10 



quality eaust's tlic jilaocs wlu'ic >uch vaiiatiuns m^'iir to bo oriiiinators of .~ocon- 

 ilarv waves 1^ S ). 



^i in. Effut <i{ liiqnrjn-l. Elastk-it^. 



Till' iai-t lliat till' clastii-ity uf must of tliu siihstaiiws wliicli maki' iij) i\v 

 earth's rnisi i> iiii|>i'iii'<l o| c latis iinwciiullv to iliiiiiiii.-h tiiu oiieruv aiul tlirirfin'o 

 till' aiii]ilitiiilr of caitli'iuaki' inoiioiis ;is tla- \ilir;itioiis spirail fioin tlu: soiiici', 

 ami roiisi'ijiirntlv to limit tlic area iliroiiuiioiit wiiirli any one ilistuihaiicc is felt. 

 1'lit' railli'iiiaki' riii'ij:;v is cxiiiinlid in ovrii-oiiiini; inti'iiial tViriidii williin tin- 

 vilaatinjr mi'diiim, ami takis tiu' I'urm of hiat. This Internal fiirtion is in 

 gcni'i'al of two kinds: in om — the visi-ositv ol' Ihiiils — the lesistanee to relative 

 motion of ailjoinin;^ parts ilepriuls essentiallv on the velocity of that motion, 

 Ijeiuj^, iof lii\v \ rliMJiii-, |iriipciriiiinal lo tln' vrlocitv. Tin- othrr is of a statie 

 charaeter ; it reseuihles the fiietion lirlween .-oliil IkkUi'S in heiug nearly indejien- 

 tlent of the velueity with wliieh the ehanires of form take ])laee, and. in any one 

 suijstanee, flepends ehietly on the extent of the deformation. \i' we cause a 

 viscous tinid to iiiiilcr<ro a cvclic chan^i' oi lorm nr \iilnmt', an aiinMuit ot rneruy 

 will he di.s-i|ialed whiih will lie lapproximatelvl jiroportional to the rapidity of 

 the cliangc, and will lie zero if the chantre taki's ]ilaee inlinitely slowly. If we 

 [lerforni tin- .sime operation with an ini]>erfi'ctlv elastic solid, an aiiiouiit ot 

 eueri^y will lie di.—ipatcd which will he nearly imlepenilent 'if the lale of de- 

 formation, and will not vani-li when the change takes phve inlinitely .-Idwlv, lint 

 will lie irrealer in prii|ioition to the whole amount of work involved in the 

 operation the j^reater the amplitude of defurmatioii is. since the body's elasticity 

 is more nearly perfect foi' small strain- than fir lari^ie ones. 



The clfcct of vixipsiiy on \ ibralion-- propiipiled by a llnid has been examined 

 mathematically by ."^tokcs-, who has -hown that besides reiiuciim- the amplitude 

 more nipidly than the .s|>readin'r of the wave involves, it makes the veliKMty of 

 prupai^atioii less than it would otherwi.si; be. IJoth elfects are irrealer fur waves 

 of short jieriod than fir waves of lontj jteriuil. 



The writer is not aci|nainti d with any inve.-tii;ation ol the effect of impel feet 

 elasticity mi \iliialions tiansmitted bv solids. if, as ajipcars probable, its etfeet is 

 to reduce tin; velocity of propagation, as well as the amjilitude, we should expect 

 to find this reduction less for waves of small amplitude than for waves of laige 

 amplitude, .since the .«trains involved in waves of small amplitude wmild lie 

 w ithin or nearer to the so e;illed limits of elasticity, inside of which the siibst.iiiee 

 obeys Hookc's Law. And further, in a uroiip of waves whosi' amplitudes were 

 uneijual, the tendency woiilil be for tlinse whuse amplitudes were large to lose 

 more energy tlian the otlicis in propoiiion to their whole stock, and henee 

 differences of amplilnde would be reibu'cil. Tims a series of waves origi- 

 nated by doiilile retlcctioiis in p.'issiiig lliiongh a stratum (|^ 7) would tend to have 



* On till' Iiili'i'tiul Ki-K-lidii of I'luiils ill Mutiuu, I'tc. C'aiiiliiiilgo Tiiiiisintioiis, \'ol. \ III : 

 or Repriut of I'upL'is, \'ol. I, p. 101. 



fe 



