1909-10.] 
Seismic Radiations. 
23 
II. — Seismic Radiations. By Professor C. G. Knott. 
(Read June 21, 1909. MS. received July 7, 1909.) 
Part II. 
This second paper is a discussion of the surface displacements associated 
with plane elastic waves reflected from the boundary of the elastic solid 
through which they are being propagated. In my first paper on Seismic 
Radiations ( Proc . Roy. Soc. Edin., vol. xxviii. pp. 217-230, 1908) my aim 
was to find a simple distribution of density and elasticity in terms of 
which the transmission of seismic disturbances could be described. The 
result was given in these words (p. 224) : — 
“The observed facts of seismic radiation can be co-ordinated on the 
assumption that throughout all but a comparatively thin crust of the 
earth the elastic waves of highest speed are transmitted with a speed of 
12’23 kilometres per second, and that within this crust, of thickness equal 
to one-tenth the radius, the speed diminishes from value 1223 kilometres 
per second at the inner surface to 6 kilometres per second at the outer 
surface.” 
Then follows the remark: — “If this wave of highest speed be a com - 
pressional wave with longitudinal vibrations, the cosine of the angle of 
incidence of the ray will give the ratio of the magnitude of the horizontal 
motion to the whole motion ” ; and subsequently it is taken for granted, in 
accordance with the usual custom of seismologists, that the so-called “ angle 
of emergence ” of the ray is equal to the supplement of the angle of incidence 
internally on the boundary. 
I am indebted to Professor Schuster for drawing my attention to an 
inaccuracy lurking in this statement. He remarks : “ The sentence would 
be correct enough if the incident ray only is taken into consideration, but 
as there must be almost total reflexion at the surface, it seems to me that 
the purely longitudinal wave would give, taking account of the reflected 
wave, a purely vertical displacement.” The criticism is, to some extent, 
just, and calls for a revision of the ordinary nomenclature; but inasmuch 
as there is a reflected distortional wave as well as a reflected longitudinal 
wave started at the surface, the amendment indicated by Schuster is not 
