PROFESSOR KELLAND ON THE THEORY OF WAVES. 521 



■+"^l,b,b,b, {-(e/°=--+e~/«->os/-2»-.0-(e-^-^'--''^+e--^-2'-«^)cos/-O 



or 



(c- 6„)2 a 2 >• 6, (/ « - + e- '■ " -") cos J- e 



+ u^rb,b,b, |- {ef''^+e-^'-'')cosf-2r.6-{e^-^''''' + e-J-^'"'')co&fe 



+ ((?•' +e •' )cos/— 2«a+ («•' +e • )(ios/—2tt) i 



=g1b, (/"■' -e-'"»') cos r a : 

 or finally 



(c-6„)' 2 rfir (e'" ■+ e- "') cos ;■ 



+ 2r6,6,6, (-(/"■ + e--''"->os/-2r0-(e-''-^'""- + e--''-^"Ocos/0 



, // — 2t«- , — / — 21,1,.:, 7 — o~ a , ,' / — 2iK.z , „ — / — 2s«^^„„„7 — STT al 



+ (e-' +e ■* ; COS /— 2 6- f + (e-^ +e •' )cos./— zr.fj 



= ^- 2 6, (e'' « -• _ e- >■ "• -) cos /• 0. 

 a. 



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

 very easily applied to any hypothesis respecting the coefficients J, , Jj • • • It may 

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

 obtained, art. 10. 



Let h, be the only value of h, then r=s=t=\, and we get 



<?b{e'-'+ e-«-)cos0-2c6-.2sin20 



= iL6(e«'-_e-«-)cos0 

 a 



or 



c^6(e"- + e~""-)cos — 8 cS'^sin 0cos0 



VOL. XIV. PART II. 4 T 



