DETEEMINATION OF EARTHQUAKE ORK^INS. 201 



Hopkins gives a method based on a principle similar 

 to the one which is here employed — namely, given that a 

 shock arrives simultaneously at three points to determine, 

 the centre. In this case, the relative positions of the 

 three points, where the time of arrival was simultaneous, 

 must be accurately known, and these three points must 

 not lie in a straight line, or the method will fail. For 

 practical application the problem must be restricted to the 

 case of three points which do not lie nearly in the same 

 straight line. 



II. The method of circles. — Griven the times t^, ^p t^, 

 &c., at which a shock arrived at a number of places Aq, Aj, 

 Ag, &c., to determine the position from which the shock 

 originated. 



Suppose Aq to be the place which the shock reached 

 first, and that it reached Aj, Ag, A3, &c., successively after- 

 wards. 



Let t^ — tQ = a 



t, -t, = b 



^3 - ^0 = ^? &c- 



With Ap Ag, A3, &c. as centres, describe circles with 

 radii proportional to the known qualities a, b, c, &c., and 

 also a circle which passes through Aq and touches these 

 circles. The centre of the last circle will be the epicen- 

 trum. The radii proportional to a, b, c, &c. may be 

 represented by the quantities ax, bx, ex, &c., where x is 

 the velocity of propagation of the shock. 



It will be observed that the times at which the shock 

 arrived at three places might alone be sufficient. If, 

 instead of taking the times of arrival of a shock, the 

 arrival of a sea wave be taken, the result would be a 

 closer approximate to the absolute truth. 



It will be observed that this method is not a direct 

 one, but is one of trial. If, however, an imaginary case 



