1918-19.] The Propagation of Earthquake Waves. 187 
be termed the reflective index for the reflection of a type of wave differing 
from the incident wave. The ratios are 
V/V' = l-27, V/U = T87, V'/U = l-47. 
With the help of these values the angles of reflection and refraction 
corresponding to any chosen angle of incidence for either type of 
wave are at once obtained, and the elastic equations referred to above 
lead to the determination of the relative energies associated with the 
various waves. 
Three cases are to be considered : (I) compressional wave incident in 
the solid elastic shell giving rise to a compressional refracted wave through 
the nucleus and two reflected waves, one compressional and one distortional, 
in the shell ; (II) distortional wave incident in the shell giving rise, as in 
the previous case, to a compressional refracted wave in the nucleus and 
distortional and compressional reflected waves in the shell ; (III) com- 
pressional wave incident in the non-rigid nucleus giving rise to two 
refracted waves in the shell and one reflected wave in the nucleus. 
In Table VII on p. 188, arranged in correspondence with the cases just 
named, the results are given in sufficient detail so as to show the distribu- 
tion of the energy among the various reflected and refracted rays, and the 
angles of incidence and refraction corresponding. 
The headings a, a v a refer to the energies in the incident reflected and 
refracted compressional waves, and b, b v b' similarly for the distortional 
waves. The angles 0, 6 V 0' are the angles of incidence, reflection, and 
refraction for the compressional ray, and , </> v <j> the like angles for the 
distortional ray. Note that the “ suffix ” always refers to reflected waves 
in the first medium, and the “ dash ” to the refracted waves in the second 
medium. 
The results are also shown graphically in fig. 8. 
In Table VII the energy of the incident ray for each angle of incidence 
is taken as unity. But when we consider the cone of rays which emanate 
from the epicentre and which fall on the surface of the nucleus, we cannot 
regard these various rays as bringing to that surface equal energies. Along 
each elemental cone the energy per unit surface falls off* as the distance 
increases, and also falls off in virtue of the obliquity of the angle which 
the axis of the elemental cone makes with the surface. 
To take this into account, suppose the energy to radiate from the 
epicentre equally all round and to fall on a spherical surface of radius 
a concentrically situated within the earth of radius b. The energy which 
crosses the spherical surface of radius ( b — a ), centre E, passes on to the 
