12 GWYTHER, Rate of Propagation of an Earth-Tremor. 



Hence the rate of change of momentum is not 

 balanced by the discontinuity of the stresses, except when 

 7 = 0, and in this case there is no finite breadth enclosed 

 within the surface of discontinuity, and the conditions 

 implied as underlying this calculation are not satisfied. 



We may, then, conclude that the requisite conditions 

 cannot be satisfied at the surface if it encloses an area 

 of finite dimensions. 



If, however, we make the further stipulation with 

 regard to the linear dimensions of this area that 2£sinhy 

 shall be comparable with qlt, a quantity of the first order 

 of small magnitudes (namely the distance passed over in 

 a small element of time), we can no longer consider the 

 entrance and exit of an element within the surface of 

 discontinuity to take place at separate intervals of time, 

 and may regard the discrepancies on the two occasions as 

 neutralising each other, and in this case we may regard 

 this as a description of a mode in which a force-system 

 causing local perturbations only, when once established, 

 might travel for some distance as a solitary earth-tremor, 

 of which the rate of propagation is proportional to the 

 eccentricity of the ellipse of discontinuity, and therefore 

 not solely dependent upon the elastic constants. 



The simple sound wave, travelling at the rate ^2li, 

 cannot be similarly treated, and in the compound wave, 

 where the discontinuities cannot be confined to a single 

 surface, the difficulties have been found so great as to 

 preclude its further consideration. 



