HoGBEN. — Oil the Earthquake of Deccmhcr 27, 1888. 471 



of a minute. The times at Greymouth, Waikari, Sheffield, 

 and Christchurch are also probably correct to half a minute — 

 that is, to the nearest minute. Those at Ashburton and Dun- 

 saudel are more doubtful ; but even the inclusion of these does 

 not give results widely divergent from the others. 



The directions noted are far less satisfactory, probably on 

 account of the apparently twisting character of the movement, 

 or, more strictly, the quick succession of the transverse move- 

 ment upon the normal movement. 



The methods emj)loyed in determining the epicentrum 

 were the methods of straight lines, of circles, and of co- 

 ordinates. The last, however, gives such definite results for 

 the origin itself that it will be enough to state those alone, 

 remarking only that the other methods do not disagree there- 

 with, or show only such slight disagreements as can be ex- 

 plained without any straining of the evidence. 



Taking Greyu:iouth as the origin of co-ordinates, its meri- 

 dian as the axis of x, and the axis of y eastwards, from the 

 times at Greymouth, Waikari, South Malvern, Christchurch, 

 Akaroa, we get the following equations (see Milne's "Earth- 

 quakes," p. 207) : — 



64X + 150//+ 9u-32v= 6,649. 

 138x--f 76// + 16zt-4w= 6,205. 

 U2x + 14:81/ + 25it- 510 = 10,517. 

 mix + 1801/ + 36u -62V = 16,561. 



The solution of these gives us — 



X = 



y = 



118 miles. 



83 miles. 



367, 



.•. V = 19-21 miles per hour (velocity of 

 propagation ) . 

 ^ w = 5,605, .'. t = 7-636 mmutes, 



and time at the origin 9h. 24-364min. p.m. 

 z = 24-2 miles (depth of origin). 

 O on the accompanying map (PI. XLII.) marks the position 

 of the epicentrum : taking this and the depth of the actual 

 centrum to be correct, we find the distances from the centrum, 

 and the time at the origin as found by reckoning back from 

 the times observed at the several places, to be as follows : — 



Greymouth 



Waikai'i 



South Malvern and Sheffield 



Ashburton 



Dunsandel 



Christchurch ... 



Akaroa 



