214 
The N.Z. Journal of Science and Technology. 
[Nov. 
considered, however, the records at Apia show a sharp initial impulse, and 
not a small preliminary tremor followed by a larger one, as would be the 
case if the above explanation were true. A consideration of the depth of 
epicentre also showed that this cannot be the reason of the too early 
arrival of the disturbances at Apia. 
It appears, therefore, that the only explanation is that the preliminary 
tremors really travel considerably more rapidly nearer to the epicentre 
than the speed given by the time curves used. 
New time curves for P, S, and S-P were therefore deduced from the 
epicentre and time of origin obtained by method (2) and the known time 
of arrival of P and S at Apia. These curves are based on the thirteen large 
earthquakes whose epicentres, &c., are given in Table I. These epicentres 
are shown on the map (fig. 1), where they are given numbers according to 
date reference in Table I. From these time curves (shown in fig. 3) the 
epicentres of seventy-seven other earthquakes of 1913-19 were deduced 
according to the first method above— i.e., from the distance and azimuth 
from Apia only. These epicentres are also shown on the map, but with¬ 
out distinguishing numbers. 
The plotted positions of these latter earthquakes show a certain 
amount of irregular distribution, which may be partly due to the error of 
azimuth. On the whole, however, along with the positions of the thirteen 
inegaseisms noted above, they show a pronounced crowding along a line 
parallel to the Tonga Deep but on the west side of it, with none actually 
below the deep. It must be remembered that the crowding is not altogether 
real, owing to the fact that distant earthquakes (say, from the Kermadecs) 
are less likely to be registered, but in spite of this there is a real concen¬ 
tration of epicentres near the Keppel Islands. 
The results do not reveal, as might perhaps be anticipated, any pro¬ 
gress with time of the epicentres in any distinct direction ; and also there 
is no progress evident in the position of a “ swarm ” of fifteen earthquakes 
from the 6th to the 14th June, 1915. These latter earthquakes are shown 
on the map but not specially numbered. The area covered by their 
epicentres was 400 km. long in the N.E.-S.W. direction, and 100 km. 
broad in a direction at right angles. 
IV. Time Curves.* 
Between 0° and 20 °.—As has been mentioned above, a study of the 
thirteen large Tongan earthquakes gives interesting information in the 
rate of travel of the P and S waves for epicentral distances between 0° and 
20°. The maximum difference between the observed travelling-times and 
those deduced from the curves mentioned is for an epicentral distance of 
6° to 7°, for which the difference for P is about 13 seconds and for S about 
25 seconds. If we assume a thickness of 50 km. for the earth’s upper crust, 
then both P and S would travel wholly through this crust for distances 
up to 6°. It must be remembered that the time curves with which com¬ 
parison is made refer to travelling-times under continents, while in our 
case the waves travel under a deep ocean-bed. It would therefore appear 
that the smaller travelling-times in the latter case may be due to the 
higher elasticity of the earth’s crust under the ocean. The number of 
observations in our time curve is too small to determine with accuracy 
the velocity of the waves in the deepest part of their path through the 
earth-crust and at various depths below the surface of the crust. The 
author hopes to obtain more material for this later, but it may be stated 
in anticipation that the above data indicate that the velocity of S in the 
upper crust under the ocean is 18 per cent, greater than under continents 
* See Hogben, loc. cit. 
