[ 4^9 ] 



/; and that the fum of the feries i — — + 



I 1.2 I. 2. 3 



— — &c. will be the natural number correfponding to 



1.2.3.4 ^ ^ 



Napier's logarithm — /. 



z 

 If / denote Napier's logarithm of the improper fraction — , 



a 



then will — /be Napier's logarithm of its reciprocal — -. 



Therefore, 



a 2 6 2+ 120 720 5040 40320 



P 2 24 120 720 5040 43320 



. ,—=il +— +-^ + — — +&C. 



ao 3 60 2520 



ab iz 300 20160 



— 2, (= )=/' + — +-r-+ T- + &c. 



ab ab ' \% 360 20160 



This feries being; divided by the feries 2 / + — 4. 1 f- &c. 



^ ' 3 ^ 60 2520 



/ /' U in I'' 



the quote will be the feries, — -\ ' • + &c. 



2 24 240 40320 



- Call 



