[ 431 ] 



whatfoever, fince — = p, — = !; then by fubftitution, — = IfJ'^ 

 i P . a ip-L 



and - r= -J— 



b 2p +L 



This abbreviation Dr. Halley has deduced from contrading into 

 one two terms of the firft feries. 



If wc unite the two firft terms of the feries _ 1 



2 2+ 240 



— - — + &c. we may obtain a method ftill more accurate, which 

 40320 



however requires a fecond operation ; but yet perhaps may be 



preferable to the application of the feries in its original form.— 



/ /' 



The terms — and — — being reduced to a common denominator, 

 2 24 ° 



their value is _ ; which, by a procefs fimilar to that 



24 



which has been ufed above, will appear to be equal to — . 



12 + /' 



— - -) &c. Then by fubftitution the feries becomes 



288 3+56 



6 / /* /' 

 1- . f- &c. It appears then, that the term 



12 + /' 1440 7560 



— - will more accurately rcprefent the entire feries than the 



12+/' ' 



/ h 



two terms 



2 24 



Assume 



