AFTER-SHOCKS AND SPACE-DISTIII I'.UTTOX OF SEISMIC WAVES. 9 



Mr. Enva, the orijrinal formula tor tlic rccoverv is not whollv 

 l»eyoiul question. The assuini)tions under which the fornuila is 

 deduced are very far from what is actually the case in an earth- 

 (juake. Tiie force acting on the rock is assumed to increase 

 intermittently, and, what adds to the difficulty, it is assumed to 

 1)1' withdrawn not suddenly but slowly and intermittently. The 

 tullowino; may be chaser to the actual case. 



Whatever view may be adopted as to the origin of th(> 

 .seismic energy, it is reasonable to consider the force as increasing 

 constantly with time, i.e. 



where k is a constant, and attaining a sufficient amount i^ it acts 

 suddenly to cause an earthquake at the time T, so that we have 



F=^k T. 



Suppose the k)garitliniic law of yielding, which was experi- 

 meiitallv established in the last series of experiments, to be 

 granted, so that 



,l7j = Kdfl0CJ [t+z], 



where ^ is the amount of yielding and K a constant specifying 

 the kind of rock, while r is a constant referring to the choice of 

 origin of time t. Then we have 



y^ = Kh (log{t-\-T) (If. 



If the total force F is suddenly withdrawn at the instant 

 f^T when the original earthquake is supposed to have taken 

 place, it may be easily ])roved that the residual strain at any 

 instant t^-T+t' is «iiven bv 



o=IcK{r^.t' + r]lo>j[^±l±^. 



