34 
Proceedings of the Royal Society of Edinburgh. [Sess. 
cotan -1 J(m/n ) — the angle of emergence differs very slightly from the 
angle which the original displacement of the incident wave makes with 
the surface. 
It is interesting to note how rapidly the normal displacement diminishes 
to zero as the critical angle is approached, while at the same time the 
tangential displacement grows steadily. Another curious point is the 
vanishing of the normal displacement when the angle of incidence has this 
critical value. The absence of the normal displacement is no doubt 
associated with the vanishing of the condensational wave ; but the absence 
of the condensational wave does not necessarily mean no normal displace- 
ment at the surface. For, as has just been proved, when the angle of 
incidence exceeds the critical value, each point of the surface executes an 
elliptic motion. 
A comparison of the table just given with the table for the condensa- 
tional incident ray discloses certain resemblances as well as contrasts. For 
example, for incidences below 20° there is a strong similarity between the 
two, except that the £ and tj displacements are interchanged. Again, the 
condensational wave with incident angle of 60 ° gives rise to exactly the 
same surface disturbance as the distortional wave with incident angle of 
30 °. In other respects, however, there is contrast rather than similarity. 
The manner in which the tangential displacement for the distortional wave 
passes through a minimum value and increases markedly as the critical 
angle is reached has no counterpart in the behaviour of either component 
in the case of the incident condensational wave. The persistence of high 
values for the tangential displacement in the distortional wave is a striking 
feature. This fits in well with the theory developed in the former paper. 
If the second preliminary tremor passes through the mass of the earth as a 
distortional wave, the magnitude of the tangential surface component at 
distant stations at which the angle of incidence is small will declare itself 
by a correspondingly large record on the recording instrument. 
The surface displacements for values of the angle of incidence greater 
than the critical angle may be tabulated in a similar manner, but because 
of the change of phase and the transformation of rectilinear motion into 
elliptic motion the meanings of the quantities tabulated are not exactly the 
same. The displacements in the original incident wave are, as before, com- 
ponents of a rectilinear sinusoidal motion. Their maximum values and 
rj 0 are the resolved parts of the amplitude, and may be represented by the 
sine and cosine of the angle of incidence. But the quantities £ and 77 are 
no longer the resolved parts of an amplitude, but are the semi-axes of the 
ellipse described by each point of the surface. 
