194 Proceedings of the Koyal Society of Edinburgh. [Sess. 
Did no nucleus of the kind supposed exist, the rays emanating from 
E within the cone of semi-angle 23°‘6 would pursue paths not deviating 
greatly from the chords (see fig. 6), and emerge on the earth’s surface 
over an area bounded by a circle whose radius would subtend at the centre 
C an angle of 47 01 '2. The effect of the nucleus is to spread these rays 
over an area the radius of whose contour subtends an angle of 56 0, 5. 
The distribution of energy will not be the same in the two cases; but 
in the latter case the whole energy has been reduced to six-tenths of 
the original on account of refraction at the two surfaces. A considera- 
tion of the distribution of energy over the various zones, as indicated 
in Table VIII, also shows that the concentration of rays in the neighbour- 
hood of the antipodal point is of slight importance. This disposes of one 
of the arguments advanced by Wiechert and Zoppritz against Oldham’s 
hypothesis of a nucleus through which the elastic waves pass with 
diminished speed. 
It is hardly necessary to consider in the same detail the effect of 
the non-rigid elastic nucleus upon the transmission of the rays originally 
distortional in the solid shell. A glance at diagram II of fig. 8 shows 
that the greater part of the incident energy is reflected back as dis- 
tortional waves in the shell. Moreover, since the speed of the distortional 
wave in the shell is less than the speed of the condensational wave in 
the nucleus, the refracted condensational waves diverge as they enter 
the nucleus, and diverge still more when they pass out into the shell 
either as condensational or distortional waves. Their divergence is so 
great and their relative energy values are so small that they will bring 
to disturbances already existing at the surface where they emerge a 
quite inappreciable addition. 
If instead of the elastic properties changing abruptly from those of a 
solid elastic shell to those of a non-rigid elastic nucleus of equal com- 
pressibility, we have a gradual transition from the solid to the non-rigid 
with viscosity resisting distortion, the broad results will not differ materi- 
ally from what has just been established. The distortional waves will be 
killed out and the energy of the condensational waves largely reduced. 
What will emerge at the surface of the earth on the further side of the 
nucleus will be predominantly in the form of condensational waves with 
no appreciable concentration in the antipodal region. The seismograms 
obtained by instruments of the horizontal pendulum type will be compara- 
tively inconspicuous and wholly devoid of the well-marked characteristics 
of seismograms obtained at arcual distances from the epicentre less 
than 110°. 
