210 PROFESSOR A. E. H. LOVE ON THE 



42. In the case of waves of dilatation the argument can lie put in a more definite 

 shape. Let us suppose that, near a place, the waves are plane, so that A is a function 

 of a; and t, and let us write 



(106) 



so that Vj is the velocity of waves of dilatation when gravitation and initial stress 

 are disregarded. We have the equation 



or 



In considering the passage of waves near a place, we may treat the term ^s*y? in 

 the coefficient of e 1>!zQ A as a constant ; and then the equation is satisfied by putting 



= B cos {2irL- l (x-x l) - V',*)}, 

 provided that 



Since the greatest values of sV are comparable with unity, the value of V\, the 

 local velocity of transmission, is a little less than V I( or the actual value of X + 2/x is a 

 little greater than the seismic effective value. The result (107) may be accepted as 

 being not far from the truth in a region large compared with the wave-length, and 

 small compared with the radius, and situated at a considerable distance from the 

 source of disturbance. 



43. Since the equations of type (104) contain the dilatation as well as the 

 components of rotation, it appears that the customary law of independence of waves 

 of dilatation and waves of distortion ceases to hold when gravitation and initial stress 

 are taken into account. It appears also that the velocities of propagation, both oi 

 those waves which are mainly dilatational and of those which are mainly distortional, 

 depend on the wave-lengths, and, for the same wave-length, they vary from place to 

 place. When the theory can be developed further, these results may possibly prove 

 to be Useful in explaining the observed irregularities in the propagation of the 

 tremors which are recorded in the case of great earthquakes. The high values which 

 seismic observations lead us to attribute to the elastic constants of the earth as a 

 whole are in accord with Lord RAYLEIGH'S view* that great initial stress increases 



the effective values both of resistance to compression and of rigidity. 



i i ' 



* Lof. fit., ante, p. 173. 



