3.20 Intelligence and Miscellaneous Articles. 



On the line SR s= sum of these as a diameter describe a semicircle 

 SXR, with an ordinate EX=y / l'54x 2-Q4=y / 3 7 1416 DE. Make 

 EY=ED; joinY,X; draw XZ J_ YX, then EZ= V 3*1416 DE, up 

 to this limit the side of the square equal in area to the circle whose 

 radius is DE ; error is only l-855275th. The pentagonal relations 

 of ADEF are obvious. Also the Hindu 3927-1 250ths. Centre of 

 circle MSNTQ is at 0*25 DE towards E ; that of semicircle SXR is 

 below E in SER. 



Further, a V~ =-805995977008235 = 13 x 31 into 



•00199999001739016 = -@2--Ql + -@:175--@n +'(16)16, 



where fij denotes x ciphers after the decimal point. It also 



1 3 



equals g V3 raised to the £ P ower +'000068528140581. 



Now 7(2 v 'l- Vi— VI) = '002661131849229... and if its 

 V = J_ fr° m G on BA,there would result 4HA 2 =3*141595008043 . . , 

 only 3-4 millionths in error. 



January 1864. 



-SECOND NOTICE. 

 BY S. M. DRACH, F.R.A.S. 



I rejoice to find that my paper in the Philosophical Magazine 



for November last has evoked Sir W. R. Hamilton's account 



of Rober's approximation. Herr Rober's Beitriige and Pyra- 



miden tracts are in the British Museum Library — memoirs of 60 



and 28 quarto pages with 4 and 1 lithographic plates. This 



2tt 

 approximation of — 0"'012 is to l-15363556th part. I regret no 



diagram accompanied Sir W. R. Hamilton's paper, but have easily 

 supplemented one from the analysis in page 125. 



If, in the annexed diagram, A C B be an equila- 

 teral triangle, with C D_L to A B, and 



CM =(-y-5=l) CD ' 



let DMK = iDCA=3°45'; then 



O 



CK = -86776704126, 



which is in defect only '000000437, or 1-2 millionth nearly. 

 M.Willich finds hept.ch.: rad : : 105:121 nearly; error 1- 777500th: 



also Y^j — -z , 10 s is wrong by 1-173 millionth, or '(8J5- 

 February 1864. 







