370 Messrs. Milne and Gray's Experiments 



necessary. The following are one or two other methods 

 which might be adopted for this purpose : — 



If the time of arrival of a shock at three stations a long 

 distance apart be taken, and an average velocity of propagation 

 assumed, it is possible to construct for each pair of these 

 stations a surface (w r hich will be approximately an hyperboloid) 

 on which the origin will be situated. The mutual intersection 

 of these three surfaces will be approximately the origin re- 

 quired. A correction on this may be obtained from succeeding 

 shocks by instituting a fourth station on a line through the 

 approximate origin and one of the previous stations, and by 

 this means approximating more closely to the velocity of 

 propagation. 



As another method, if we have the times of arrival at three 

 stations close together accurately measured (these give us the 

 direction of propagation and the horizontal velocity), a fourth 

 station at some distance, say one or two miles, but placed ob- 

 liquely to the determined direction, and worked in conjunction 

 with the first three, will give us an hyperbola; and the point on 

 which the direction obtained from the three stations inter- 

 sects this gives us the epicentrum, or point vertically above 

 the origin of the disturbance or centrum. It is possible that in 

 some cases two points of intersection may exist; but the relative 

 intensity of the shock at the two points will be sufficient to allow 

 the proper one to be chosen. A fifth station would render the 

 determination of the epicentrum perfectly definite. 



The most general case for the determination of the centrum 

 from time-observations requires six stations ; and these six 

 stations must not be in the same line through the origin: and 

 even here it is assumed that the velocity of propagation has 

 been the same in all directions. 



By varying the elements which are known — as, for instance, 

 the number of stations at which time was observed, the 

 relative positions of these stations, the directions of vibration 

 observed at various points, the angle of emergence (if for small 

 shocks such an angle is determinable), &c. — we see that a large 

 number of problems may be presented the solution of which 

 will give to us more or less correctly the centrum or epicentrum 

 of the shock. 



The duration of an earthquake-shock is seldom less than 

 one minute, in Ye do, and is often two or three minutes. It 

 must be remarked, however, that, judging from our senses, 

 many of the shocks seem to last only a few seconds. 



The intensity of a shock is evidently best estimated from 

 the maximum velocity of translation produced in a body during 

 an earthquake. This is evidently the element according to 



