Determination of the Origin.
1. By Direction of the Shock.—By drawing straight lines on a map through the given places in the directions named, and at right angles thereto in case these directions may be those of the transverse vibrations, we find three possible circles to cut or touch a fair number of the lines drawn, within which the epicentrum is to be looked for: (1.) A circle, centre A (see Pl. XLI.), radius ten miles and a half, an epicentrum within which would agree roughly with Lyell, Sheffield, Greymouth, Hokitika, Rangiora, Waiau, and Kaiapoi (almost). (2.) A circle, centre B, radius thirty miles, agreeing with Hokitika, Sheffield, Rangiora, Christchurch, Lyell, Waiau, Greymouth. Note that this circle has to be made very large to include a fair number of the directions, and is not quite consistent with the probable correct assumption that east to west is the direction of the normal wave at-Greymouth. (3.) A circle, centre C, radius seventeen miles and a half, agreeing with Christchurch, Lyell, Sheffield, Hokitika, Waiau, Rangiora, Oxford, Greymouth, Hurunui, &c.
The circle, centre B, answers to the facts which give at first sight the impression of an origin near Castle Hill; but it is worthy of remark that I did not, with any combination of
the time-observations employed, get an epicentrum situated within that circle.
2. By Time - observations.—Those used were—Rangiora, 7.33;* Greymouth, 7.33;* Westport, 7.34;* Lyttelton, 7.36 ¾;* Lyell, 7.35; Kumara, 7.35; Hokitika, 7.37; Christchurch, 7.37. The remaining times are either of doubtful value, or are inconsistent with any possible theory.
3. Method of Straight Lines (Milne, p. 200).—Four lines are available—those got, namely, from the times at the following pairs of places: (a) Rangiora—Greymouth, (b) Westport-Sheffield, (c) Lyell-Kumara, (d) Hokitika-Christchurch. The intersections of these lines give as possible positions of the epicentrum the six points marked with dots on the map. (d is one of the intersections of the last-named line, Hokitika-Christchurch.) All the points except (d) are within the circle C, and immediately to the north of Lake Sumner. The intersection of (a) and (b) gives D, within a mile of F (see below).
4. Method of Circles (Milne, p. 201).—I tried fourteen or fifteen combinations of the given data, and the positions obtained for the epicentrum are shown with small crosses on the map. Most of these lie in the north-east quadrant of the circle A. E is obtained from Lyttelton, Rangiora, Sheffield, Greymouth, and nearly agrees with Westport. It corresponds to a surface-velocity of six miles per minute, and a time at the centrum of 7.23 ¾ or 7.24 a.m. Its position is about 16 miles almost due north of the south-east end of Lake Sumner.
5. Method of Co-ordinates (Milne, p. 206).—The most satisfactory results are given by the first five of the times named in Method 2. The equations give an epicentrum F, 10 or 10 ½ miles north of the middle of Lake Sumner, 172° 16′ E. long., 42° 34′ S. lat.; velocity, 7.18 miles per minute. The equations show themselves not exact enough to determine either the time at the centrum (they give 7·27 ¼) or the depth of the latter. By trial it is found, however, that a time at the origin 7·26 a.m., and some depth less than ten miles (perhaps less than five miles), will agree best with the position and velocity found.†
Intensity.—Whether we take F, E, or D, the velocity appears to have been very small—only 500ft. or 600ft. per
[Footnote] * Most reliable.
[Footnote] † The occurrences reported to have been witnessed at Lake Sarah (N.Z. Journal of Science, vol. i., p. 176; Trans. N.Z. Inst., vol. xv., p. 533) can very well be explained as secondary effects of the earthquake. The statements of damage to the buildings, as far as they are opposed to our conclusion, can hardly weigh against the remaining evidence. Indeed, the damage done to the south-east corner of the Castle Hill Hotel suggests the transverse vibration of a wave proceeding from the north-east—that is, from the epicentrum found.
second—and the earthquake, therefore, a very slight one, as measured by the intensity of earthquakes in other parts of the world.
The technical assumption has been made that the epicentrum is a point; the argument seems to show that it is not of large extent; with our data we cannot determine its size or shape. F, E, D, are all within a few miles of the epicentrum as determined by Professor Hutton (Trans. N.Z. Inst. vol. xx1.), of the earthquake of 1st September, 1888. It is noteworthy also that the geographical distribution of the shock, though not quite so great, is the same, as far as it goes, as the distribution of that earthquake. The fact that both the earthquakes that have injured the Christchurch Cathedral have proceeded from the same place may be worthy of practical consideration in any attempts that may be made to guard against possible damage in the future.