then.' will ill iiriuTal lie :i ijivat deal ol c|inVa<-tioii : tlir liinil> i>t lln' >liailii\v 

 will lie ill (lefiiiod, ami iinlfss tlie olistai-lc i.< vi'iy laru,e or (he ohsiTviiii;' station 

 very near it, a connilctc absence of distiirhanee will rarely be found. This is beeaiise 

 of the eonijiaiatively ji-reat ■\vave-lenfj;tli of eaitluinake vibrations: to east a clear- 

 ly defined shadow tlie dimensions of the obstacle ineasnred transvci^se to the path 

 of the incident ray nuist be great coni|)arcd with the wa\'e-li'nirtii of tin' constitn- 

 eiit vibrations — a condition difficnlt to lind fultilled when we are «h'aling with 

 the long-period waves which make np an carthnuako. 



§ 9. Entir/if of Vibiatioiix. 



The energy which must be expended in jirodueiiin' an elastii- wave, and 



which is carried bv the wave as it spreads, depen<ls amongst othei- tilings on (lie 



form of the wave — that is to s:iy, on the relation of displacement to time (hiring 



the passage of the distiirl)ance. In a wave of the simple harmonic type, the 



enei'gy iK-r unit of aiva of wave front is 



2 --r' f> V «- 

 » 



where y is the mean density of the medinm, V the velocity of transit, a the 

 greatest I lisi)lacement oi' a particle from its niulistiirbed position, and r the period 

 of the wave, ^\'le■|| a sjiiiiriral waxc spreads in a imii'orm and [HiCecilv elastic 

 mediiiin, its energy remains constant but is distributed over an area which 

 increases with the stjiiare of" the distance c from tiic origin, and siiu'c the other 

 «piantities are constant (except very near the souri'e), riie aiiiplitudc ol vibration 

 will diminish as the distance from the origin increases, or 



'/ c/: r '. 

 \\ hen, however, till' di>tiirliaikc oeciiis in a stratum « lio.-.c properties diU'cr much 

 from tlioM- ol" adjoining strata, so that lilth' of (Iw energy of the ear(li'|nake is 

 traiisfeiTcd to them, ;ind ihr xilnalions >pread le^aiiy In one plan.' ius(cad of 

 -pliirically, the cncrgv per unit ot area o( \va\r iVoiit will diiiiiiii>ii inailv as (he 

 di>(aiii-e Croiii (I rigiii inci'ea.ses, ami 



'/ cr, r - approxiinalriv. 



I lieri- i.> -onic eviileiice that a c|i>|iirbaii<'i' oi'iiirriiig mi the >iirlaie i>|' tin' soil is 



ill eirtaiii can's propaiiati'd lo .-iirinniidiiiu |>ails of iln' -iiiTaic moic in'aih' in 



this mamiei' tliaii by spliirii-al di^ttibiiiion. 



W hill lelleelioii .'Hid I'el'r.ietioii oreiir a( the boillldar\ of Iwn m.-diiim^. llic 



eiic-igy ol'ihi- inciileiit wave will be .-hau 'd b\- (lie rrlhclcl .-ind rclVail'd waves 



willioiit los'j, exeept in the special casi' where liic a<llicsioii of (he (wo mediums is 



iii-iidicieiit to |(reven( iela(ive sliding during the p;i.s-age of the vibradmis, when 



a poi(ion of the eiicigy will be dis-ipalcd by friction a( the lioiindaiv. A >imilar 



dissipation will oi-eiir a( a lis-nrc in a single mcdiiiiii, if the parts separad'd by 



the lis-iirc <lo not cohere lirinly enough <o |ir<'vent relative motion, .\nolher 



eaiiw of jo^f* of energy by the principal wavt's of an earthi|iiake is the he(eroge- 



iii'itv o|' the vibr.iling iiicdliim, in which everv local variation of mccliaiiical 



