318 



Intelligence and Miscellaneous Articles. 



To be closer to the real arrangement presented by nature, the index 

 of refraction of this sphere, 23 millims. in diameter, would be 1*34 ; 

 that being admitted, a condensing lens would be fastened upon it 

 slightly projecting from it (the cornea), and representing a focal 

 distance of fa millim., in the medium 1'34. 



Secondly, in the optical centre of the apparatus, a second con- 

 densing lens would be suspended of the same focal power, fa 

 millim. Their sum, 



1 JL^ 1 



18-50 + 30 ~~ 11-50' 



represents a lens of 11*50 focal length, as is necessary, in fact, to 

 give clear images on the retinie screen. — Comptes Rendus, February 

 22, 1864. 



ON THE GEOMETRY OF MY EIGHTH DECIMAL APPROXIMATION TO 

 THE CIRCULAR CIRCUMFERENCE (PHIL. MAG. JAN. (sUPPL.), 

 FEB., APRIL 1863). BY S. M. DRACH, F.R.A.S. 



In the above-quoted papers I showed that 



21 



63 



3-14159265= — (3,000,000-8007)= — (997331 = 1000 2 -2669), 



20 



20 



and 2669 = 50 2 +13 2 = 35 2 -f 38 2 . This simple approach arose from 

 successively considering 



3-15, 3-15 — -00840 = 3-14160, 3-15--00840--00000735 ; 



where 315, S40, 735 = 3, 8, 7 times 105. In the annexed diagram 



let diameter AB=1000, and 



in the auxiliary right-angled 



triangleDF=50(or38),and 



FE=13 (or 35); whence 



D E= ^2669 = chord B G : 

 supplementary chord 



GA=V 997331. 



Make B K = one-eighth B A. 

 BL = one-sixth BA; KM, 



B KL 



LN J_to BA to circle ; .-. KM 2 : LN 2 : : BK.KA : : BL.LA : : J^'~ 



ChordAH = ™AG 



iber 314159265, true to the eighth decim 



Angle FDE (iorl^S =14° 34' 27"-18 ; for || =42° 48' 48"' 13 

 \ o0/ oo 



GAB = 2°57'40"-87. 



