44 / MODERN SEISMOLOGY 
Second—Incident transversal disturbance, displacement per- 
pendicular to the plane of the paper. 
In this case it is found that no longitudinal disturbance 
arises and that the incident effect is reflected as a transversal 
effect without change. The motion of the ground is entirely 
horizontal and equals twice that of the incident disturbance. 
In this case it is possible to have a tranversal disturbance pro- 
pagated parallel to the surface, the displacement being at right 
angles to the direction of propagation and parallel to the sur- 
face. 
Third—\ncident transversal disturbance, displacement in 
the plane of the paper. 
We assume as the incident disturbance 
xcosé+ésin j) 
(&,, 7, G,) = A(- sin e, 0, cos e) f (e+ V; 
which gives rise to the reflected transversal effect 
x cOS €é-2 sin ‘) 
(Eo, ta» &) = Aa(sin ¢, 0, cos ¢) f (e422 
2 
and the reflected longitudinal effect 
(Es, 73) G) = Az( - cos é’, 0, sin é) f(t+* cos = Z sin ay 
1 
Application of the surface condition gives 
A-A,= — pA, cos 2 e/sin 2 e 
I , , 
A+A,= - ms sin 2 é/cos 2 e 
where yp cos e=cos e’ and p= V,/V, 
the apparent direction of motion of the ground is given by 
ee Al as 
¢/E=tan €=-— sin ée’ cos e/cos 2 e. 
Mb 
This holds as long as cos e+ 1/, but when e is less than the 
value given by cos e= I/y, é’ is imaginary, and complex values 
have to be assumed for A, and A;. The result is a reflexion 
of transversal disturbance with a change of phase while there 
exists a type of longitudinal disturbance in which the amplitude 
diminishes rapidly away from the surface, but which cannot 
in any true sense be regarded as propagated as there is no real 
wave front. 
It is important to note that at the critical angle the vertical 
