﻿PHYSICS 
  OF 
  THE 
  UNIVERSE 
  JEANS 
  165 
  

  

  able 
  to 
  regard 
  the 
  earth's 
  present 
  store 
  of 
  uranium 
  as 
  the 
  remains 
  of 
  

   a 
  supply 
  it 
  originally 
  brought 
  out 
  of 
  the 
  sun. 
  An 
  initial 
  store 
  of 
  about 
  

   10^^ 
  gm. 
  would 
  suffice. 
  

  

  This 
  uranium 
  can 
  not 
  have 
  existed 
  from 
  all 
  time 
  for 
  the 
  average 
  life 
  

   of 
  a 
  uranium 
  atom 
  is 
  only 
  about 
  7,000,000,000 
  years. 
  How, 
  then, 
  did 
  

   it 
  come 
  into 
  being? 
  Was 
  it 
  created 
  in 
  the 
  sun, 
  or 
  did 
  the 
  sun, 
  like 
  the 
  

   earth, 
  start 
  life 
  with 
  a 
  supply 
  which 
  has 
  continually 
  diminished, 
  and 
  

   is 
  destined 
  ultimately 
  to 
  vanish 
  entirely? 
  

  

  The 
  answer 
  to 
  this 
  question 
  must 
  of 
  course 
  depend 
  on 
  the 
  age 
  we 
  

   assign 
  to 
  the 
  sun, 
  and 
  an 
  attempt 
  to 
  fix 
  this 
  takes 
  us 
  rather 
  far 
  afield. 
  

  

  THE 
  AGES 
  OF 
  THE 
  SUN 
  AND 
  STARS 
  

  

  In 
  a 
  classical 
  paper 
  published 
  in 
  1878, 
  Clerk 
  Maxwell 
  studied 
  the 
  

   behavior 
  of 
  a 
  gas 
  whose 
  molecules 
  were 
  supposed 
  to 
  be 
  massive 
  points 
  

   repelling 
  one 
  another 
  with 
  a 
  force 
  which 
  varied 
  inversely 
  as 
  the 
  fifth 
  

   power 
  of 
  the 
  distance. 
  There 
  was 
  no 
  possibility 
  of 
  direct 
  collision, 
  

   since 
  the 
  molecules 
  were 
  supposed 
  to 
  be 
  of 
  infinitesimal 
  size, 
  but 
  as 
  

   each 
  molecule 
  threaded 
  its 
  way 
  through 
  its 
  fellows, 
  pairs 
  occasionally 
  

   approached 
  so 
  close 
  as 
  to 
  influence 
  one 
  another's 
  motion 
  much 
  as 
  a 
  

   direct 
  collision 
  would 
  have 
  done. 
  At 
  each 
  such 
  encounter 
  a 
  transfer 
  

   of 
  energy 
  took 
  place, 
  the 
  general 
  tendency 
  being 
  towards 
  equalizing 
  

   energies: 
  the 
  molecule 
  with 
  the 
  greater 
  energy 
  of 
  motion 
  was 
  ever 
  

   being 
  slowed 
  down, 
  and 
  that 
  with 
  the 
  lesser 
  energy 
  speeded 
  up. 
  If 
  

   the 
  molecules 
  were 
  of 
  different 
  weights, 
  their 
  continued 
  encounters 
  

   tended 
  to 
  bring 
  about 
  a 
  state 
  in 
  which 
  heavy 
  and 
  light 
  molecules 
  all 
  

   moved 
  with 
  the 
  same 
  energy, 
  the 
  lighter 
  molecules 
  making 
  up 
  for 
  the 
  

   smallness 
  of 
  their 
  mass 
  by 
  the 
  rapidity 
  of 
  their 
  motion. 
  

  

  It 
  was 
  no 
  new 
  discovery 
  that 
  the 
  molecules 
  of 
  a 
  gas 
  tended 
  to 
  assume 
  

   such 
  a 
  state. 
  This 
  had 
  been 
  known 
  for 
  some 
  years, 
  but 
  Maxwell's 
  

   investigation 
  gave 
  a 
  means 
  of 
  calculating 
  the 
  time 
  required 
  to 
  bring 
  

   about 
  this 
  final 
  state 
  of 
  equipartition 
  of 
  energy. 
  Maxwell 
  calculated 
  

   a 
  time, 
  which 
  he 
  called 
  the 
  time 
  of 
  relaxation, 
  such 
  that 
  all 
  deviations 
  

   from 
  the 
  final 
  state 
  of 
  equipartition 
  of 
  energy 
  were 
  reduced 
  to 
  1/e 
  

   (37 
  per 
  cent) 
  of 
  their 
  original 
  value 
  in 
  this 
  time. 
  For 
  ordinary 
  air 
  it 
  is 
  

  

  found 
  to 
  be 
  about 
  second. 
  

  

  6X10« 
  

  

  Maxwell's 
  massive 
  points, 
  repelling 
  according 
  to 
  the 
  inverse 
  fifth 
  

   power 
  of 
  the 
  distance, 
  do 
  not 
  form 
  a 
  particularly 
  good 
  model 
  of 
  a 
  gas, 
  

   but 
  on 
  changing 
  the 
  law 
  of 
  a 
  force 
  to 
  an 
  attraction 
  varying 
  as 
  the 
  

   inverse 
  square 
  of 
  the 
  distance 
  (the 
  law 
  of 
  gravitation), 
  we 
  obtain 
  an 
  

   absolutely 
  realistic 
  model 
  of 
  the 
  stars, 
  the 
  diameter 
  of 
  the 
  stars 
  being 
  

   so 
  small 
  in 
  comparison 
  with 
  their 
  mean 
  distances 
  apart 
  that 
  the 
  possi- 
  

   bility 
  of 
  direct 
  collisions 
  may 
  be 
  ignored 
  entirely. 
  Just 
  as 
  Maxwell 
  

   calculated 
  the 
  time 
  of 
  relaxation 
  for 
  his 
  ideal 
  gas, 
  we 
  can 
  calculate 
  it 
  

  

  