﻿ARTICLE 
  VII. 
  

  

  A 
  Remarkable 
  Arrangement 
  of 
  Numbers, 
  constituting 
  a 
  Magic 
  

   Cyclovolute. 
  By 
  E. 
  Nutty, 
  Philadelphia. 
  Read 
  before 
  the 
  American 
  

   Philosophical 
  Society, 
  June 
  With, 
  1834. 
  

  

  The 
  Magic 
  Circle 
  of 
  Dr 
  Franklin 
  has 
  been 
  long 
  admired, 
  as 
  em- 
  

   bracing 
  the 
  most 
  ingenious 
  arrangement 
  of 
  numbers 
  ever 
  formed. 
  It 
  

   consists 
  of 
  five 
  sets 
  of 
  circles, 
  of 
  which 
  the 
  first 
  or 
  principal 
  includes 
  

   nine 
  circumferences, 
  bounding 
  eight 
  concentric 
  rings. 
  These 
  rings 
  

   are 
  equally 
  intersected 
  by 
  four 
  diameters 
  or 
  eight 
  radii, 
  on 
  which, 
  and 
  

   in 
  the 
  middle 
  of 
  each 
  ring, 
  are 
  placed 
  the 
  series 
  of 
  integral 
  numbers 
  

   from 
  12 
  to 
  75, 
  both 
  inclusive. 
  In 
  addition 
  to 
  this 
  series, 
  there 
  is 
  an 
  

   auxiliary 
  12 
  occupying 
  the 
  common 
  centre 
  of 
  the 
  rings; 
  and 
  the 
  total 
  

   sixty-five 
  numbers 
  thus 
  disposed, 
  have, 
  as 
  respects 
  the 
  eight 
  rings 
  and 
  

   eight 
  radii, 
  the 
  following 
  remarkable 
  properties. 
  

  

  First. 
  The 
  eight 
  numbers 
  round 
  each 
  ring, 
  with 
  the 
  auxiliary 
  or 
  

   central 
  number, 
  amount 
  to 
  360, 
  the 
  number 
  of 
  sexagesimal 
  degrees 
  

   in 
  a 
  circle. 
  

  

  Secondly. 
  The 
  eight 
  numbers 
  along 
  each 
  radius, 
  with 
  the 
  auxiliary 
  

   number, 
  amount 
  to 
  360. 
  

  

  Thirdly. 
  The 
  four 
  numbers 
  in 
  each 
  semi-ring 
  terminating 
  in 
  a 
  

   principal 
  diameter, 
  intermediate 
  between 
  two 
  particular 
  radii, 
  with 
  

   half 
  the 
  auxiliary 
  number, 
  form 
  the 
  sum 
  180, 
  the 
  degrees 
  in 
  a 
  semi- 
  

   circle. 
  

  

  vol. 
  v. 
  — 
  3 
  B 
  

  

  