DETERMINATION OF EARTHQUAKE ORIGINS. 207 



t^ = t — 7n 



t^ = t - p 



t^ = t - q 



t^ = t ^ r. 



Subtracting equation No. 1 from each of the equations 

 2, 3, 4, and 5, we obtain. 



2a^ X 



2«3 X 

 al + bl — 2a^ x 





2\y 

 2h,y 



v^ (tl - f) = v^ (m2 - 2t m) 







v-'iq' 



2t2y) 

 2tq) 

 2tr) 



Now let v"^ = u, and 2v^ t = w. 

 Then 



1. 2«i X + 2h^y -Y li m"^ — w m — a\ + h\ 



2. 2^2 X + 2h.^y + u p"^ — w p = al -^ h% 



3. 2^3 X •¥ 2h^y + u q^ — w q = a% -^ h% 



4. 2a^ X + 2Z>4 y + u r^ — 7« r = a| + &| 



We have here four simple equations containing the 

 four unknown quantities x, y, u, and w. 



X and y determine the origin of the shock. The absolute 

 velocity v equals \/ u. From v and w we obtain t. Sub- 

 stituting X, y, V, and t in the first equation we obtain z. 



We have here assumed that the points of observation 

 have all about the same elevation above sea level. 



If it is thought necessary to take these elevations into 

 account, a sixth equation may be introduced. 



If the propagation of the wave is considered as a hori- 

 zontal one, as would be done when calculating the position 

 of the epicentrnm or point above the origin, by means of 

 the times of arrival of a sea wave, the ordinate z of the 

 first five equations would be omitted. Working in this 

 way the resulting four equations, viz. 



2^1 a; + 26i 2/ + um? — ww} = af + bf 

 &c. &c. &c. 



remained unchanged. 



Applying this method to the same example as that 



