Til (lie niiirc general oa«e, when ;i ict'ia' ti'd as well as a nflcctfd wave exists, 

 if \vu call the amplitiKk' of (lisplacrintiit in the incident wave unity, tlie anipli- 

 tudo of the relletted wave Ls 



/;, cot Ol 



(I cot 



<> cut 



where// anil //, are the densities (if the first and second medium respectively.'^ 

 Also the umj)lifiide of the refracted wave is 



2 sin 

 sin Of 



II, cut li, 

 ' + 



f) cot 



sin . V , 



J' or . we mav wiite ,. > aiul 



sin 0, ■ V, 



I 



cot II, V / V,* \ „ „ 



cot II V, \ \ V- / 



5i 4. I'lcumplc : Cti.\c of an E((i llnjiKiki rrjlci-lnl iil tlit .sHrfiicc. nf ii ■«■d nr hike. 



Observations i>f tlie veloeitv of sound have shown that tiie .sjinil of transit 



of elastic waves is al ion t 1435 metres per second in fresh water, and almnt 332 



V 

 metres jK'r second in air. Ileiice for an earthijuake leaeliing the upper snr- 



face of a sheet of water is 4.3, and 



'■"^ f' = 4.3 y/TTöMn^^. 



cot U 



The ratio of densities '"' is alioiit ().(X)13. The.se data !j:ive f,ir tlic ratio of the 



aniplitiidc ol'iiic relleetcd wave lo the an)])litiide <if the incident wave the val 

 1 — 3300 i/TTl).<)47 tan- 



ue 



1 -j 3300 J 1 + 0.047 tair 



Vt\ writiii;^ this 



— ], 



1 ■ I- 3.300 I ' 1 + 0.047 tair n 

 we see at oiicc that tiu' aiii|)lilude of the relleeted wave i> a Miiuiuiuni \\ hen the 

 |iath ol tile iiicidiia \\a\r is iierpeiidieuhii' to tlie lioinidarv, and inerea-es to 

 unity as the ainileni' iiK-idenci' approaiih'S !(0\ Mveii in perpendicular incidence. 

 however, the relleeted wa\e has an amplitude of O.90iJ4, tliat of the incident 

 wave heinjj unity. From this, and from the fact that the encrsiv of the two 

 waves is a.s the square of their amplitudes, it appears that an eartlipiake is in all 

 oases reflecte<l from the free surface of water with exeeediiiLily little loss. 



* See Green's Jr;illit'iiia(ii';il Papers, p. 238. en- l.nnl liiiyli'igh's '•Soiuit!", !; 270. 



