At any .-tation 5 within the >tiatiini ur 'S' in the intiliiiin lioyuiid, tlio lirst 

 wave ti> anive will lie the tlirwt result of the lelVaetimi ol' the iiieiileiil wave at 

 R. A little later a second wave will arrive, due to a dirteient |iiiiti<ia oC the 

 same original wave-iVuut, whieii has .struck the stratum at 1', heeu ]iaitially re- 

 Heotecl at Q and ao^in partiallx' nllnteil at IL Tin' iutcixal i4' (imi' inlwcin the 

 first wave and this one will I"' the time taken i'or tiie wave to tiavt'l in tiie 

 .-tratuni from ]> to () and IVum (> {<> I,', ji (determined hy drawing;' a iierpen- ' 

 dioular from li on P(^l liein>; tiu' |iiiint ahcady reached in the line J'(t hy (he 

 wa\e-fViint /'/■' when it strikes the stratum at J?. And hy extiiidini; tlie 

 same con.-tinetioM it is olivioiis that a tliini wave will reacii the ohservin^ station, 

 after snU'erinn- fiiur rellections, a fourth after sulfeiine- six reflections, and so on, 

 the iu(er\;d licfween the ,-.ucee.->ive arrival.- heiiij; the same as tlial .-fated almve, 

 namely 



_ 2PQ-Pp 



where A', is tlie velocity of transit tiirnnnh the stratum. 



W'v thus find at any point to the right uf AL, as the result of a .sinjijle in- 

 cident wave, an indefinite series of waves of the same ty|ie, havinj;- the .same 

 direction, with a con.-tanl period r and with amplitudes diminishine; in a i;eome- 

 trical proj;;ressioii. Writiui^' /■ for the perpeiidienlar lliiekiii,~s of the ,-lratuin, and 

 tf^ for the angle whieh the waves in it make with the noinial to its sides, we have 



b , 2/' sin -^, .. 



PQ=: ^ and J',, = ^ '. Heneo 



cos H, cos r/j 



26 eo.s d, 



21, 

 which is a maximum, eijual tu . when the path nf the ineiilent wave is 



* r 

 |H ipendicular U> the stratum, 'i'hc amplitude uf ea<li wave is less than (hat i4' 

 its pri'ilecc.-.<<ir in the ratio n „' : I , w heie /, ; I i> (he ratio in which a wavi' in the 

 stratum is refle-etcd at CD, and u' : I i- the latio in which a wave in fh(! stratum 

 is ifflected at Ali. 



As a simpl(! example, take liie ca.-c i<[' a siin;lc wave uf" cumprc>siun and 

 dilatatiuM iu-ccndinj^ vertically ihruuf^h .a sheet of still water of a uniform ilepth 

 i'[ 10 metres. .\ series of dunhly reflecteil waves will folluw thi- first at a 



. 2x 10 I , 

 iiiiifurm interval of '"' r-, of'a><'coiid. The rate of «Iccay of amplitude in 



the .-crie^ will dcpi'ud .almust whollv on the lii'triec of in)piafectiun of the internal 

 rellecliun at the hottum of the water, since rclleclion isalniusf pcif'c<'t at the upper 

 slirfac«' ( § 4). The ratiu uf |li<' internally reflected to (he ini'idi'Ut wa\e at the 



iMiltiim will l)c cun-iderahle provided fliaf ' ' is not neailv coiial to , |J^ .'?), and 



in .'ictual ca<«'s it will prohaldy he ahoul 4 : .''>. In these cundifions a confinnou- 

 Miiind may he |iriMlu<-e<l with mpidly diminishing londiie.s>i, and he andihie for an 



