174 



REPORT — 1895. 



Fig. ]G. 



1. Hypotheses of Hupldns and Seebach. 



In 1847 Hopkins drew attention to the fact that the velocity with 

 which a wave passes from one point of the surface of the earth to another 

 point is only an apparent horizontal velocity which may be denoted as v. 

 For example, if in fig. 16 the origin of a disturbance be O, C be its 

 epicentre on the surface of the earth H' H, and Op, Opj be the direction of 

 two earthquake rays, then the apparent velocity is the distance p, p., 

 divided by the time interval between the observations at the two points 

 p, andp,,. During this interval the distance travelled by the wave within 

 the earth has been sp.2. 



The true velocity which may be called V is that with which it travels 



within the earth, as, for example, 

 between the centrum and the epi- 

 centre. To show the relationship 

 between these two velocities it is 

 assumed that the true velocity is 

 constant. On this assumption if C) 

 is a centrum, wave fronts may be 

 represented by circles of coseismals, 

 the distances apart of alternate 

 members of which are equal and 

 represent the distance travelled 

 in unit time, which for conveni- 

 ence may be taken at one second. 

 The true velocity Y is therefore 

 equal to spj, while the apparent 

 velocity recorded on the surface 

 is Pi p.,. Erom the construction 

 sp2=pi p2 sin W, or V=^v sin B. 

 points near to the epicentre C, the 

 greater than the true velocity, while 

 between points at some distance from C tlie two velocities tend to become 

 equal to each other. The law of this decrease in the apparent velocity is 

 shown geometrically by drawing Seebach 's hyperbola, which runs from C 

 through a series of ordinates the lengths of which are equal to the 

 differences between the time at which C was shaken and p, p^, etc, were 

 disturbed. The asymptote to this curve intersects the seismic vertical ac 

 the origin, and therefore if we are satisfied with the hypothesis, having 

 given a number of time observations and knowing the position of the 

 epicentre, the method may be used for determining tlie depth of a seismic 

 focus. 



This hypothesis indicates why a disturbance should apparently be pro- 

 pagated with a high velocity near to its epicentre, but that this rapidly 

 approaches a constant value. 



From this it follows that for 

 apparent velocity is very much 



2. Hypothesis of Schmidt. 



As pointed out by Dr. A. Schmidt, directly we deal with an earthquake 

 which has been propagated over a great distance it is necessary when 

 constructing the velocity curve to take into consideration the curvature 

 of the earth. 



This curve (fig. 17), which has lost its hyperbolic character, shows by 



