THE PROPAGATION OF THE DISTURBANCE. 119 
Table 9 shows the differences in the time of arrival in seconds, of the first preliminary 
tremors at stations at various distances, when the focus is at the given depth or at the 
surface, calculated under the supposition that the velocity is 7.2 km. /sec. Table 10 
gives similar results for the second preliminary tremors, whose velocity is taken at 
4.8 km. / sec. (see p. 117). In these tables z is the depth of the focus and D the distance 
of the station from the epicentrum measured along the earth’s surface, in kilometers. 
TaBLE 8. — Distances from the Centrum (in kilometers). 







TABLE 9. — Differences between the Times of Arrival of the First Preliminary Tremors 
when the Focus is at the Surface or at the Depth a (in seconds). 




TABLE 10. — Differences between the Times of Arrival of the Second Preliminary Tremors 
when the Focus is at the Surface or at Depth za (in seconds). 






A glance at these tables will show that, for any probable depth of focus, stations at a 
distance from the origin of two or three times this depth would be wholly incapable of 
supplying time records which could be used in determining the depth. Let us take an 
example. Suppose the focus of an earthquake was at a depth of 50 km., and that it was 
recorded at two stations, one 50 km. and the second 100 km. distant from the epicenter ; 
the first would record it 2.9 seconds and the second 1.6 seconds later than if the earth- 
quake had occurred at the same time at the surface. The difference of these numbers, 
namely, 1.3 seconds, is the difference in the interval between the recorded times at the 
two stations, for earthquakes at a depth of 50 km. and at the surface. It would be quite 
impossible to determine so small a difference with any instruments now in use, and there- 
fore such observations could only tell us that the depth was probably not much greater 
than 50 km. But an accurate record at a station, say, 200 km. distant from the origin 
might be used in connection with the records of nearer stations, to show that the focus 
was not very deep. In our determination of the location of the focus of the California 
earthquake we had observations of four stations, and by the method of least squares we 
found its most probable location. The observations at Ukiah and Mount Hamilton had 
no practical influence in determining the depth, but helped to locate the epicenter ; whereas 
the observations at the nearer stations determined the approximate depth. 
The actual points of inflection of the hodographs are not so very near the epicenter, 
their distances being 252, 357, 463, and 796 km. for the depths of focus 10, 20, 50, and 
