PROFESSOR KELLAND ON THE THEORY OF WAVES. 521 



-+^'2,6,6,6, {_(,/«% ^-A^)cos7^^27.0-(^-^-2'--«"+e-/^^'-«^) cos/a 



+ (e/-2*.«.^^-/-2f.«.)^^g^_2^^^(^^/-2s«^^^-/-2..«^^^^gJ3^^ j 



■9' * ^/ V 7, /„»• « ^ »• « ^ 



h. 



or 



2 6y (e " — e *" " ") cos r ^ : 



(c- 6,)2 « 2 7- 6, (e*" " ^ + e- '■ « ^0 cos ?• ^ 



+ 2a2(e 4-e ) r brbgSmr — s a (c — d„) 



-2al(e''-"'' + e-'—'''')rbrb,smrTse(c-b„) 



+ a^rb,b,b, {- (e>"«^+e-/«^)cos/-2y.a-(/-2''"^ + e--^-^''"^)cos/0 



or finally 



(e-6„)' 2 r br if' - + e~ '•«-) cos ?• 



+ 2,{c — bg)l.r o^bsl {e +e )sinr—so — (e +e )sn\r + sd [ 



+ 2rbrb,b, {-(/"%e--^"^)cos7:^27a-(e-^-2'-"^ + e--^-2'-«0cos/^ 



= -"^- 26,(e'"«--e-'-"-)cosra. 



20. This expression is exceedingly simple and symmetrical, and might be 

 very easily applied to any hypothesis respecting the coeflBcients b^ , bi . . . It may 

 be satisfactory, in the first place, to deduce from it the particular form already 

 obtained, art. 10. 



Let b, be the only value of b, then r=s=t=l, and we get 



c'b^e^^+e- "■') cos ^-2 c 6^ 2 sin 2 

 = iL6(e«--e-«^)cosa 



or 



c^ 6 (e" ' + e~ " ^) cos — 8 c b^ sin 6 cos 6 



VOL. XIV. PART II. 4 T 



