DETERMINATION OF EARTHQUAKE ORIGINS. 205 



latter place sixteen minutes or 960 seconds after it was 

 experienced at the former. Calling these places H and 

 M respectively, round m draw a circle equal to the 960 

 multiplied by the velocity with which the wave was pro- 

 pagated. It is then evident that the origin of this dis- 

 turbance must be the centre of a circle which passes 

 through H and touches the circle drawn round M. Join 

 H M, cutting the circle round m in Y. Bisect Y H in v. It 

 is evident that V is one possible origin for the disturbance. 

 Next, from M, in the direction of H, draw any line M z P ; 

 join z H ; bisect z H at right angles by the line o p N. 

 Because ph = PZ, it is evident that P is a second possible 

 origin. Proceeding in this way a series of points lying to 

 the right and left of V on the curve R v T may be found, 

 and we may therefore say that the origin lies somewhere 

 in the curve RVT. By increasing or decreasing our 

 velocity we vary the position of the curve RVT, and, in- 

 stead of a line on which our origin may be, we obtain a 

 band. As the assumed velocity increases, the circle round 

 M becomes larger, and has its limit when it passes through 

 H, where the two arms of the curve RVT will close to- 

 gether and form a prolongation of the line M Y H as the 

 assumed velocity diminishes. The circle round M becomes 

 smaller until it coincides with the point M. At such a 

 moment the curve R v T opens out to form a straight line 

 bisecting M H at right angles. The curve R v T is a hyper- 

 bola with a vertex v and foci H and M. Inasmuch as 

 PM— PH=a constant quantity. If we have the time 

 given at which the shock or wave arrived at a third 

 station as at Iquique, it is evident that a second hyper- 

 bola r' v' t' might be drawn with Iquique and Huanillos 

 as foci, and that the mutual intersection of these two 

 hyperbolas with a third hyperbola, having for its foci 

 Iquique and Mejillones, would give the origin of the wave. 



