26 
Proceedings of the Royal Society of Edinburgh. [Sess. 
2. Distortional Wave Incident in the Rock. 
(p. 
B . 
Bj. 
0. 
Ai. 
9'. 
A '. 
0 
1 
1 
14 ° 2 ' 
1 
0-534 
25 ° 
0-466 
l°-6 
0-00002 
26 34 
1 
0-025 
51 
0-975 
3 
0-00006 
33 40 
1 
0-003 
74 
0-997 
3 -7 
0-00006 
35 13 
1 
1 
90 
0 
3 -8 
o-ooooo 
39 48 
1 
0-9998 
imaginary 
4 -3 
0-00019 
45 
1 
0-9998 
V 
4 -7 
0-00016 
59 2 
1 
0-9999 
5? 
5 -7 
0-00014 
73 18 
1 
0-9999 
?5 
6 -3 
0-00014 
84 17 
1 
09999 
55 
6 -6 
0-00006 
Thus in both cases for angles of incidence in the neighbourhood of 20° 
to 30° a large part of the energy which has come in the form of one type 
of wave is reflected in the form of the other. Associated with this process 
of reflexion there will be surface displacements which I now proceed to 
calculate. 
The equations of motion for plane waves in an elastic solid are given 
in suitable form for the present discussion in Part III. of the Philosophical 
Magazine paper already cited. A recapitulation seems necessary in order 
to make the calculations intelligible. 
Let the plane wave impinge at a given angle on the plane boundary or 
interface separating the elastic solid from some other elastic medium, and 
let the plane perpendicular to the wave-front and to the boundary be 
taken as the XY plane, the ^c-axis being perpendicular to the interface, 
the ^/-axis in the interface, and the £-axis parallel to the wave-front. 
Following the notation of Thomson and Tait’s Natural Philosophy, we 
have P, Q, R, S, T, U as the components of stress, k the incompressibility, 
n the rigidity, p the density, and m = k+n/3. 
Let £, rj, £ be the components of the displacement at the point xyz, and 
let <p and \/s be two functions defined by the equations 
£| 
dcf> ^difr _ d(f) 
dx dy ’ ^ dx 
01 f/ 
dy ' 
Then the equations of motion for plane waves are expressible in 
the form 
