ON THE AFTER-SHOCKS OF EAETHQUAKES. ^25 



slioclxs of a Given Earllupuûc. — If the time relation of the frequency of 

 after-«hocks of an earthquake be represented by an equation, we can 

 readily calculate from it their approximate total number. Thus, if 

 //(I' :'/ij !li---!l„ ^^t' values of 7/ corresponding to x — 0, 1, 2..:)), we see that 



from which inequaliiy we can approxijnately estimate the total number 



(or activity) of after-sliocks, namely, ^z/,,,, // being made suitably 



I) 

 great. To take an example, we have, from e( [nation (c), for the Mino- 



Owari earthquake, — 



145S , 1459^0 3] \ i«.i 



2^'« > ^40.7 X log J — ';,■>. ' X log.io > 2/y« 



Höh 145'.1 



01- Xum > 2840 > £//,„, 



in which /^ denotes the number of shocks at Gifu during twelve 

 hours, from to 12 a.m., on Octo1)er 29th, 1891, and is equal to 

 190, the total number of shocks during two complete years, from 

 October 29th, 1891, to October 27th, 1893, being denoted by the sum 



1459 



^//,„. The calculated value of the latter thus comes out to be 290t) or 

 II 

 2950. The corresponding actual number is 3257. 



Similarly the calculated total number of shocks during ten years, 



73m 



or the sum ^y,„, is found to be some 3600. 







Now the great earthquake of October 28th, 1891, took place at 

 0.37 a.m., and the record of after-shocks at Gifu was not taken till 

 about 2 p.m. of the same day, the number recorded during the 

 remaining 10 hours, from 2 to 12 p.m., being 101. The total 

 number of shocks during the above initial d ly was prob:d3ly not less 

 than 300. 



From these considerations I conclude tliat the entire number 



