193 
1918-19.] The Propagation of Earthquake Waves. 
practically the same as at the first refraction. Hence the condensational 
waves as they pass through the nucleus and enter the shell again will 
carry with them , 596( = ( 762) 2 ) of the original energy, or almost exactly 
six-tenths. The remainder of the energy will be partly reflected as con- 
densational and distortional waves in the shell at the first surface and 
as condensational waves in the nucleus at the second surface, and partly 
transmitted as refracted distortional waves in the shell at the second 
surface. As may be inferred from diagram III in fig. 8, the refracted 
distortional wave in the shell (B') accounts for most of the energy not 
carried on by the refracted condensational wave (A'). Since *76 is the 
fraction of the original energy which penetrates into the nucleus, the 
fraction of the original energy which proceeds as distortional waves in 
the shell is not greater than -76x - 24=’18. This will reach the outer 
surface considerably later than the condensational wave, and will be 
simply superposed upon the existing disturbances and quite in- 
distinguishable. 
It is interesting to see how the refracted condensational waves will 
emerge at the outer surface. Let a complete ray be EPP'P" (fig. 9), 
meeting the outer surface in P". What is the angle P"CA in terms of 
the angle CEP ? It is easily shown by the simple laws of geometrical 
optics that if y is the angle P"CA and n the refractive index of the 
nucleus, then 
Ay = sin -1 ^— sin r) — sin -1 (^ sin ft) + R 
\an / \a J 
• =sin -1 (P545 sin /3) - sin -1 (2‘5 sin /3) + /3 . 
The following are the values of y corresponding to the successive 
values of /3 increasing by 3° : — 
3° 
6° 
9° 
12° 
15° 
18° 
21° 
23° 35' 
y 
+ 0° IP 
+ 
o 
0 
1— 1 
oo 
0 
o 
1 
-1° 4' 
-3° 28' 
1 
00 
00 
- 17° 56' 
-56° 30' 
The negative signs mean that the corresponding rays EPP'P" intersect 
the diameter EC A somewhere between C and A and meet the surface 
of the earth on the other side of CA. Of the half cone of rays which 
fall upon the upper hemisphere of the nucleus, as shown in fig. 9, those 
whose directions lie between 8 0, 6 and 23 0, 6 emerge on the lower half 
of the terrestrial sphere : and of the rays which form the lower half of 
the cone, the vast majority similarly emerge on the upper part of 
the plane. 
VOL. XXXIX. 
13 
