34 ART. 6.— S. KUSAKABE : 



APPENDIX. 



Relation between the Velocity of Propagation and 

 the Amplitude of Seismic Waves. 



It is a well known fact that, in any earthquake, the principal 



shocks are always preceded by tremors of small amplitude. On the 

 supposition that the waves of the tremors arid of the principal shocks 

 are all generated simultaneously at one and the same origin, the 

 above facts show that the velocities of the tremors are much greater 

 than that of the principal shocks. Indeed, according to Professor 

 Ümori (1) , the velocities of the first and second tremors are equal to 

 12*8 and 7*2 kilometres per second, while that of the principal shocks 

 is only about o\3 kilometres per second. An explanation of this fact 

 is given by Professor H. Nagaoka in his essay above cited, from the 

 consideration that there exists a stratum of maximum velocity of 

 propagation in the earth's crust. The causes of this simple fact must 

 possibly be of a very complicated nature. In so far, however, as the 

 wave-velocity is a function of the elastic constants, the elastic yielding 

 can never be disregarded in the determination of the velocities of 

 seismic waves. In the case of sound waves, the Newtonian Velocity 

 deduced from Uoyle's law is much smaller than that found by observ- 

 ation. Taking, however, the heating by condensation and cooling 

 by rarefaction into account, Laplace obtained a result agreeing with 

 experiment. So, in the case of seismic waves, the greater part, at 

 least, of the discrepancy must be due to the assumption of llooke's 

 law. Even in the weakest earthquake, the strain associated with the 

 principal shocks must be, I think, far beyond'the limits of elasticity. 

 If what I have stated above be the case, the effect of the yielding 



(!) F. Omori. Publi. or the E. I. Committee in Foreign Languages. No. 5. 1901. 



