ALGEBRAIC FORMULA. 261 



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



, I / 2'pCoi'P 



IS equal to — 7 / ttt' 



From our aflumed equation, fin i^ = . _ . > we have 

 found 4,cof^J. = ^Ii^^lf££^±2£i:^, (Art. 8.) ; but, fincefrom 



(l + e'' 2£ Cof. IpJT 



the fame equation it appears that 



cof ^ = w/i-fm^^= /°'l-' ^, . 



t^^^^fO^^' l/l+E'-.EC0f^' - O+E^-.ECof^^ ■ '■ 



and, dividing both fides by ^-^^^^4=^, 



T i+£» — 2ecofp ' 



Again, from our aflumed equation, we have 

 E' fin '-^ = /^'''."'"fcofV a"'! therefore, 



•i — e'fin'|^= ^ i-.cof^ ^ 



Let the produdl of the correfponding fides of the equations 

 («) and (/3) be taken, and we get 



<).\/i-a'fin'<)/'=:p- ^(^-^'^°^^>' , . 

 Now we have found, (Art. 8.) ^^ cof ^f. = ?Ii=lE££^££^l>=il)^ 



(l + £* 2EC0f?)T 



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



" (i — e')i?'(i ECOf^) 



. . . ^ . (I+e"^ — 2EC0f?>)'^ 



■i VI — e" fin 4- + 64' cof 4- ^ • , • 



Vol. II.— P. II. LI Taking 



