![Thumbnail: [Volume 21, 1888 page 283]](/journals/rsnz/images/rsnz_21/thumbnails/rsnz_21_00_0338_0283_ac_02.gif)
Velocity of Propagation.
Westport, Boatman's, and the epicentrum are nearly in a straight line; and, if d is the distance of the centrum from Westport, and d1 its distance from Boatman's, t and t1, being the time taken by the wave to pass to each place respectively, then we have, on the assumption that the velocity is the same in both cases—
[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]
d2 = v2t2; d12 = v2t12; and t − t1 = 2 minutes. ∴ d2/t2 = d12/t12. (1.) d1t − dt1 = 0. (2.) t − t1 = 2.
Eliminating t1 from these two equations, we have—
[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]
t = 2d/d − d1. Also v = d/t.
The values of d and d1 depend upon the depth at which we place the centrum, and consequently t and v depend upon it also. The following results are obtained for different values of z, which is the depth of the centrum below the surface; the distance of Westport from the epicentrum being sixty-two miles, and Boatman's thirty-six miles:—
If z = 15, then t = 5.15 and v = 12.39, or 1,090ft. per second.
If z = 20, then t = 5.46 and v = 11.92, or 1,049ft. per second.
If z = 25, then t = 5.81 and v = 10.74, or 945ft. per second.
![Thumbnail: [Volume 21, 1888 page 284]](/journals/rsnz/images/rsnz_21/thumbnails/rsnz_21_00_0339_0284_ac_02.gif)
The time the shock took place at the centrum will be between 4h. 4·85m. and 4h. 4·19m., or, say, 4h. 4m. 30s.
But at stations like Ashburton and Christchurch, which are at a considerable distance from the epicentrum, the depth of the centrum will affect the distance very little, and therefore the velocity of propagation calculated from these places will be almost independent of z. Assuming that the time of shock at the centrum was 10h. 4·5m., and that the depth of the centrum was 20 miles, the distance of Christchurch from the centrum will be about 79 miles, and that of Ashburton about 104 miles. The time of shock at Christ-church was 4h. 12m., and at Ashburton 4h. 13·5m.; consequently the velocity of propagation to Christchurch was 10·5 miles per minute, and to Ashburton 11·5 miles per minute, the mean being 11 miles per minute, or 968ft. per second. This indicates the depth of the centrum at 24 miles, and probably about 20 miles is as near an approximation as the nature of the data at our disposal will admit of. The size of the centrum we have no means of estimating.
From this it follows that the wave arrived at the epicentrum at about 4h. 6m., and that the average velocity of propagation along the surface was, from the epicentrum to Boatman's, 1,584ft. per second, and from Boatman's to Westport 1,232ft. per second.
In attempting to locate the epicentrum from time-observations it is assumed that the rate of propagation was the same in different directions; and the result of that attempt agrees so closely with the result arrived at by the methods of greatest intensity and of direction of shock that we may conclude that, to the places used for this purpose, the rate of propagation was approximately the same, and that it was about 12·3 miles per minute, or 1,082ft. per second, along the surface.
If, however, we take the distant stations, we find a much faster rate: to Timaru, 28·4 miles per minute; to Dunedin, 27·4; to Invercargill, 36·1; and to New Plymouth, 29·7 miles per minute. As it is impossible to suppose that the earthquake travelled faster at a distance than it did near its origin, it looks at first as if there must be errors in the time. But if we assume that it travelled at the rate of 12 miles per minute all round, it should have arrived at Timaru at 4h. 18m.; at Dunedin at 4h. 26m.; at Invercargill at 4h. 33m.; and at New Plymouth at 4h. 28m. This supposes errors in time of from seven to eighteen minutes, which could not have been the case. The only possible explanation that occurs to me is that the shock was transmitted with great velocity along the mountains in a south-west direction to Queenstown, and that Invercargill and Dunedin received the shock from there. This would agree with the direction of the shock given at Dunedin,
![Thumbnail: [Volume 21, 1888 page 285]](/journals/rsnz/images/rsnz_21/thumbnails/rsnz_21_00_0340_0285_ac_02.gif)
but it would not agree with the time given at Bealey. The postmaster at Queenstown informs me that the shock occurred there at about 4h. 10m., but he cannot guarantee the accuracy of the clock observed: the direction he gives is N.W. to S.E. The same explanation, however, will not apply to New Plymouth, although, on the other hand, we cannot believe that there is an error here of thirteen minutes in the time. I give this problem up.
Judging from the slow rate of propagation, this earthquake ought to be considered as a small one, notwithstanding the great area over which it was felt; but until we have seismographs to register the amplitude of the wave it will not be possible to compare our earthquakes with those of other countries.