212 The N.Z. Journal of Science and Technology. [Nov. 
at the time was of the order was of *5 to 1 mm., corresponding to a true tilt 
of about half a second of arc.* 
From the. test we may conclude that even in the shaking area the true 
tilt does not highly exceed that which may be expected from z and x — 
i.e., there are no large undulations a few minutes after the time of sensible 
shaking. 
The vibration of the massive pier (IT m. X 0*5 m. X 0-5 m.) supporting 
the telescope could not have affected the observations, being of much too 
large a frequency. 
III. Calculation of Earthquake Epicentres. 
To obtain the epicentres of the thirteen large Tongan earthquakes of 
1907-19 the observations made by the inhabitants of neighbouring islands 
were taken into account, but it was impossible to obtain the correct 
epicentres in this way, as may be done in populated countries, especially 
also as the earthquakes generally originated under the sea. 
For the correct determination of epicentres the records of neighbouring 
seismograph stations were used. Of these stations only one, namely Apia, 
was in the shaking area. The epicentre was determined in two different 
ways, as follows :— 
(1.) Using the records of Apia only. The azimuth of the epicentre 
was deduced from the relation of the components of the ground-motion 
determined from the amplitudes of the first preliminary tremor on the 
north-south and east-west seismograph records. The distance of the epi¬ 
centres was taken from the S-Pf interval according to the known time 
curves. The Gottingen time curve of Gutenberg was compared with 
the time curve of Mohorovicic for the earthquake of the 16th November, 
1917, and that of Zeisig, and the curves found in agreement with one 
another to within one to two seconds for the particular distances used. 
(2.) The epicentres were calculated from the combined records of the 
stations in and around the Pacific, excluding Samoa. The distances of 
the epicentres from the stations used were between 30° and 80°. For 
every earthquake six or seven stations were used, if possible distributed 
in different azimuths, preference being given to those stations with the 
most sensitive and quickest recording instruments. The method of calcu¬ 
lation of the epicentre and time of origin was by successive approxima¬ 
tions, using a graphic method or the method of least squares, and in this 
way reliable results were obtained. 
A comparison of the two methods of calculation yielded interesting 
results. The azimuth from Apia determined by the first method showed 
no systematic error, although, as might be expected, there were individual 
errors. (The various results are given in Table II.) 
Taking the time of origin given by method (2), we can from the known 
time of arrival of the P (or the S) waves at Apia deduce the epicentral distance’ 
of Apia, using the ordinary time curves. The distances measured in this 
way, however, are in all cases too small, the maximum difference being 
2-4° and the mean 1-3°. This difference may possibly be explained by 
assuming that in a tectonic earthquake from an extensive fault there may 
be a lighter disturbance which precipitates the main earthquake. The 
preliminary tremor from the smaller disturbance will be registered at a 
near station but not on far-distant seismographs. In most of the cases 
* It is interesting to note that A. A. Rambant and W. H. Robinson observed an 
oscillation of amplitude 2 seconds of arc in R.A. during the Chinese earthquake of the 
16th December, 1920 (see Monthly Notices Roy. Astron. Soc., 81, p. 454, April, 1921). 
f S = Transverse waves. P = Longitudinal waves.* See Hogben, N.Z. Jour. Sci. 
& Tech., 1920, vol. 3, p. 106. 
