8 ART. 1. S. KÜSAKABE ! FREQUENCY OF 



a formula, however, was lately deduced from the loii^arithmic law 

 of yielding, as it was given in the author's papers above cited. 

 The formula is 



„.. J,, /'(27>+i) ir{p+t+i)Y 



' '{r{p+\)jr{2p+t-\-\)r\t+\) 



where'-' ;> is the total amount of recovery at the instant t, both 

 /' and t being reckoned from the instant when the external force 

 is wholly withdrawn, while k and p are constants, of which the 

 former specifies the I'ock and the latter the time-lapse required 

 by the force to attain its maximum. 



Let F be the frequency, then if c is a constant, we have 



Thus we have a logarithmic form for the frequency of at'ter-shocks. 

 A little consideration of the nature of the constant p will make 



it reasonable to neglect the term —^ so long as t is not very large. 



Then we have, for first approximation, 



F=k'logil+ , V„ I 

 -^ I A + Btf 



which is the same as that of Mr. Enya. Again, expanding the 



logarithmic function and taking its first term only, we have Prof. 



( )niori's formula 



h + t 

 Though the resulting formula' for the frequency are tolerably 

 well formed inasmuch as they were tested by Prof. Omori and 



* Tlie Rvmbol F stands for Gaininà-fiinctinn whidi may 1) ■ found in any text-book 

 in intf-gral calciiliis. When p i« a positive integer we have the relation F (p + l; = ]. 2. .3..., 

 (I'-D- P- 



