42 PROFESSOE HOKACE LAMB ON THE PROPAGATION OF TKEMOBS, ETC. 



whilst fig. 9 shows the corresponding orbit of a surface-particle. In fig. 10 a sketch 

 is attempted of the whole progress of the disturbance. 



These results are of a fairly definite character, but they are based, as has been said, 

 on purely ideal assumptions, and it remains to inquire how far they are likely to be 

 modified by the actual conditions of the earth. The substitution of an internal source 

 for a surface impulse will clearly not affect the general character of the results at a 

 distance great compared with the depth of the source, although differences of detail 

 in the wave-profile at the critical epochs will occur, and we can no longer assume that 

 the disturbance is the same in all vertical planes through the source. Again, the 

 chief qualitative difference introduced by the curvature, of the earth will be that 

 the minor tremor, whose main features are evidently associated with the outcrop of 

 spherical elastic waves at the surface, will be propagated directly through the earth, 

 so that the first two epochs Avill (at distances comparable with the radius) be 

 accelerated relatively to the main shock,* which being due to the Tlayleigh waves 

 will travel, with the velocity proper to these, over the surface.^ 



It is a more difficult matter to estimate the nature and extent of the modifications 

 produced by heterogeneity. It is, perhaps, possible to exaggerate these, for the 

 qualitative effect of a gradual charge of elastic properties would not be serious, and 

 even considerable discontinuities would have little influence if their scale were small 

 compared with the wave-length;}] of the primitive impulse. A covering of loose 

 material over the solid rock probably causes only local, though highly irregular, 

 modifications, with some dissipation of energy. 



It must be acknowledged that our theoretical curves differ widely in two respects 

 from the records of seismographs. In the first place, they show nothing corresponding 

 to the long successions of to-and-fro vibrations which are characteristic of the latter. 

 It would appear that such indications, so far as they are real and not instrumental, 

 are to be ascribed to a succession of primitive shocks, in itself probable enough. 

 Again, the theory gives vertical and horizontal movements of the same order of 

 magnitude, and in the case of the Rayleigh waves, at all events, where a definite 

 comparison can be made, the vertical amplitude is distinctly the greater. The 

 observations, on the other hand, make out the vertical motion to be relatively small. 

 The difficulty must occur on almost any conceivable theory, and appears indeed to be 

 clearly recognised by seismologists, who are accordingly themselves disposed to 

 question the competence of their instruments in this respect, 



* Cf. E. D. OLDHAM, he. cit. 



t The theory of free Rayleigh waves on a spherical surface is known ; see Professor BROMWICH, loc. cit. 



| This term is used in the same general sense in which in hydrodynamics we speak of the " length " of 

 a solitary wave travelling along a canal. There is no question, in the present connection, of anything 

 analogous to " oscillatory waves." 



