﻿348 
  Dr. 
  S. 
  Tolver 
  Preston 
  on 
  some 
  Physical 
  Relations 
  

  

  We 
  may 
  notice 
  then 
  that 
  the 
  " 
  mean 
  length 
  of 
  path" 
  of 
  an 
  

   ideal 
  stellar 
  mass 
  (generated 
  by 
  inverse 
  aggregation 
  out 
  of 
  

   corpuscules) 
  would 
  be 
  the 
  same 
  multiple 
  of 
  the 
  radius 
  of 
  the 
  

   stellar 
  mass, 
  as 
  the 
  mean 
  length 
  of 
  path 
  of 
  a 
  corpuscule 
  was 
  

   (beforehand) 
  of 
  its 
  radius. 
  Nevertheless, 
  in 
  view 
  of 
  the 
  

   familiar 
  phrase 
  " 
  sparsely 
  scattered 
  stars," 
  the 
  first 
  case 
  

   would 
  be 
  considered 
  as 
  illustrative 
  of 
  Vacuity, 
  while 
  the 
  

   second 
  exemplifies 
  the 
  Continuity 
  of 
  some 
  medium 
  where 
  

   the 
  dimensional 
  elements 
  elude 
  our 
  direct 
  powers 
  of 
  mea- 
  

   surement. 
  Yet 
  in 
  both 
  cases, 
  the 
  dimensional 
  elements 
  (as 
  

   we 
  may 
  note) 
  may 
  actually 
  be 
  similar. 
  

  

  By 
  supposed 
  progressive 
  subdivision 
  of 
  the 
  material 
  under 
  

   the 
  conditions 
  cited, 
  we 
  may 
  observe 
  the 
  globular 
  corpuscules 
  

   thus 
  set 
  free 
  gradually 
  approaching 
  each 
  other 
  (as 
  to 
  their 
  

   geometrical 
  centres) 
  asymptotically, 
  without 
  assignable 
  limit 
  

   as 
  to 
  proximity 
  : 
  — 
  all 
  the 
  dimensional 
  properties 
  of 
  the 
  

   medium 
  thus 
  constituted 
  [including 
  length 
  of 
  mean 
  path] 
  

   diminishing 
  in 
  a 
  like 
  proportion. 
  The 
  recognized 
  Relativity 
  

   of 
  the 
  results 
  reached 
  does 
  not 
  exclude 
  the 
  possibility 
  of 
  

   practical 
  or 
  useful 
  consequences 
  in 
  connexion 
  with 
  the 
  

   economy 
  of 
  Nature, 
  which 
  mental 
  realization 
  may 
  go 
  further 
  

   to 
  develop. 
  

  

  Elementary 
  illustrative 
  methods 
  (wherever 
  possible), 
  may 
  

   be 
  not 
  without 
  their 
  value. 
  If 
  we 
  suppose 
  a 
  cubical 
  element 
  

   of 
  space, 
  with 
  portions 
  of 
  material 
  in 
  spherical 
  form 
  situated 
  

   at 
  the 
  eight 
  corners 
  of 
  this 
  cube, 
  and, 
  for 
  the 
  concept 
  of 
  

   ready 
  subdivision 
  into 
  parts, 
  suppose 
  the 
  material 
  to 
  be 
  a 
  

   continuous 
  or 
  perfect 
  fluid, 
  with 
  a 
  central 
  force 
  acting 
  to 
  

   maintain 
  any 
  portion 
  thereof 
  globular 
  when 
  set 
  free 
  : 
  then 
  

   it 
  becomes 
  evident 
  (illustratively) 
  that 
  when 
  by 
  the 
  sub- 
  

   dividing 
  process, 
  the 
  radius 
  of 
  a 
  fluid 
  globe 
  is 
  reduced 
  to 
  

   one 
  half, 
  eight 
  times 
  as 
  many 
  then 
  become 
  available 
  ; 
  — 
  per* 
  

   mitting 
  eight 
  times 
  as 
  many 
  cubical 
  space-elements 
  to 
  be 
  

   furnished 
  with 
  portions 
  of 
  material 
  at 
  their 
  corners. 
  Then, 
  by 
  

   the 
  simple 
  subdivision 
  of 
  our 
  material, 
  (obviously) 
  the 
  side 
  of 
  

   each 
  cubical 
  space-element 
  [representing 
  the 
  distance 
  of 
  the 
  

   portions 
  of 
  material 
  from 
  centre 
  to 
  centre], 
  becomes 
  exactly 
  

   halved. 
  

  

  Clearly, 
  in 
  this 
  way, 
  by 
  a 
  progressively 
  finer 
  stage 
  of 
  sub- 
  

   division 
  of 
  material, 
  we 
  have 
  reached 
  an 
  exactly 
  similar 
  

   configuration 
  (geometrically) 
  , 
  in 
  regard 
  to 
  relative 
  radii 
  of 
  

   the 
  globules 
  [corpuscules], 
  relative 
  distances, 
  reckoned 
  from 
  

   centre 
  to 
  centre, 
  &c. 
  as 
  those 
  with 
  which 
  we 
  started 
  : 
  — 
  this 
  

   continuing 
  to 
  hold 
  true 
  if 
  the 
  process 
  of 
  subdivision 
  of 
  material 
  

   were 
  carried 
  out 
  without 
  assigned 
  limit. 
  

  

  Accordingly 
  we 
  may 
  observe 
  that 
  whatever 
  multiple 
  of 
  the 
  

  

  