Rev. G. Phillips on the Summation of Series. 435 



On index cut by the edge of the slide, is 186 miles nearly, for 

 the difF. of long, required between the two places. 



The long, of St. Thomas, E.pt 64° 40' 



Thelong. of Antigua, E.pt 61 40 



Diff. of long, as above 186'= 3 6 



Note. — In like manner may the diff. of long, be found in any 

 other case with the above proportion. 

 37, Windsor Terrace, City Road, Feb. 1st, 1832. 



LX. On the Summation of Series. By the Rev. George 

 Phillips, B. A. Fellow of Queen's College, Cambridge. 



[Concluded from page 344.] 



To ' • 1 ^ 



4. 1 O sum the series ^.^ + ^^^^J^ + ^^^r^^ + &c. 



'1/ 1-J/ 

 And 



Jy \-y ^ 2-^ 3 



I — / — ... m — \ I -, — = H 1 + 



Jy yJy y J y ^-y ,»' cf^ 3'" 



r «-2/'J_ /'J_ _ J■^ r ^ _ /' I y"' ' 



'Jy'y Jy.yJyy '" ^^ ^Jy^-y x'^.n s'^jT+T 



&c. 



re+l 



+ ^"+' + &C. 



s'^.llT^^ 



JyyJy v Jy ^-y 



1 hen I XI ■ u = •^-=-'" - ' I y • u 



Jy- m-\ n-\\ n—^Jy.^ m-'. 



w— 1 n — \ n^^^ 



1 "-1 



,7— pm-l - «+l' Jy \^y 



3 K 2 Now 



