10 ART. 1. S. KUSAKABE : FREQÜEXCY OF 



Now, HS tlie frequency is assumed to be proportional to the 

 rate of recovery, we have 



da 



^—'di 



c. k. K. T 



-c. 



h.K.logi^l-^ jLJ^, 



f+T 



where ^, c, k, K and T are all constants, and t is written for 

 t' whose origin may be any instant, provided the proper value is 

 given to the constant ^. 



Hei-e tlie frequency F may be considered to be composed 

 of two terms F^, which is hyperbolic and F2, which is log;nithmic, 

 so that h being a constant 



As the constant T is, in all probability, very great as compared 

 with the other constants c, h and K, the main term is the first, 

 so that the curve of frequency i^ is a little different from a 

 hyperbola. 



When h is given, the curve F^ takes a definite form, but 

 the curve Fi is wholly indefinite so long as T, i.e. the time 

 required by the force to become sufficient to cause the earth- 

 quake, is not known. That is to say, if the time during ivhich the 

 causal agent of the earthquake existed is long, the curve of frequ- 

 ency appi'oaches the hyperbola represented by Fi, but it deviates 

 more and "more from the latter curve as the duration T diminishes. 

 For example, the number of after-shocks of an earthquake of an 

 explosive nature is necessarily smaller than that of an earthquake 

 qI' geofertonic origin, and the frequency curve differs more from 



