520 PROFESSOR KELLAND ON THE THEORY OF WAVES. 



+ y(e'-»+'«- + e-'^-* + '«--) cos »• + «-?( 



s(e''-'^*'"+e^~' + ^'")cosr + s + ee 



Or since 



+ s(e''-'-* '"' + 6-^-^''') cos r + s-tO] 



&c. &c. 

 this term may be written 



+ 2r(/ + '^"*' + e~' + *-*"")cosr + ;-«0 



which may be written 



c^a. 



= ZlL2rbrb,bA - («/"--+ e-Z-'O cos 7:^27 d - {ef-^^l"' + e-/-^'"/"^) cos/0 

 6, I 



+ (e/-2«/«'- + e-/-2«/«^)cos(/-2*) . + (e/-2»/«^ + e-/-2s/.^) cos (/-20 ^j (3) 

 if r + s + t be denoted by/ 



] y. The remainder of the lower side of our equation is 

 ■?-p 2 6, (e'- « - - e-' « ^) cos >• . 



By collecting these several terms our equation is reduced to the following 

 very simple form : 



(c-6„) a 2r 6, (e"-' + e-'""^) cos r 



— a 2 (e +e )r brbsSair + so 



