592 Transactions. — Chemistry and Physics. 



are considering the same particle — that is, the waves have a 

 period ~ seconds. 



Again, if t be constant, the potential will have the same 

 value when x = Xi, x = Xi -}- 27rO/i, x^ + ^irUji, &c., or the 

 same phase will occm' at intervals from the origin of 27rO/i, 

 which is therefore the wave-length. 



Hence the velocity of propagation = distance between the 

 equipotential surfaces divided by the period = O, which is 

 independent of i, and therefore the same everywhere in an 

 isotropic elastic solid. fi will be the same for all the waves 

 proceeding from the same origin by the same path, provided 

 they travel through an isotropic solid. Hence there will be 

 no confusion between the different phases of the normal 

 waves of an earthquake, or what in seismology we term the 

 " maxima," as at different places they will succeed one another 

 at equal intervals, unless their paths have been through strata 

 differing greatly from one another in character for some con- 

 siderable distance : mere differences in surface strata would 

 not appreciably affect the question. 



The value of fi is given by O'^ = — j^ g, where h = elas- 

 ticity of volume, n = rigidity modulus, in the usual gra- 

 vitation units ; and d = density in units of mass per unit- 

 volume. 



Major Button has shown that the velocity of propagation 

 is constant within the limits of errors of observation,''' and I 

 have always made this assumption in calculating the elements 

 of New Zealand earthquakes. It is here shown theoretically 

 to depend on the hypothesis fhat the waves have travelled for 

 the greater part of the distance through w^hat may prac- 

 tically be regarded as a homogeneous sohd. Hence we may 

 infer that their path has been for the most part through the 

 deeper strata, and that the origins are deep. All these infer- 

 ences are borne out by the investigations of the best-observed 

 shocks in New Zealand, by their self-consistency, and by the 

 comparatively great depth — often twenty to twenty-five miles 

 — which must be assigned to the origins in the cases where the 

 data have been sufficient to determine them. It seems likely 

 that we may, especially with the new instruments, have the 

 means of determining the period of vibration, and (less truly) 

 the amplitude ; these, with the transit velocity, would enable 

 us to draw conclusions as to the structure of the underlying 

 rocks (from the value of fi), and as to the character or amount 

 of the impulse at the origin of disturbance. I have shown 

 elsewhere that the transit-velocity of the normal waves in the 



"Charleston Earthquake." 



