Intelligence and Miscellaneous Articles. 



159 



bell-jar filled with pure carbonic acid. Ignition was effected by 

 means of an electric current. The mean duration of the combustion 

 under a pressure of 715 millims. was 8 S, 57. Hence it is the purely 

 physical part of the change in pressure which so strongly influences 

 the activity of the combustion of the fuses. — Comptes Rendus, 

 Nov. 24, 1862. 



SUPPLEMENT TO MR. DRACHMS PAPER ff ON THE CIRCUMFERENCE 

 OF THE CIRCLE^ (PHIL. MAG. SUPPL. DEC. 1862). 



I have since discovered a more rapid series for — , 



viz. 3 



('♦■>•(* 



J _ 



10 4'10 f 



10 13 9-10 1 ' 



+ 



a-io" 



&c. 



t io 18 9\10 s 10 22 10 2 V' 



which must be multiplied by 1+ — - + STjT^y 



If the last, ,be 



2000 



1 2 11 



multiplied by r^ + tttts + T7p> we g et a value true to the thirty-first 



decimal. 



Example. 



1 00 00 07500 00100 04445 77777 



31500 23625 00315 14004 20000 do. X 315 



+ 30 00000 



-11 11111 11111 11563 



31500 23613 89204 02923 0S436 66666 



315 00236 13892 04029 23084 

 15 75011 80694 60201 46154 



36666 

 21833 



66666 

 66666 

 33333 



1575 01811 

 3 15002 

 17325 



Finally, 



=31830 98861 83790 67153 77675 26745 00164 

 In my mode of finding 7r, 



A=3000000-S007 = 2991993 = 3 x 127 X 7853 ; 



21 

 this x =r =3*14159265 = square of circle whose diameter is 2, to 



the 8th decimal place . A = 3 ( 1 000 2 — 5 2 — 1 3 2 ) . 



As 127 is decomposable 5 ways into four squares, as 7853 is thus 

 decomposable 185 ways, and 315 in 17 ways, it is evident that by 

 properly applying Euclid 47, 1., we can construct the side of a square 

 which up to the above numerical limit is equivalent to the aforesaid 

 circle: 7853 = 67 2 +58 2 . 



