﻿984 
  Mr. 
  J. 
  W. 
  Stewart 
  on 
  a 
  New 
  

  

  the 
  calculated 
  and 
  observed 
  values 
  : 
  — 
  

  

  m. 
  

  

  x 
  c 
  . 
  

  

  K 
  

  

  i. 
  

  

  1 
  

  

  7304 
  

  

  7445 
  (?) 
  

  

  — 
  

  

  2 
  

   3 
  

  

  Standards 
  used 
  

   for 
  calculation 
  

   of 
  constants. 
  

  

  J 
  3472-68 
  

   1 
  2932-82 
  

  

  6 
  

   2 
  

  

  4 
  

  

  2735-71 
  

  

  2736-19 
  

  

  1 
  

  

  5 
  

  

  2639-28 
  

  

  26399 
  

  

  1 
  

  

  I 
  desire 
  to 
  express 
  my 
  thanks 
  to 
  Professor 
  Rutherford, 
  in 
  

   whose 
  laboratory 
  the 
  experimental 
  part 
  of 
  this 
  work 
  was 
  carried 
  

   out, 
  and 
  to 
  Mr. 
  H. 
  G. 
  Lacell 
  for 
  his 
  kind 
  gift 
  of 
  some 
  neon. 
  

  

  Trinity 
  College, 
  Cambridge. 
  

   October 
  1913. 
  

  

  LXXXVII. 
  A 
  New 
  Solution 
  to 
  an 
  Historical 
  Theorem 
  in 
  

   Geometry. 
  By 
  James 
  W. 
  Stewart, 
  B.A., 
  Assistant 
  

   Mathematical 
  Master, 
  Ayr 
  Academy, 
  Ayr 
  *. 
  

  

  CONCERNING 
  the 
  theorem 
  of 
  this 
  article, 
  a 
  letter 
  was 
  

   published 
  in 
  the 
  Philosophical 
  Magazine 
  for 
  the 
  year 
  

   1874 
  (p. 
  354). 
  It 
  had 
  been 
  sent 
  to 
  the 
  Vice-Chancellor 
  of 
  

   Cambridge. 
  The 
  writer 
  refers 
  to 
  an 
  article 
  which 
  appeared 
  

   in 
  the 
  Magazine 
  for 
  1852 
  (p. 
  366), 
  by 
  Prof. 
  Sylvester, 
  who 
  

   gives 
  reasons 
  for 
  supposing 
  that 
  no 
  proof 
  which 
  does 
  not 
  

   employ 
  reductio 
  ad 
  absurdum 
  is 
  possible. 
  Along 
  with 
  the 
  

   letter, 
  however, 
  a 
  direct 
  proof 
  is 
  sent. 
  It 
  had 
  been 
  discovered 
  

   by 
  a 
  Mr. 
  Hesse 
  as 
  early 
  as 
  1842. 
  

  

  In 
  the 
  course 
  of 
  her 
  letter, 
  the 
  writer 
  says 
  the 
  theorem 
  

   appears 
  to 
  have 
  been 
  given 
  out 
  at 
  Cambridge 
  some 
  years 
  

   previous 
  to 
  1852 
  and 
  to 
  have 
  excited 
  the 
  attention 
  of 
  some 
  of 
  

   the 
  first 
  mathematicians 
  in 
  Europe. 
  A 
  direct 
  solution 
  was 
  

   demanded 
  and 
  after 
  a 
  protracted 
  discussion 
  it 
  was 
  concluded 
  

   that 
  none 
  was 
  possible. 
  

  

  Besides 
  Mr. 
  Hesse's 
  proof 
  there 
  are 
  two 
  other 
  apparently 
  

   direct 
  proofs 
  ; 
  they 
  appear 
  in 
  the 
  ' 
  Lady's 
  and 
  Gentleman's 
  

   Diary/ 
  the 
  one 
  in 
  the 
  volume 
  for 
  1857 
  (p. 
  58) 
  and 
  the 
  other 
  

   in 
  the 
  volume 
  for 
  1860 
  (p. 
  84). 
  In 
  the 
  Philosophical 
  

   Magazine 
  for 
  1853 
  (April) 
  a 
  hint 
  as 
  to 
  a 
  direct 
  proof 
  is 
  given, 
  

   but 
  as 
  far 
  as 
  the 
  writer 
  knows, 
  has 
  not 
  been 
  worked 
  out. 
  

   The 
  proof 
  given 
  below 
  is 
  perhaps 
  sufficiently 
  interesting 
  to 
  

   deserve 
  publication 
  and 
  is 
  probably 
  simpler 
  than 
  any 
  of 
  the 
  

   three 
  referred 
  to. 
  It 
  is 
  original 
  and 
  was 
  discovered 
  before 
  

   consulting 
  any 
  of 
  the 
  periodicals 
  mentioned. 
  

   * 
  Communicated 
  by 
  the 
  Author. 
  

  

  