206 EARTHQUAKES. 



The obtaining of a mutual intersection would depend on 

 the assumed velocity, and the accuracy of the result, like 

 that of the method of circles, would depend upon the 

 trials we made. The method here enunciated may be 

 carried farther by describing hyperboloids instead of 

 hyperbolas, the mutual intersection of which surfaces 

 would, in the case of an earth wave, give the actual 

 origin or centrum rather than the point above the origin 

 or epicentrum, 



IV. The method of co-ordinates, — Given the times at 

 which a shock arrived at five or more places, the position 

 of which we have marked upon a map, or chart, to deter- 

 mine the position on the map of the centre of the shock, 

 its depth, and the velocity of propagation. 



Commencing with the place which was last reached by 

 the shock, call these places ^, pj, p^^ p^, and p^, and let 

 the times taken to reach these places from the origin be 

 respectively t, ^,, t^^ t.^, and t^. 



Through p draw rectangular co-ordinates, and with a 

 scale measure the co-ordinates of Pi^p^f Vzt and _2?4, and 

 let these respectively be a^ h^ ; ^3, h^ ; (Xg, 63 ; a^, 64. Then 

 if a?, 2/9 and z be the co-ordinates of the origin of the 

 shock, cZ, c?j, c?2, <^3, and c?^, the respective distances of 

 p9 Pv P2' i^3? and p^ from this origin, and v the velocity 

 of the shock, we have 



1. X"- + y2 + ^2 ^ ^2 = ?j2 f2 



2. («i - xy + (&, - yy -t- ^2 = ^2 f>^ 



3. (a, - xy + (&2 - yy + «2 = ^2 fi 



4. («3 - xy + (&3 - yy + 22 = ^,2 1% 



5. («, - xy + (5, - yy + z" = v' ti 



Because we know the actual times at which the waves 

 arrived at the places p, Pi, p^, p^, p^, we know the values 

 t — ij, t — ^29 ^ — ^35 ^ — ^4* ^^^^ these respectively m, p, 

 q, and r. Suppose t known, then 



