ON THE AFTER-SHOCKS OF EAETHQUAKES. 127 



examined particularly, however, there are to he seen in the variations? 



of the latter various .sets of periodic fluctuations (see Figs. 1, 2, 8, 5, 



etc.). 



Earthquakes being isolated or discontinuons events from the 

 nature of tlieir causes, we can from analogy readily conceive why 

 the frequency of those after-shocks which happen in close succession, 

 should present a series of well-marked maxima and minima. 



The fhiduatlons in the decrease of the frequency of after-shocks 

 of an earthquake may he of two kinds ; namely, those which are 

 proper to the earthquake under consideration, and those whose 

 maxima and minima occur at fixed epochs. The former are of the 

 nature of forced oscillations and may disappear after a time; while the 

 latter are of the nature of free oscillations and may hecome finally 

 predominant. 



The amplitude of the fluctuations would evidently increase with 

 the maiïuitude of the earth(iunke. 



As far as I can ascertain from the records of after-shocks there 

 are, besides the diurn:d and annual fluctuations, six diiferent series of 

 periods in the variation of the frequency, whose lengths range from ;i 

 il'W liours to severa.l months. 



These varioii;-. periods h:ive Ijccn obtained by drawing curves 

 tlirough the mean p(«itions of points whose abscissae are equal time- 

 intervals of 1 hour, 2 hours, (i liours, 1 day, 2 days, 5 days, 10 days, 

 or 1 month, and whose ordinates are the numbers of earthquakes during 

 the corresponding intervals. The results given below were obtained 

 by a direct measurement from Figs. 1, 2, o, 5, etc. 



§ 20. The Kumamoto Earthiiiicéc. 



The curves of daily and 2-daily earthcpiake frequencies (Figs. 2 

 and o) respectively indicate periods whose average lengths are 4.() 

 and 12 da vs. 



