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Art. LVI.—*Notes on the Earthquake of 7th March, 1890, felt at Napier, Gisborne, and other Places*.

[*Read before the Philosophical Institute of Canterbury, 7th August, 1890*.]

#### Plate XLIII.

By the courtesy of Dr. Lemon, I have, since December, 1889, been allowed to receive memoranda of earthquake-shocks as observed by officers of the Telegraph Department at various places in the colony. Up to the present time there has been only one earthquake (the one that forms the subject of these notes) for which the returns received have been sufficient in number to be used for the determination of the position of the earthquake-origin; but the means thus adopted will, I trust, secure what has generally not been secured in the past, a sufficient number of reliable data for determining the origin of any important earthquake in the future.

I need scarcely point out that the officers of the Telegraph Department, most of whom seem to take considerable interest in the subject, have unusual opportunities of aiding the determination of the chief centres of earthquake-disturbance by the only exact method that is possible at present in New Zealand—namely, by means of careful time-observations.

In regard to the particular earthquake referred to, I have rejected all other notices (newspaper and otherwise) as too inexact for the present purpose.

The returns from the several telegraph-offices are as follows:—

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1. Place of Observation. | 2. Observed Time of Beginning of Shock. (N.Z Mean Time.) | 3. Direction of Wave, as reported to have been observed. | 4. Nature of Shock as reported. | 5. Duration. |
---|---|---|---|---|

Napier | 5·25 p.m. | N. to S.(apparently) | Sharp. Clocks stopped. Previous rumbling |
15 seconds. |

Gisborne | 5·25 p.m. | N.E. to S.W. | Very sharp | 30 seconds. |

Feilding | 5·29 p.m. | Not defined | Slight. Vibration continued evenly for | 35 seconds (exactly). |

Taupo (Tapuaeharuru) | 5·29 p.m. | S.E. | Sharp. Peculiarly undulating motion | ½ minute. |

Wanganui | 5·30 p.m. | N.E. to S.W. | Sever (?) | 33 seconds. |

Wellington | 5·30 p.m. | S. to N., then N. to S. | Slight | 4 seconds. |

Blenheim | 5·30 p.m. | N. to S. | Slight. Previous rumblings for a few seconds | 5 seconds. |

Bull's | 5·31 p.m. | N.E. to S.W. | Sharp. | |

Tauranga | 5·35 p.m. | S.E. to N.W. | Severe | 5 seconds. |

*Remarks upon the Above*.—These are all the places from which returns were received: none were sent from Kaikoura, Nelson, Foxton, Masterton, Ohinemutu. The times in all cases are stated to have been checked by New Zealand mean time. The remarks in column 4 are given nearly in the words of the observers (abridged). As usual, very different ideas of the severity of a shock exist in the minds of different persons. The only definite effect noted at any place was the stopping of several clocks at Napier. At Wanganui the shocks are called “severe,” but the effects (for which a separate heading is provided in the forms supplied to the telegraph officers) were only very slight—the shaking of crockery and utensils, without any breakage.^{*} The items in column 3, in the absence of special instruments, are of small or, at least, uncertain value: the newspaper reports in many cases give almost every point of the compass for the apparent direction of the wave, and an officer of the Telegraph Department can hardly be expected to form a much better idea on this point than an outsider.

From the general character of the memoranda forwarded from time to time I should be inclined to place most reliance on the returns from Wellington, Wanganui, Napier, and Gisborne, in the order named; and to these, on account of the internal evidence, I would add the present return from Taupo. The times at Bull's and Blenheim must either be rejected as inconsistent with any hypothesis of the origin—that at Bull's palpably so—or it must be supposed that in those cases local causes gave rise to considerable retardation and acceleration respectively of the rate of propagation.

The first impression on comparing the observations with the map (Pl. XLIII.) would probably be that the epicentrum must be looked for at some point between Ruapehu and Napier. This obviously would not agree with the return from Gisborne, or with the difference of one minute only between Wanganui and Wellington (which must both be taken as good observations).

*Origin found by the Direction of the Wave*.—If we remember that what an observer generally records is the apparent direction of the vibration, not that of propagation; that the normal and transverse movements of an earthquake are at right angles to one another; and that the longitudinal (or normal) motion generally reaches a place first, we should have, when both movements were felt, a fairly good guide of a rough kind to the direction from which the shocks proceeded (assuming the absence of reflection or deflection of the vibrations). When movement of one kind only is reported, as we cannot tell which of the two it is, we must draw two lines on our

[Footnote] * This fact, and the small velocity of propagation, show that the earthquake must be classed as “slight.”

map through each place, one in the given direction, and the other at right angles to it. Doing this with our present data, and attempting to describe the smallest circles that shall touch or cut as many of these lines as possible, we find that two such circles can be described: (1) one, with its centre almost in the centre of the triangle Taupo, Napier, Gisborne (no point within or near this circle could be assumed to be the epicentrum in face of the returns from Wellington, Wanganui, and Tauranga); (2) another circle can be described with a radius of about 38 miles, and a centre (marked A on the map) in the Pacific Ocean east of New Zealand, about 232 miles from Napier or Gisborne, and 300 miles from Wellington. It will be seen that this is consistent with what follows.

