374 
MR. GEORGE W. WALKER ON 
There is no doubt that observation supports the view that these effects actually 
occur. But there are difficulties. The times of arrival are not always in agreement 
with theoretical calculation from the curves for P and S, and the relative magnitudes 
of the reflected waves to P and S undergo changes at different distances that are 
difficult to understand. Thus it is doubtful if the reflexions are shown at all at less 
than 3000 km.; at 8000 km. PRj is about as large as P, while at 12,000 km. PR^ is 
substantially larger than P. 
The present investigation w^as undertaken with a view to throwing some light 
on these peculiar phenomena. Owing largely, no doubt, to the circumstance that 
most observatories possess instruments for recording only the horizontal components 
(some have only one), discussion has in many cases been confined to the phenomena 
shown in that component. The introduction of a really reliable apparatus for the 
vertical component by Prince Galitzin, about seven years ago, has led to results of 
great value, and has shown how important it is to study the vertical and horizontal 
components in conjunction. 
Analysis of the time curves for P and S led Wiechert and Zoppritz to the 
conclusion that the corresponding seismic rays do not travel in straight lines from 
the focus, but that they dip down into the earth as if the speed of propagation 
increased with the depth. The results of their investigation will be found in 
Galitzin’s ‘ Lectures on Seismometry,' or my own monograph on ‘ Modern 
Seismology.’ 
The surface values are 7 17 km. per second for P and 4‘01 km. per second for S. 
These are substantially higher than the values found for surface rocks, and emphasize 
the fact that in using the term surface we do, on this view, imagine the heterogeneous 
crust of the earth replaced by a purely ideal surface at which the speeds acquire the 
values stated. The justification of this assumption and the determination of the true 
effect of the crust will have to be undertaken before long. 
We have now to consider the magnitude of the ground movement experienced 
when a wave is incident on the surface. This 
problem has been dealt with by Knott (‘ Phil. 
Mag.,’ 1899) and Wiechert (‘Gott. Nach.,’ 
1907), but only partially. We shall assume 
that at reflexion the waves may be treated as 
plane and the surface as plane. 
In the figure (l) let OX represent the inter¬ 
section of the earth’s surface supposed plane 
with the plane of the paper and let OZ be 
drawn vertically downwards. The lower side 
of OX represents the earth, in which the speeds of propagation of longitudinal and 
transversal waves are Y i and V 2 at the surface. The upper side of OX is a vacuum 
in which no waves are propagated. 
