For some hours, and even for days, after a great earthquake, the shocks are so numerous that it is often impossible to keep count of them. Many local centres spring into activity in different parts of the epicentral area; and, though only the strongest shocks can be identified elsewhere, it is clear that as a rule the shocks felt at any one station are quite distinct from those observed at another. The enormous number of after-shocks that follow some earthquakes can only be realised when they are subjected to continuous seismographic registration; and, even then, countless earth-sounds and the slightest tremors must escape detection. The shocks may, indeed, succeed one another so rapidly that one begins before another ends, and the result is an almost incessant tremulous motion rendered manifest by the quivering of water-surfaces or the swinging of chandeliers. Of the total number of after-shocks, we may form some idea from recent records in Japan. After the Mino-Owari earthquake of 1891, 3,365 shocks were recorded within little more than two years at Gifu, and 1,298 at Nagoya, but neither of these figures includes the shocks felt within the first few hours. Of the Kumamoto earthquake of July 28th, 1889, the after-shocks recorded at Kumamoto until the end of 1893 amount to 922; and those of the Kagoshima earthquake of September 7th, 1893, recorded at Chiran until the end of January 1894, to 480. During the first 30 days, the numbers recorded were 1,746 at Gifu, 340 at Kumamoto, and 278 at Chiran; showing, as Professor Omori remarks, that the after-shocks diminish in frequency with the size of the disturbed areas,[92]--_i.e._, roughly with the initial intensity of the shocks. Next to absolute number, the rapid decline in general frequency is the most marked characteristic of after-shocks. Professor Omori has shown that, excluding minor oscillations, it follows the law represented geographically by the curves in Fig. 51, and algebraically by the equation y = k / (h + x), where _y_ is the frequency at time _x_ and _h_ and _k_ are constants for one and the same earthquake. By means of this formula, it is possible to estimate roughly the interval of time that must elapse before the seismic activity of the central district resumes its normal value. For the Mino-Owari earthquake, this proves to be about forty years, for the Kumamoto earthquake about seven or eight years, and for the Kagoshima earthquake about three or four years. In a recent memoir on Italian after-shocks,[93] Dr. Cancani has urged that other factors besides initial intensity determine the duration of a seismic period, and prominently among these he places the depth of the seismic focus. When the depth is very small, the duration of the period is short, not much more than ten days; when the depth is moderate, the duration may extend to three months; and, when great, it may amount to several years.