THEORY OF A SOLID ISOTROPIC EARTH 4i 
We may thus expect a pronounced effect at a time 
4R 
ae sin ie 
It isa longitudinal effect and may be identified with Wiechert’s 
first reflected effect PR, In practice it is often more pro- 
nounced than P in the case of distant earthquakes, and is then 
of considerable value in determining the position of the earth- 
quake region. The argument may be extended to further 
subdivisions of the arc EO. 
The second or transverse phase begins with S at a time 
z mek sin — 
DONT 2 
Next consider the longitudinal effect which travels by EA 
with velocity V, and is diffracted as a transversal effect along 
AO with velocity V,. The time of arrival is 
rs 2R sin 6,/2 i 2R sin 0,/2 
V; V2 
For different positions of A these effects, which begin im- 
mediately after P, arrive at later and later instants and culmin- 
ate in the brachistochronic path of maximum time which is 
that of regular reflexion determined by 
Vi 
Vz 
But here an interesting point arises. Since 6,+0,=0 we 
get 
cos ,/2 =—cos 6,/2. 
Gi (Ni ON: 
tan a= ‘a — cos = isin 6/2 
and thus we cannot get a real positive value of 9, unless cos 0/2 
is << V,/V,. This implies that if @ is less than the value given 
by cos 6/2 = V,/V, the diffracted effects continue up to S with- 
out any pronounced movement, but if @ exceeds this critical 
value the diffracted effects may be expected to culminate in a 
maximum transversal effect at a time 
_2R sin 0/2 
ZUIN A cos0,/2 
which is later than the arrival of S. This point is of real 
practical importance. With the values of V, and V, as given, 
