TIooBKN.— 0// the EartlKjnake of March 7, ISOO. 475 



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 Welhngton, Wanganui, and Tau- 

 ranga) ; (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 froin Wellington. It will 

 be seen that this is consistent with what follows. 



MctJiod of Straight Lines. — This method may be used with 

 three pairs of places at which the tiiues are alike : Welliug- 

 ton-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. — ^Witli a velocity of 15 or 15i 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 ascer- 

 taining the epieentruni. It is, however, not reliable for ascer- 

 taining 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 ob- 

 servation 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 Earth- 

 quake in the Anmri," Trans. N.Z. Inst., 1888, p. 283. =■= 



* 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 wliich mis- 

 talies, 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. 



