■)12 



or 



PROFESSOR KELLAND ON THE THEORY OF WAVES. 

 (l-^.a e'^'^e-^sm e\ b cos 6 (e" "' - p— ') = 



^^ cosa (a £"-■ + /«-'•) {c-6 sin 6 («'-'+ «-«-") } : 

 A 



b (e--- e-' •') _^6 (e"-- e-"-*) {ae'^'-fe-' ') sin 



= ^c(ae'--+/e.-«--)-^6sin0(e«-'+e-«--)(««"-" + /^~"') 



Hence 



1 , 2^ 

 J=-a and "=-sr «<^: 



« = /« + ie"" — e "') sin Q 



■a cos6 (e*~ — e""') 



+ -^-a sm6 — (€"+ e 'n 

 A ax 



~acoae(e'=-e-'^ 

 A 



l_?^a sin (?«-- + <;—-) 

 A 



which being substituted in equation (8), reduces it to 



-'^ b Ub8me-(e''\ ■'-"■•) c\ cos e ^1-^sin d{e"+e-")\ 



b ( £'?■ 



:- COS0 («"-— e""")!^— ^ be sin 6 (e**— e~ 

 c A 



:) + '^6'2(^2. = _,_2..;^ 1 



that is 



_^^Ubc sin 6 -c" {e"+ e-")-4b's\n^ 6 (e'-+ €-"-') + be sin^ (e« = + ?-"•)' | 

 ^* |^>-'_ e-" -^ 6c sin (e'-'- «-'-•)' + X ''' (''"■'- «-"') («^°-'- «-^''-''> ) 



or, therefore, 

 Sir 



27r 



Stt 



27r 



2:11! 6c sin + V^ C-' {e"+ e-'--) + ^ i' sitf {e'=+ e-'-') - ^ 6<r sin (f'--+ f— -? 



^ ^ (,. .- _ s— --) _ ^ 6 ,. sin e {e' •' - e-' -■)-' + ^ 4-' (e"-" - e— -■) (e 

 Let 0=0, then ^=A, and the equation gives 



') (fl) 



^'T » /„«/. 



'" c^ (««'' + e-«")=^(, 



h\ _ „ /^« '» . 



Stt, 



" '') + rlZT i2 . (e« A _ e-« '') (e2 «A _ «-2 « A) 



= ^ (e«A _ e-«*) + (^"J V c^ (, 



g-./.-) ^,;.'«A _g-2./.) 



