170 JiEPORT — IfcOC). 



(c) On the Prohahle JVature and Vdocitij of Propaijation of the 

 Movements resulting from an Earthquake Disturhance. 



If it is assumed that the crust of the eartli has the character of an 

 isotropic elastic solid, then from an earthquake centrum two types of 

 Avaves may emanate. In one of these the direction of vibration of a 

 particle is parallel to the direction of propagation of the wave or normal 

 to its fi'ont, as in a sound wave, whilst in the other it is transverse to such 

 a direction, or, so far as this character is concerned, it is like the move- 

 ments in a ray of light. 



These two types of movements, which are respectively known as 

 condensational and distoi'tional waves, are j^ropagated with different 

 velocities, which depend upon certain elastic moduli and the density of the 

 material. 



These velocities may he respectively expressed by the quantities 

 \/' mjp and s/ njp, where i> is the density of the material, n the modulus 

 of rigidity or resistance to distortion, and ni a modulus depending upon 

 the modulus of rigidity and the bulk modulus or resistance to compression 

 k, which is equal to k + \n. 



The first conclusion to which the theory leads is that the condensa- 

 tional wave has a higher velocity than the distortional wave, and therefore 

 the first ought to outrace the latter. With artificially produced disturb- 

 ances at jwints near to origins in fairly homogeneous earth, a phenomenon 

 similar to this has been observed, but whether the preliminary tremors 

 preceding more decided movements observed at great distances represent 

 condensational waves propagated from an origin is yet uncertain. I'rom 

 experiments made in conjunction with Professor T. Gray to determine the 

 elastic moduli of granite, marble, tufl', clay rock, and slate, and the veloci- 

 ties with \\hich normal and transverse movements have been projDagated 

 in alluvium. Dr. C. G. Knott drew iip the following table as representing 

 aAerage constants involved when determining the velocities with which 

 di.sturbances may be propagated through fairly solid rocks : — 



Density . , . . , . . p = 3 



Eigidity ?i= 1-5 x 10" C.G.S. units 



Eatio of t lie wave moduli . . . mjn = o 



With the above numbers the velocity of a distortional wave would 

 be 2-235 km. per second, while the condensational wave would have a 

 value about double this quantity. Should we accept the i-ecords made of 

 decided movements which had their origin in Japan, but which have been 

 recorded in Europe as representing distortional waves, then our expecta- 

 tions based upon theory closely accord with what has been observed. 



On the other hand, because it has been shown that small vibrations 

 have been noted which have travelled at rates of from 9 to 12 km. per 

 second, the fact must not be overlooked that we are not yet in possession 

 of sufficient constants to apply the theory to all the cases which have been 

 observed. Even if we had the constants referring to the elasticity and 

 density of material in the interior of our earth, when we consider the 

 heterogeneity of the materials through which a disturbance probably 

 passes, as Dr. C. G. Knott and other writers point out, there are serious 

 objections to the assumption that waves with a high velocity are due 

 to the transmission of normal motions, while those with a lower velo- 

 city represent the less rapid transversal vibrations. At every boundary 



