THEORY OF A SOLID ISOTROPIC EARTH 43 
First—Plane longitudinal disturbance incident. The dis- 
placement &, 7, ¢, due to the incident disturbance may be 
written 
Z 
X 
Q 
Fic. Io. 
: rcosé+zsine 
(&, 1 &)= - A (cos ¢, 0, sin e) flee) 
1 
This gives rise to a reflected longitudinal disturbance ex- 
pressed by 
4 cosé- 2 sin ‘) 
(&,, 12) f) = > As (cos, (AO) sin e)ifi (1+ V 
1 
and a reflected transversal disturbance 
xcose —2Z sin ) 
(Ge) =A (sine) @.«cos:e))iif7 (2+ v 
9 
As the surface must be free from traction we have 
Z,=2,=2Z,=0. 
This leads to the following relations 
A-A,=p A, cos 2é/sin 2e 
I ° , , 
A+A,=— Ag sin 2 e/cos 2 € 
12 
where yw cos & =cos e and p= V/V, 
Thus the apparent direction of motion of the ground is given 
by ¢/&=tan e= — cos 2¢ 
Hence cos emai ( 5 
This relation is of considerable practical importance. 
We have to note that for e=o the resulting motion of the 
ground is mz/ whatever A may be. It is thus impossible to 
have a longitudinal disturbance in which the direction of dis- 
placement is parallel to the surface propagated along the 
surface. 
