220 
The N.Z. Journal of Science and Technology. 
[Nov. 
N. 36° E. In Apia the displacement was 2*02 mm. in a direction N. 30° W., 
whereas the azimuth of the epicentre is N. 23° W. In the later waves 
there would probably be a larger peicentage of movement due to L q 
waves. The actual amplitudes compared above had the same period at 
both stations—namely, 31 seconds. 
In a former paper the author has calculated the coefficient of absorp¬ 
tion of the main waves from the relative amplitudes of the main phase 
and of W 2 the wave through the antipodes of the epicentre.* Measure¬ 
ments have also been made by other observers, and the mean of all the 
measurements (over a hundred) gives for a the value -00027. The 
individual observations are all within 16 per cent.' of the mean value. 
Owing to the great number of earthquakes used in obtaining the value 
of a we may assume that the proportions of the mean paths of the waves 
used under ocean and continent are practically in the ratio of the relative 
areas of ocean and continent on I lie earth’s surface. If we add to the 
continent the area of shallow sea to a depth of, say, 400 metres, the ratio 
is 64 : 36. 
If S 0 be the path under ocean, and S c the path under continent, the 
whole path, S = S c + S c . Then, assuming a wave goes first under ocean, 
and is reduced to intensity I 1 , then under continent, where the intensity 
is reduced to the final I, we have 
I = I 1 e “ <:Sc ,I 1 =I 0 e n ° 8 °, I = I 0 e aS ; 
Wi ence I = I.e“ 8 ° + “ c S< ^= T e~ a ^° + ^ ■ 
S. 
a o + a c S c — a (S G + Sc). 
Sc 
Now, =—p-Q- — ‘64, and " - "cT — ‘36 , 
fc>o -f- fee 
0-64 a Q + 0*36 S c = a = *00027. 
Combining with equation (1) above we may obtain a Q and a c . 
results are as follows :— 
The 
Period 
in Seconds. 
1 
a 
Ocean. 
Continent. 
r 
31 
0-00032 
0-00017 
Horizontal motion .. J 
25 
0-00038 
0-00010 
l 
20 
0-00037 
0-00009 
Yertical motion 
24 
0-00030 
0-C0022 
It will be seen that in all cases the waves are more damped under ocean 
than under continent. For large periods, where there is a large propor¬ 
tion of Rayleigh waves, the difference of damping is smaller than for shorter 
periods. For the vertical component the difference is smaller than for 
horizontal. 
The large absorption of energy under ocean for waves of short period 
(20 seconds) may be due to the fact that in these waves there is a large 
admixture of the natural vibrations of the upper crust (L q ). It may be 
that we have a more fluid magma under the continent block than under 
the ocean, with consequently less damping. It has already been suggested 
* G. Angenheister, Nachr. d. k. Ges. der Jftss. zu Gott., p. 1, 1906. 
