476 



TransacUons. — 2Iiscellancous. 



Taking the times from all the places except Bull's aud Blen- 

 heim, with Tanranga as origin of co-ordinates, and the line 

 Tauranga-Wanganui as the axis of x, then, forming the equa- 

 tions of ohservation as in Milne's "Earthquakes," p. 206, and 

 forining the normal equations from them (see Merriman's 

 " Method of Least Squares," chap, iii.), we have for our normal 

 equations — 



.r), 559,406,r + 97,780// -f62,892»--9,5o2/f = 58,622,552, 



?/), 97,780a; + 93,196// + 45,732?t- 4,952^ = 11,688,384, 



)i), 62,892,r-f 45,732// -i-23,842«-2,682u'= 6,722,086, 



»'), 9,552.1'-}- 4,952;t'-|- 2,682?t- 322/6'= 1,008,386; 



from which we get 



.r=109 miles (nearly), ?/ = 305 miles (nearly) ; 



the deduced values of r, 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 tin:ies 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 observa- 

 tion 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 oA the Origin. — Erom the same five places the fol- 

 lowing table gives the deduced time at the origin : — 



The first thi-ee columns are calculated on the assumption 

 that the distances from the origin = distances from E ; the 



