24 
Proceedings of the Royal Society of Edinburgh. [Sess. 
itself complete. I propose to examine the problem here suggested. Its 
solution follows almost immediately from the equations of vibratory 
motion which I discussed in my papers on the Reflexion and Refraction 
of Elastic Waves, first in 1888 in the Transactions of the Seismological 
Society of Japan, and in 1899 somewhat more fully in the Philosophical 
Magazine, vol. xlviii. 
The experimental determination of the real angle of emergence depends 
on the comparison of the vertical displacement of the ground with the 
simultaneous maximum horizontal displacement. On the simple hypothesis 
of plane elastic waves impinging internally on the surface of the earth, we 
know (see Seismic Radiations, vol. xxviii. p. 219) that the sine of the 
angle of incidence is equal to the ratio of the real speed of propagation 
of the wave to the apparent fictitious speed of propagation of the surface 
disturbance. Both these speeds can be obtained with fair accuracy by 
study of the time curves of the first and second preliminary tremors. On 
the other hand, we have not as yet any instruments capable of measur- 
ing the real displacements in a trustworthy manner. The vertical 
displacement is particularly difficult to measure ; and it is very doubtful 
if the horizontal pendulum, at present the favourite seismographical 
instrument, gives an even approximate reproduction of the horizontal 
motion of the earth. 
Let us suppose, however, that we have instruments capable of accurately 
determining the horizontal and vertical displacements, and thus affording 
the data for calculating the real angle of emergence. The question then 
arises, what relation will exist between this externally measured angle of 
emergence and what is generally called this, viz. the angle of incidence of 
the radiation impinging internally on the surface ? 
In the earlier discussion my purpose was to show that with small values 
for the angle of incidence the vertical effect at the outcrop of the seismic 
ray became the more important, so that a horizontal pendulum at more 
than 90° arcual distance from the source of the earthquake disturbance 
would record only a very small part of the whole motion. This conclusion, 
it will be seen, is not materially affected when the real angle of emergence 
is considered. 
As pointed out in the papers of 1888 and 1899 already referred to, a 
wave of condensational type passing through an elastic solid and falling 
on the surface backed by air or water produces not only a reflected wave 
of the same type in the solid and a refracted wave in the fluid, but also a 
reflected wave of the distortional type in the solid. Similarly, a ray of 
distortional type will give rise to a refracted condensational wave and two 
