﻿COSMICAL 
  PHYSICS 
  — 
  JEANS 
  169 
  

  

  inch 
  of 
  surface 
  — 
  the 
  sun, 
  for 
  example, 
  radiates 
  approximately 
  

   500,000 
  calories 
  a 
  minute, 
  which 
  is 
  about 
  the 
  energy 
  output 
  of 
  a 
  

   50-horgepowcr 
  engine, 
  from 
  each 
  square 
  inch 
  of 
  its 
  surface. 
  The 
  

   hottest 
  stars 
  of 
  all 
  probably 
  radiate 
  at 
  least 
  a 
  thousand 
  times 
  as 
  

   much 
  per 
  square 
  inch 
  of 
  surface. 
  

  

  In 
  this 
  way 
  we 
  can 
  estimate 
  a 
  star's 
  radiation 
  per 
  square 
  inch 
  of 
  

   its 
  surface. 
  We 
  can 
  also 
  estimate 
  the 
  radiation 
  from 
  its 
  whole 
  sur- 
  

   face; 
  this 
  can 
  be 
  calculated 
  at 
  once 
  from 
  its 
  distance 
  and 
  apparent 
  

   brightness. 
  Simple 
  division 
  gives 
  the 
  area 
  of 
  the 
  star's 
  surface, 
  and 
  

   hence 
  its 
  radius 
  and 
  volume. 
  Calculated 
  stellar 
  radii 
  range 
  from 
  

   about 
  three 
  hundred 
  times 
  the 
  sun's 
  radius 
  for 
  Betelgeuse 
  to 
  about 
  

   three 
  one-hundredths 
  times 
  the 
  sun's 
  radius 
  for 
  the 
  companion 
  of 
  

   Sirius. 
  

  

  As 
  is 
  well 
  known, 
  the 
  diameters 
  of 
  certain 
  stars 
  have 
  recently 
  been 
  

   observed 
  directly 
  with 
  the 
  Michelson 
  interferometer, 
  and 
  the 
  meas- 
  

   ured 
  values 
  agree 
  almost 
  perfectly 
  with 
  those 
  calculated 
  in 
  the 
  simple 
  

   way 
  just 
  explained. 
  The 
  interferometer 
  method 
  is 
  only 
  available 
  

   for 
  the 
  largest 
  stars, 
  but 
  at 
  the 
  extreme 
  other 
  end 
  of 
  the 
  scale 
  the 
  

   theory 
  of 
  relativity 
  has 
  come 
  to 
  the 
  rescue. 
  The 
  shift 
  of 
  spectral 
  

   lines 
  toward 
  the 
  red, 
  which 
  Einstein 
  predicted 
  to 
  be 
  a 
  necessary 
  

   consequence 
  of 
  the 
  theory 
  of 
  relativity, 
  has 
  been 
  observed 
  in 
  the 
  

   light 
  received 
  from 
  the 
  companion 
  of 
  Sirius, 
  and 
  its 
  amount 
  corre- 
  

   sponds 
  exactly 
  to 
  the 
  radius 
  calculated 
  for 
  the 
  star 
  in 
  the 
  way 
  just 
  

   explained. 
  So 
  much 
  of 
  a 
  sensational 
  kind 
  has 
  been 
  written 
  about 
  

   the 
  observational 
  measurements 
  of 
  the 
  diameters 
  of 
  Betelgeuse 
  and 
  

   of 
  the 
  companion 
  to 
  Sirius, 
  that 
  it 
  may 
  be 
  well 
  to 
  remember 
  that, 
  

   while 
  the 
  methods 
  were 
  novel 
  and 
  of 
  the 
  greatest 
  interest 
  and 
  im- 
  

   portance, 
  the 
  results 
  were 
  precisely 
  those 
  that 
  were 
  generally 
  ex- 
  

   pected, 
  and 
  such 
  as 
  a 
  simple 
  arithmetical 
  calculation 
  showed 
  to 
  be 
  

   practically 
  inevitable. 
  Indeed, 
  this 
  calculation 
  could 
  only 
  have 
  

   failed 
  in 
  one 
  way. 
  It 
  is 
  based 
  on 
  the 
  assumption 
  that 
  the 
  surfaces 
  

   of 
  the 
  stars 
  emit 
  their 
  full 
  temperature 
  radiation 
  like 
  the 
  surface 
  of 
  

   the 
  sun. 
  If 
  the 
  stars 
  had 
  been 
  transparent 
  bodies 
  like 
  the 
  planetary 
  

   nebuljie, 
  or 
  solid 
  bodies 
  like 
  the 
  moon, 
  this 
  assumption 
  avouIcI 
  have 
  

   been 
  false, 
  and 
  the 
  obserA^ations 
  would 
  have 
  revealed 
  its 
  falsity. 
  

  

  Our 
  gain 
  of 
  positive 
  knowledge 
  from 
  these 
  observations 
  is 
  that 
  

   Betelgeuse 
  and 
  the 
  companion 
  to 
  Sirus 
  are 
  neither 
  transparent 
  nor 
  

   solid 
  bodies, 
  but 
  full 
  radiators 
  like 
  the 
  sun. 
  Moreover, 
  as 
  the 
  three 
  

   stars 
  just 
  mentioned 
  are 
  about 
  as 
  different 
  as 
  any 
  three 
  stars 
  pos- 
  

   sibly 
  could 
  be, 
  representing 
  approximately 
  the 
  two 
  extreme 
  ends 
  and 
  

   the 
  middle 
  of 
  the 
  scale 
  in 
  almost 
  any 
  ordered 
  arrangement 
  we 
  please 
  

   to 
  make, 
  it 
  seems 
  reasonable 
  to 
  suppose 
  that 
  all 
  stars 
  are 
  full 
  

   radiators 
  and 
  so, 
  as 
  regards 
  their 
  mechanism 
  of 
  radiation, 
  are 
  

   essentially 
  similar 
  structures. 
  

  

  