178 Proceedings of the Royal Society of Edinburgh. [Sess. 
velocity of the Primary wave becomes constant. This constancy implies 
that the particular elastic constant is increasing at the same rate as the 
density, although at less depths in the earth it is increasing at a greater 
rate. Thus the elastic modulus of the Secondary wave-velocity shows signs 
of flagging at less depths than does that of the Primary wave-velocity. 
There is, in other words, a fall-ofl* in the rigidity before the incompressi- 
bility shows a similar fall-off in rate of increase. At this critical depth of 
about 2000 km. below the surface of the earth the ratio of the incompressi- 
bility to the rigidity increases from 1*9 to 2T6. 
Consider now the form of the seismic rays as shown in fig. 6. The 
manner in which they radiate from the epicentre is particularly interesting. 
The shallower rays — that is, those which penetrate to the smaller depths 
in the earth — are concave outward. With Primary Ray VII, however, a 
new feature comes to light. The ray although concave outwards for the 
shallower portions becomes during a certain part of its course convex out- 
wards, suggesting somewhat the form of a Parthian bow. The same 
peculiarity appears also in the corresponding Secondary ray, but not 
quite so distinctly marked. 
The rays, both Primary and Secondary, whose forms were first 
calculated were II, III, VII, VIII, IX, X, which correspond to vertex 
distances from the earths centre equal to *905, *815, *725, -635, *545, and 
*455 of the radius of the earth. This series is in arithmetical progression, 
each distance differing by (109 from its neighbour. But this simple pro- 
gressive variation does not hold either for the arcual distances between 
the epicentre and the points of emergence of the successive rays or for 
the corresponding angles of emergence. This is brought out in the 
following table for the Primary rays just named : — 
Ray. 
Radius of Vertex. 
Arcual Distance. 
Angle of Emergence. 
r. Sr. 
2a. 2 da. 
<p d</>. 
II 
III 
VII 
VIII 
IX 
X 
*905 .qq 
‘ 815 *09 
>725 *09 
•635 99 
' 545 *09 
*455 Uy 
^ j*? 14 28 
73 Si f \l 
91 36 20 50 
112 26 29 ™ 
120 8 ' 
42 32 12 1^ 
30 18 
24 3 9 l6 R 
20 55 2 54 
18 1 2 54 
15 00 * 1 
The striking increase in the value of 2a with the transition from Ray 
III to Ray VII, taken in conjunction with the sinuous shape of Ray VII 
