§ 2. ]'r/i)rlllf^ of Traii.til. 



Tlic vc'locitv i>r transit :if':i wave tlirouiih an clastic .siilistancu is 



/ M ' 



where II is tlic density (if tlic material ami M is the iiKiihihis uf elasticity I'nr the 

 ])artien!ar kind <if" strain uf which the wave e(ln^ists. I'or liansverse wa\cs in an 

 isotnp|iie solid M i-- the nioduhis of rlL;idity, which, iiilliiwini;- the ndtation uf 

 'riiiinison and Tail (Nat. I'hil. ( 'Iki|i. \' 1 I.I, \\c -ludl (hiiut.' liy )/. 'I'he strain 

 inv(dv((l in the transmission of tlic normal wave consi.^ts in the comjiression and 

 expansion of ;phei'ical shells. At ,anv ]ii>int not m^ar tin' orii;in, this ajiproxiniates 

 vprv olnselv to simple loni:itndinal sli.-iin (extension or comjiression in one <liree- 

 tioii without cliiinL;;e of Intei'al dimensions!, for this the nvxlnhis is /,• -{- ^ n, 

 where /.■ is the modnhr- of volunie elasticity, or reciprocal of the culii<' eomprpss- 

 iliilitv, and ii has the same meaning- as hefori'. Tlie (piantities » and /, have no 

 a.=certain<'d relation to e;ieli other, and mn>t he -e]>arately detei-mined hy exjieri- 

 nienl for any Li'ix'cn suhstaiice. 



As hotli /. and // are e-;sentiallv jiositive the modnlus for the normal wave 

 is the ii'renter of the two, and hence the normal wa\c always travels faster than 



1 • /• 1 • I • • 1 • 1 /t -f- 4 " 'IM 



the transverse wave, tln' ratio o| their veloeitics liemi; . ilie two 



\ n 

 waves will liecome more and more se])arated the farther thev spread. 



When, as will often he the case, the orii;inatinLj imjinlse is iKit siiiiile hut 

 consists of a nnmher of snci'essivi' displaceincnts, ther<' will lie two eronps of 

 waves, normal and transverse. Each irrouii will spread in the form of a spheri- 

 cal shell whose ihichiiess is eipial to (he veloeitv of propati'.at ion of th<' corres- 

 ]iondinu' Iv|k- of v.aves mnlliplicd hy the time diirinL;- \\liiih the orii^inatiiiij; 

 distnrliance has lasted. At a snilicieiit distance fiom the ori<;'in the.sc two groups 

 will, on ai'connt of thcii- dilferent velocities oi propagation, he completelv 

 .•separated", and a ]iai'ticle there will make (list a series of oscillations in the 

 direetion of the lin( el' transit of the wave, and inunedialely afteiwards a .second 

 series in directions pi'rpeiidicnlar to the Ih'st. A parti<le more distant from the 

 origin w ill ex|)erience two corres];onding sets of niovcment.s with an interval of rest 

 hetween them. ( >n the other hand, at jioints nearer the oi'igin the two gronjis 

 will he moi'e or less snper|)osed, hut the iuiti.il di--|ilacement ol' a jiarticle au\'- 

 where will he along the line of transit, ]irovided that any normal wave is 

 transmitted whosi' origination did not oci^ur hit« r than that of the earliest ti-ans- 

 verse wave. The iintial mox-emeni niav he either away from (.r towards the 

 origin, according' to whethci' the initial str:iiii there is one of compression or 

 dilatation. I'rovideil that none ot' the displacements are large and the medium 

 is perfictly elastic, the speed of transit of all the .sej'arate waves in each group 

 will ho the .same. 



