The point where these wave paths start thickest is at a depth not greater than three geographical miles, and this is considered to be the vertical depth of the focal cavity itself. For the Yokohama earthquake of 1880, from the indications of seismometers, and by other means, certain angles of emergence were obtained, leading to the conclusion that the depth of origin of that earthquake might be between 1½ and 5 miles. Possibly, perhaps, the earthquake may have originated from a fissure the vertical dimensions of which was comprised between these depths. A source of error in a calculation of this description is that the vertical motions may have been a component of transverse motions or perhaps due to the slope of surface waves. The following table of the depths at which certain earthquakes have originated has been compiled from the writings of several observers. +---------------------------------+-----------------------------+ | | In feet | +----------------+----------------+---------+---------+---------+ | | | Minimum | Mean | Maximum | | Rhineland | 1846 (Schmidt) | | 127,309 | | | Sillien | 1858 (Schmidt) | | 86,173 | | | Middle Germany | 1872 (Seebach) | 47,225 | 58,912 | 70,841 | | Herzogenrath | 1873 (Lasaulx) | 16,553 | 36,516 | 56,477 | | Neapolitan | 1857 (Mallet) | 16,705 | 34,930 | 49,359 | | Yokohama | 1880 (Milne) | 7,920 | 17,260 | 26,400 | +----------------+----------------+---------+---------+---------+ A table similar to this has been compiled by Lasaulx.[86] With the exception of the determination for the two last disturbances these calculations have been made with the assistance of the method of Seebach, which depends, amongst other things, on the assumptions of exact time determinations, direct transmission of waves from the centrum, and a constant velocity of propagation. Admitting that our observations of time are practically accurate, it appears that the other assumptions may often lead to errors of such magnitude that our results may be of but little value. From what has been said respecting the velocity with which earth disturbances are propagated, it seems that these velocities may vary between large limits, being greatest nearest to the origin. If we refer to Seebach’s method, we shall see that a condition of this kind would tend to make the differences in time between various places, as we recede from the _epicentrum_, greater than that required for the construction of the hyperbola. The curve which is obtained would, in consequence, have branches steeper than that of the hyperbola, and the resultant depth, obtained by the intersection of the asymptotes of this curve with the seismic vertical, indicates an origin which may be much too great.