ALGEBRAIC FORMULA. 261 



the next coefficient B ; which, as we have already feen (Art. 7.) 



1 /"* 2<pco£<P 



is equal to —7 / —7. 



From our aflumed equation, fin -1> — , , ' f ■ > we have 



* 7 y/l+E 2 2ECOf<f> 



found $ cof + = K'-'cor»)(cof»-0 (Art g0 bu| fmce froiri 



(i + E 1 2£ COl. <p)^ 



the fame equation it appears that 



cof J, — \/i — fin 2 4/ = . co f ~~ s ==- ; 



T T ^/l+£ 2ECof(p » 



^ (cof <P e) <?(' — £C 0f <?) (cof <P f) 



therefore, •x + e »_ a ecof,' - ( I+e .- atC ofO*' * 



and, dividing both fides by y^'j^^?, 



5 Kl-EC0f^) ( v 



T I+£* 2SCofp ' 



Again, from our aflumed equation, we have 

 e* fin ^ = t'+'.l^c^V and therefore, 



•1 — .• fin *V = , '-'<»** t .^ 



-/i +S* -^2£COf<? * \P) 



Let the product of the correfponding fides of the equations 

 («) and (/3) be taken, and we get 



Cl + e* — 2£Cof <p)t 



Now we have found, (Art. 8.) 4 cof -J, = P('-'cof»)Qcof -.Q 



(i + £* 2£C0f<?) T 



therefore, taking the fum of thefe two equations, it follows that 



"__ (1 — £ 2 )(p (1 — ecof?) 



. , R v . (l+£ l — 2EC0f?>) T 



X \/i — s 2 fin X-f il cof I <! . : ' ••• " ;. 



r rTeTlu I — __l(L=i!l£ ,£(i_s*)g>cof<p 



L (i + e* 2EC0f<p) X (i+f 1 — 22Co£<py 



Vol. II. — P. II. LI Taking 



