boundary either longitudinal waves with displacement 
parallel to the surface or transversal waves with displacement 
perpendicular to the surface. But by combining two types in 
which the direction of the wave front is expressed by imaginary 
angles, Lord Rayleigh (Collected Papers) has shown that the 
surface conditions may be satisfied and that a system of waves, 
in which the amplitude diminishes exponentially from the sur- 
face, appears to advance parallel to the surface. 
If Poisson’s ratio for the material = 1/4 or V,?= 3V,” which 
is very nearly the case for the earth’s surface, Lord Rayleigh 
finds that we can have a system of waves in which the dis- 
placement & parallel to the surface and in the direction of 
apparent propagation is given by 
E=(€"~— 5773 27 *) sin (7472) 
and the vertical motion is 
