The Origin of the Shock or Shocks.
To ascertain this I employed, as usual, the methods depending on the direction, time of beginning of shock, and intensity—the timemethods being, as a rule, by far the most reliable.
1. By the Method of Directions.—Drawing lines through all the places where the apparent direction was noted, we find that a circle with centre B and a radius of 10 miles can be drawn to cut or touch the directionlines for Nelson (N.E. to S.W.), Wellington, Picton, Blenheim, Christchurch, Greymouth, Hokitika, Wanganui; and a circle with centre A and radius 26 miles would agree with these, and with Takaka, Westport, Karamea, Marton, Kaikoura, and nearly with Collingwood, Hawera, Opunake, Otaki. These form most of the places. We should therefore expect the epicentrum to be within or near the circle (B), and almost certainly within the larger circle (A).
(The directionlines must be drawn in the direction noted for each place and at right angles thereto—to include cases where the direction of only the transverse vibrations is given. One of the two directionlines will then be the direction of the line of propagation, unless there has been reflexion, or some other cause of deviation of the waves.)
2. By Timemethods.—(æ) Straight lines, (β) circles, (γ) coordinates. (See Milne's “Earthquakes.”)
(æ) The method of straight lines is available when we have several pairs of places at which the shock was simultaneous; the epicentrum must be equally distant from each of the pair. I have used four such pairs: WellingtonWestport, KaikouraWellington, WestportKaikoura, OpunakeHokitika (an independent pair). All the positions given by the intersections of the equidistant lines are near together, and E_{3}, the mean position, would thus be the epicentrum. This corresponds to a velocity (superficial) of about 58 miles per minute. E_{3} is near the circle (B) and within the larger circle (A).
(The limits of the velocity for E_{3} are 46 miles and 61 miles per minute.)
(β) The method of circles: From the times at Opunake, Wellington, Christchurch, Hokitika, with an assumed velocity of 40 miles per minute, we get the epicentrum E_{1}. To suit this, the Nelson time should have been 8h. 1min. 8sec.; we can hardly allow it to have been quite so early, hence the velocity is probably too small (i.e., if the other times are good). Using Wellington, Opunake, Christchurch, and Nelson (origin deep), with an assumed velocity of 55 miles per minute, we obtain E_{2} for our epicentrum.
The point F is found from the times at Nelson, Wellington, Christchurch, Kaikoura, Opunake. The velocity of
propagation assumed is 50 miles per minute, and this solution agrees also with Wanganui (8·4), and Westport (8·3) nearly, and is only ¼min. out for Picton (8·2).
(y) The method of coordinates: The times in the list (a)—all verified by New Zealand Mean Time, and apparently good times, referring to the same phase of the same shock—were employed. Christchurch was taken as the origin of coordinates, the line ChristchurchHokitika as the axis of y, and the axis of x at right angles (northeasterly).
The reduced equations are—

Opunake), 544x + 196y + ¼u  ½w = 83,588

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Kaikoura), 186x  8y + 9/4u  3/2w = 8,665

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Wellington), 384x  16y + 9/4u  3/2w = 36,928

Nelson), 300x + 110y + 9u  3w = 25,525
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Hence x = 145·15 miles, y = 59·6 miles, v = 493/4 miles per minute = 4,378ft. per second (velocity of propagation), and the time at the origin = 8h. 1min. 20sec. A.M. The point K near F, five miles and a half W.S.W. of Nelson, is the point thus found for the epicentrum. By trial we find that a depth of about 5 miles for the centrum best suits the data.
This agrees within the limits of errors of observation with Westport, and also with Wanganui, if we take the mean of the two observations (both by good observers).
The degree of agreement is shown by the time at the origin as calculated back from each place; it should be the same, of course, from whatever place we reckon.
Time at Place of Observation.  Time at Origin below K, in Minutes and Decimals.  

Christchurch  8·41/2  1·35min.past 8. 
Kaikoura  8·3  1·32" 
Wellington  8·3  1·32" 
Nelson  8·11/2  1·33" 
Opunake  8·4  1·33" 
—  —  — 
Westport  8·3  1·21min.past 8. 
Wanganui  8·4  1·20" 
Picton  8·2 (not checked)  0·88" 
The other places do not give a time at the origin agreeing with this; but the errors are all (or very nearly all) of one sign, and vary from1min. to  3·96min., occurring in groups. Examination of the several groups leads us to suppose that there were several shocks, all nearly below K, the first deep, about 25 miles down, the second higher up, and the third about 5 miles below the surface. At some of the more distant
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places only the deepseated shocks were felt. At Wanganui Mr. Field noted vibrations for 4 or 5 minutes with several distinct shocks (but possibly several maxima of the same shock). At Timaru the first shock, and a later one (about 11/2 or 2 minutes later), were observed. Of all these positions found for the epicentrum, E2 best corresponds with the Nelson observations of direction; but it is possible that, if these observations were those of the transverse vibrations, K, or a place a little to the north of it, would agree equally with them.
It is, of course, most likely that the epicentrum would be an area large enough to include all the places, K, F, E_{2}, E_{2} (epicentric area on map, PI. XLI.). The amount of damage done at Nelson was greater—far greater—than that reported from any other place. It is probable, therefore, that the angle of emergence there was nearly that of the maximum intensity—i.e., between 56° and 45°. This would agree with either K or E2, with a depth of 5 miles for the origin.
The origin might be guessed at with a tolerable degree of probability by the use of isoseismals. Looking at the last column in the table given above, we see that the isoseismal of intensity, vii. on the RossiForel scale, would be drawn outside Picton, Takaka, Collingwood, Wellington, Blenheim; but would have all the other places outside it. An ellipse might be so drawn with a focus not far from the epicentric area (K, F, E3, E2).
3. Intensity.—The maximum intensity of this earthquake was as far above the average of our ordinary mild New Zealand shocks as its velocity of propagation was. The intensity at Nelson was evidently viii. (RossiForel scale), or a little above it.
If a = amplitude of the largest vibration in the motion of any earthparticle, and T = the period of the largest wave, then 4π^{2}a/T^{2} = intensity of shock defined mechanically = destructive effect = maximum acceleration due to the impulse.
Now, Dr. Holden, Director of the Lick Observatory, has given equivalents of the degrees of earthquakeshocks on the RossiForel scale in terms of the acceleration due to the velocity of the shock itself (American Journ. Sci., 1888, No. 210).
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Thus a shock of intensity viii. corresponds to 500mm. per second. We should not probably be far wrong if we gave 600mm.800mm. per second as the measure of the intensity of our present earthquake—or, in other words, from 1/16 to 1/12 of the acceleration due to gravity.
Summary.—The earthquake of the 12th February; 1893, originated below an area within 5 or 6 miles of Nelson, 23
to the south and west. The principal shock took place at 1min. 20sec. past 8 a.m., or thereabouts, at a depth of 5 miles approximately. The velocity of propagation was 4,378ft. per second; the intensity of the shock, measured by the velocity of the earthparticle, about 2ft. per second, or rather more than viii. on the RossiForel scale.
Theory suggested.—The principal shock was preceded by others at a much greater depth, and we may, if we please, imagine a succession of rockfalls (or slidings or crushings) to have taken place in the interior of that portion of the earth's crust underneath the epicentric area K, F, E2, E2.