384 
MR. GEORGE W. WALKER ON 
from the focus it undergoes reduction of amplitude by spherical divergence and 
general scattering as the wave proceeds through the earth ; (2) at each reflexion 
a sudden change of amplitude takes place. # The first factor appears to be much 
too difficult to deal with at present. A tentative law of diminution of amplitude 
suggests itself, viz., S _1 e _AS , where S is the length of the path. The factor would 
then be The numerical labour of testing this is rather serious, and from 
some rough trials I do not think it contains much promise of explaining the 
observations. 
Accordingly, I pass to the second factor, which is within our powers and which 
goes a considerable way to explaining the facts. In so far as it fails it may give a 
clue to the proper form of the first factor. 
Starting with epicentral distance A, Table III. give the corresponding angle e and 
fig. 2 the values of H and V for the first impulse P. For PR„ we divide A into 
(w+l) parts and obtain the value of e corresponding to A/(n+l). Fig. 2 then gives 
the corresponding values of „A 2 , H„ and V„. Thus the horizontal and vertical 
components of motion where PP,„ meets the surface are („A 2 )’ ! H„ and („A 2 ) n V n . 
Table IV. shows the results obtained in this way for different distance A, and 
between each column of magnitudes the time interval between the disturbances has 
CD 
Table 
IV. 
Epicentral 
distance 
A in 
kilometres. 
p. 
Time 
differ¬ 
ence. 
hH 
C'-' 
Time 
differ¬ 
ence. 
Time 
differ¬ 
ence. 
pr 3 . 
Time 
differ¬ 
ence. 
pr 4 . 
seconds. 
seconds. 
seconds. 
seconds. 
1,000 jy 
1-62 
2 
0-25 
1 
0-12 
0 
0-076 
0 
0 
045 
0-83 
0-086 
0-047 
0-031 
0 
021 
2,000 <f y 
1-60 
15 
0-084 
O 
O 
0-018 
1 
0-0091 
1 
0 
011 
1-20 
0-043 
0-0080 
0-0039 
0 
0049 
f H 
3,000 | y 
1-38 
40 
0-17 
10 
0-0044 
4 
0-00078 
1 
0 
00040 
1-48 
0-094 
0-0022 
• 
0-00036 
0 
00018 
6,000 
0-93 
144 
0-59 
55 
0-067 
25 
0-0018 
9 
0 
000023 
1-79 
0-64 
0-050 
0-0011 
0 
000013 
9,000 
0-86 
213 
0-71 
118 
0-26 
62 
0-032 
24 
0 
00094 
1-82 
1-12 
0-27 
0-027 
0 
00065 
12,000 |y 
0 ■ 68 
256 
0-70 
182 
0-42 
106 
0-11 
68 
0 
014 
1-89 
1-35 
0-59 
0-12 
0 
012 
been inserted. It should be understood that for each distance the primary incident 
disturbance is taken as unity. 
* It may even be the case that disturbances travelling in different directions from the focus have 
different magnitudes. 
