﻿affecting 
  Matter 
  in 
  Diverse 
  Stages 
  of 
  Subdivision. 
  349 
  

  

  radius 
  of 
  a 
  globule 
  [or 
  globe] 
  the 
  mean 
  length 
  o£ 
  path 
  was 
  

   at 
  the 
  commencement, 
  it 
  will 
  remain 
  that 
  same 
  multiple, 
  

   however 
  far 
  the 
  process 
  [whether 
  of 
  subdivision 
  or 
  of 
  inverse 
  

   aggregation] 
  be 
  conceived 
  to 
  be 
  carried. 
  In 
  some 
  relational 
  

   sense, 
  in 
  respect 
  to 
  small 
  scale, 
  we 
  might 
  even 
  speak 
  of 
  an 
  

   setherial 
  medium, 
  or, 
  in 
  respect 
  to 
  big 
  scale, 
  of 
  a 
  stellar 
  medium. 
  

  

  Somewhat 
  in 
  correlation 
  with 
  the 
  present 
  subject 
  — 
  in 
  

   1 
  Nature/ 
  September 
  28, 
  1893, 
  p. 
  517, 
  I 
  ventured 
  critically 
  

   to 
  comment 
  a 
  view 
  of 
  M. 
  Delboeuf, 
  given 
  in 
  Bulletin 
  de 
  

   VAcademie 
  de 
  Belgique, 
  No. 
  6, 
  1893, 
  who 
  contests 
  Laplace's 
  

   conclusion 
  as 
  to 
  the 
  Relativity 
  of 
  all 
  dimensions, 
  velocities, 
  &c, 
  

   in 
  regard 
  to 
  the 
  visible 
  universe. 
  In 
  the 
  abstract 
  of 
  

   M. 
  Delbceuf's 
  paper, 
  Laplace's 
  view 
  is 
  quoted 
  as 
  follows 
  : 
  — 
  

  

  " 
  According 
  to 
  Laplace, 
  if 
  the 
  dimensions 
  of 
  all 
  the 
  bodies 
  

   in 
  the 
  universe, 
  their 
  mutual 
  distances 
  and 
  velocities 
  were 
  to 
  

   increase 
  or 
  diminish 
  in 
  a 
  constant 
  proportion, 
  these 
  bodies 
  

   would 
  describe 
  the 
  same 
  curves 
  as 
  they 
  do 
  now. 
  The 
  appear- 
  

   ances 
  presented 
  to 
  observers 
  would 
  be 
  the 
  same, 
  and 
  inde- 
  

   pendent 
  of 
  the 
  dimensions 
  assumed. 
  Hence 
  the 
  only 
  facts 
  

   we 
  are 
  able 
  to 
  appreciate 
  are 
  ratios/'' 
  (' 
  Nature,' 
  August 
  24, 
  

   1893, 
  p. 
  406.) 
  

  

  It 
  is 
  added 
  (in 
  the 
  abstract 
  in 
  ' 
  Nature 
  ') 
  that 
  conside- 
  

   rations 
  pursued 
  by 
  M. 
  Delboeuf 
  into 
  directions 
  other 
  than 
  

   concerning 
  dimensions 
  alone, 
  " 
  go 
  to 
  show 
  that 
  real 
  space 
  is 
  

   different 
  from 
  geometric 
  space, 
  and 
  that 
  the 
  dimensions 
  of 
  the 
  

   universe 
  are 
  absolute'-' 
  (p. 
  406). 
  

  

  But 
  surely 
  Laplace 
  must 
  have 
  implied 
  that 
  not 
  only 
  velo- 
  

   cities, 
  but 
  forces 
  &c. 
  were 
  supposed 
  to 
  vary 
  in 
  correspondence, 
  

   so 
  as 
  to 
  maintain 
  the 
  previous 
  state 
  of 
  equilibrium 
  undisturbed. 
  

   For 
  if 
  equilibrium 
  were 
  upset, 
  there 
  would 
  be 
  no 
  fair 
  test 
  

   possible 
  of 
  the 
  power 
  of 
  observation 
  to 
  detect 
  a 
  change 
  of 
  

   dimensions 
  accomplished, 
  — 
  which 
  is 
  the 
  point 
  of 
  debate. 
  

  

  In 
  my 
  communication 
  to 
  ' 
  Nature 
  ' 
  or 
  the 
  above 
  date, 
  under 
  

   the 
  same 
  title 
  as 
  that 
  chosen 
  by 
  M. 
  Delboeuf 
  — 
  u 
  Megamicros" 
  — 
  

   I 
  offered 
  as 
  an 
  illustrative 
  case 
  a 
  human 
  being 
  grasping 
  a 
  

   metrically 
  graduated 
  staff 
  equal 
  in 
  length 
  to 
  his 
  own 
  height. 
  

  

  By 
  any 
  supposed 
  reduction 
  in 
  size, 
  simultaneously 
  with 
  the 
  

   dimensional 
  scale 
  of 
  our 
  universe 
  (in 
  extent 
  conceived 
  * 
  ra- 
  

   dially 
  finite), 
  there 
  would 
  be 
  nothing 
  positive 
  to 
  indicate 
  that 
  

   a 
  change 
  of 
  size 
  had 
  effected 
  itself, 
  while 
  the 
  metrical 
  staff' 
  

   grasped 
  by 
  the 
  observer 
  would 
  still 
  be 
  the 
  same 
  length 
  as 
  

  

  * 
  Without 
  necessarily 
  postulating 
  any 
  particular 
  limit 
  to 
  the 
  Cosmos, 
  

   we 
  may 
  perfectly 
  well 
  suppose 
  the 
  above 
  modifications 
  to 
  he 
  confined 
  

   to 
  our 
  universe, 
  i. 
  e. 
  to 
  the 
  known, 
  within 
  the 
  range 
  of 
  telescopic 
  vision, 
  

   — 
  leaving 
  the 
  unknown 
  entirely 
  out 
  of 
  consideration. 
  

  

  