ON THE AFTER-SHOCKS OF EARTHQUAKES. 121 



January ord and September 7th, LSOl, were pretty severe and followed 

 by their own (secondary) after-shocks, fifty or more in number. Their 

 residual eifects were, however, of very short durations, being sensible 

 only for a month or two. Besides, in deducing equation (c), all the 

 after-shocks durins: the first eiofhteen months, some of which were due 

 to the severe ones above named, were taken account of, and, therefore, 

 the conclusion stated at the end of the last paragraph will not be 

 materially atfected by the occurrence at future times of similar severe 

 after-shocks in the Mino-Owari district. 



§ 13. TJie Kumamoto Eartliquake. 



The district about Kumamoto is steadily settlinir down to e(iuili- 

 brium, and there has thus far been no new great earthquake.' The 

 rate of decrease of the frequency of after-shocks seems in this case to 

 tend finally to be a little quicker than according to equation (h). The 

 mean annual frequency at Kumamoto is very well represented by the 

 following equation, — 



1 



•^ 0.0048 -i-=rx 0.0021 4- 2-2 X0.U043 (e) 



in which x denotes time, in years, 1890 being the origin, and ?/ the 

 corresponding yearly number of earthquakes. The values of y cal- 

 culated from this equation for the years 1890, 1891, 1892, and 1893 

 are respectively 208, 89, 38, and 20, ngreeing exactly with the actual 

 numl^rs for these years. 



According to equation (c), the numbers of earthquakes for the 

 years 189-1, 1895, and 1896 would be respectively 12, 8, and 5. 

 Xow, before the earthquake of July 28th, 1889, the average yearly 

 number of shocks at Kumamoto had been 3 or 4. AVe may, therefore, 

 conclude that it would be about seven or eight years from the date of 



1 See Fis. 4. 



