1909-10.] 
Seismic Radiations. 
35 
Angle of 
Incidence. 
Displacements. 
Semi-axes of Ellipse. 
Phase Re- 
tardation. 
Ratio 
Normal. 
Tangential. 
Normal. 
Tangential. 
35° 16' 
0-577 
0-816 
0 
3-462 
0° 
0 
36 
0-588 
0-809 
1-348 
2-322 
52-4 
0-381 
40 
0-643 
0-766 
1-552 
0-621 
85-2 
2-5 
45 
0-797 
0-707 
1-414 
0 
90 
Oo 
50 
0-766 
0-643 
1-305 
0-349 
87-7 
3-74 
60 
0-866 
0-5 
1-118 
0-866 
75-5 
1-291 
70 
0-940 
0-342 
0-897 
1-326 
57-4 
0-676 
80 
0-985 
0-174 
0-528 
1-798 
31-3 
0-294 
90 
1 
0 
0 
2 
0 
0 
Instead of tabulating in the second last column the quantity tan ~\£/r]), 
which in the present instance has no immediate physical significance, I 
have entered the phase difference tan -1 jp in accordance with the notation of 
equation (2). 
For angles of incidence a little greater than the critical value the 
tangential rectilinear motion opens out into an elliptic motion with quickly 
changing lengths of axes as the angle of incidence goes on increasing. When 
the angle of the incidence is 37° the axes are equal and the motion of the 
surface point is circular. At 45° angle of incidence the motion becomes 
again rectilinear but this time perpendicular to the surface. The vanishing 
of the tangential displacement depends upon the presence of the factor 
(c 2 — 1), and as this is independent of the particular values of the elastic 
constants and density, it follows that a distortional wave totally reflected at 
45° internally from the plane boundary of any elastic medium will produce 
a normal motion only of the boundary. At no other angle of incidence 
does this vanishing of the tangential displacement occur. 
As the angle of incidence is further increased beyond 45° the tangential 
displacement again comes into existence, and into greater and greater 
prominence as the angle of incidence grows. In short, elliptic motion is 
once more established. Up to incident angle 63° 42' the ellipse has its 
major axis perpendicular to the surface. At this particular angle of 
incidence the motion is for a second time circular. It is certainly curious 
that as the grazing incidence is approached the tangential displacement 
should be by far the more prominent. Such a conclusion could hardly have 
been expected on general grounds. The simple kinematic theory of total 
reflexion suggests the existence at the reflecting surface of a normal dis- 
placement only ; but a complete investigation along the lines of a rigorous 
elastic theory shows the insufficiency of this view. 
