PHILOSOPHICAL SOCIETY OP WASHINGTON. 



61 



The computation to 30 places of decimals stands thus : — 

 Ratio of Cikcumference to DiAMETEK = 7r to 30 Decimals. 



FIRST SERIES. 



2.4 

 .16 



.0128 



.001097142857142857142857142857 



97523809523809523809523810 



8865800865800865800865801 



818381618381618381618382 



76382284382284382284382 



7 ! 88920883038530097354 



681055662603650219749 



64862444057490497119 



6204233779412134507 



595606442823564913 



57354694494121066 



5537694640811683 



535905932981776 



51966635925506 



5048187489906 



491174999018 



47858076827 



4669080666 



456049739 



44591530 



4364277 



427521 



41914 



4112 



404 



40 



4 



2.574004435173137547211236914869 



SECOND SERIES. 

 2.40 



.0320 

 .000512 



8777142857142857142857143 



156038095238095238095238 



283705627705627705t;277 



52376423576423576424 



977693240093240092 



18403637460578637 



348700429253070 



6641914271487 



127062707802 



2439603990 



46984965 



907296 



17560 



341 



7 



2.432520936071381533934599150330 



7 



30)17.027646552499270737542194052310 



.567588218416655691251406468410 

 First series == 2.574004435173137547211236914869 



7r= 3.141592653589793238462643383279 



The series (b) 

 ^ = 2 tan - * 



tan ~ ^ — = 2 sin ■ 



2 • 7 



1 



4 2-7 v^S v/50 



could also be used, and the second series is exactly the same as 

 the first, with the consecutive figures removed one figure further 

 to the right, but it does not converge so rapidly as the preceding. 