*Method of Straight Lines*.—This method may be used with three pairs of places at which the times are alike: Wellington—Wanganui (5·30 p.m.), Napier—Gisborne (5·25 p.m.), Taupo—Feilding (5·29 p.m.). The first two pairs of places (the lines joining which differ most in direction) would give an epicentrum (B) nearly on the 180th meridian, in latitude 40° 54′ S. This point is about 6 miles from the nearest part of the circle (centre A).

*Method of Circles*.—With a velocity of 15 or 15½ miles per minute an epicentrum (C) can be found from the data of the five places Gisborne, Napier, Taupo, Wanganui, Wellington, It is in longitude 179° 38′ W. (180° 22′ E.), latitude 40° 47′ S., about 200 miles from Napier, 290 miles from Wellington.

*Method of Co-ordinates*.—This method includes the two preceding, and, being a fuller application (analytically) of the same facts, must be at least as reliable as a means of ascertaining the epicentrum. It is, however, not reliable for ascertaining the velocity, time at the origin, and depth of the centrum, unless the times are very exact indeed. This is especially the case when the distances of the places of observation from the origin are too nearly equal, as they are in the present instance.

It is important, I think, to note the different value this method has for finding the co-ordinates of the epicentrum and for finding the other unknown quantities. The distinction I have made would take too much space to discuss fully; but I believe it to be mathematically sound. Professor Hutton has omitted to draw this distinction in his paper on “The Earthquake in the Amuri,” Trans. N.Z.Inst., 1888, p. 283.^{*}

[Footnote] * When more than five equations can be formed, the most probable solution is to be got by forming the normal equations, according to the Theory of Errors, from all the equations, rejecting those in which *mistakes*, as distinguished from *errors of observation*, are likely to occur. My remark, of course, is not to be taken as a criticism upon the value of Professor Hutton's paper, which appears to me to be a model for all future workers in the same field in New Zealand.

Taking the times from all the places except Bull's and Blenheim, with Tauranga as origin of co-ordinates, and the line Tauranga—Wanganui as the axis of *x*, then, forming the equations of observation as in Milne's “Earthquakes,” p. 206, and forming the normal equations from them (see Merriman's “Method of Least Squares,” chap. iii.), we have for our normal equations—

*x*), 559,406*x*+97,780*y*+62,892*u*− 9,552*w* =58,622,552,

*y*), 97,780*x*+93,196*y*+45,732*u*−4,952*w* = 11,688,384,

*u*), 62,892*x*+45,732*y*+23,842*u*-2,682*w* = 6,722,086,

*w*), 9,552*x*+4,952*,w*+2,682*u*−

322*w*= 1,008,386;

from which we get

*x*=109 miles (nearly), *y* = 305 miles (nearly);

the deduced values of *v*, *t*, and *z* being, as I have pointed out, unreliable.

The epicentrum thus given (D) is situated in longitude 179° 9′ W. (180° 51′ E.) latitude 40° 38′ S.; it is distant from Wellington 320 miles, from Napier 221 miles, from Gisborne 205 miles. The above normal equations give us the most likely position for the epicentrum, if the observations be of equal weight. I believe we are justified, however, in taking the times of the five places named as of superior weight; but, being unable to assign any figures that shall accurately mark the difference in value, I take the four equations of observation for those places alone, and find an epicentrum (as near the true one as we can get) at E, 179° 49′ W. (or 180° 11′ E.), 40° 54′ S.; 280 miles from Wellington, 198 from Napier. This is very near B and C—10 or 12 miles from either—and is within the circle whose centre is A.

*Time at the Origin*.—From the same five places the following table gives the deduced time at the origin:—

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Place | Distance from E, in Miles. | Time at Origin if Velocity in Miles per Minute be | Time at Origin if Velocity= 15 ½ Miles per Minute, and Depth of Centrum 20 to 30 Miles. | ||
---|---|---|---|---|---|

15 | 15 ½ | 16 | |||

P.M. | P.M. | P.M. | P.M | ||

Gisborne | 197 | 5h.11.9m. | 5h.12.3m. | 5h.12.7m. | 5h. 12.2m. |

Napier | 198 | 5h.11.8m. | 5h.12.2m. | 5h.12.6m. | 5h.12.1m. |

Wellington | 280 | 5h.11.3m. | 5h.11.9m. | 5h.12.5m. | 5h.11.9m. |

Taupo | 265 | 5h.11.3m. | 5h.11.9m. | 5h.12.4m. | 5h.11.8m. |

Wanganui | 280 | 5h.11.3m. | 5h.11.9m. | 5h.12.5m. | 5h.11.9m. |

The first three columns are calculated on the assumption that the distances from the origin = distances from E; the

last column on the assumption that the centrum is at a depth of twenty to thirty miles.

The result of the method of circles shows that we. cannot assume a velocity greater than about 15 ½ miles per minute; hence the time at the origin must have been 5.12 p.m. nearly.

Velocity of propagation =1,364ft. per second, nearly.

*Depth of Centrum*.—No plausible estimate can be made as to the depth of the centrum, the distances being too great, or at least, too great for the degree of accuracy of the time-observations. The origin was probably deep—say between twenty and thirty miles.

*General Remarks*.—I have not received or seen any notice of any extraordinary sea-wave being observed. I do not know that any previously-recorded earthquake can be referred to the same origin, unless it be that of the 30th October, 1879 (though this is doubtful).

The epicentrum has been assumed throughout to be a point, which of course, it is not. It might very well be an area that would include B, C, E, and even D. But we have no means of determining the extent of the disturbed area.