﻿Theory 
  and 
  Planetary 
  Temperatures. 
  463 
  

  

  layer 
  from 
  1 
  cm. 
  to 
  1 
  j^q 
  cm., 
  the 
  radiating 
  surface 
  being 
  

   only 
  one-third 
  as 
  much 
  as 
  before, 
  we 
  should 
  have, 
  if 
  there 
  

   were 
  no 
  loss 
  of 
  heat 
  by 
  convection, 
  three 
  times 
  the 
  thermal 
  

   effect, 
  giving 
  an 
  excess 
  of 
  27°'5 
  by 
  the 
  fourth-power 
  law. 
  

   But 
  if 
  the 
  thin 
  strip 
  were 
  backed 
  by 
  nonconducting 
  material, 
  

   the 
  radiating 
  surface 
  would 
  be 
  only 
  one-sixth 
  of 
  that 
  of 
  the 
  

   cube, 
  while 
  the 
  thermal 
  effect 
  of 
  the 
  same 
  solar 
  radiation 
  

   would 
  be 
  six 
  times 
  as 
  great, 
  and 
  the 
  excess 
  would 
  be 
  49°'4. 
  

  

  Now, 
  where 
  a 
  layer 
  of 
  conducting 
  material 
  of 
  indefinite 
  

   thickness 
  is 
  to 
  be 
  heated, 
  a 
  day 
  is 
  too 
  short 
  a 
  time 
  to 
  reach 
  

   thermal 
  equilibrium 
  j 
  but 
  for 
  an 
  infinitesimal 
  layer 
  a 
  day 
  is 
  

   relatively 
  an 
  infinite 
  time 
  ; 
  and 
  since 
  the 
  glass 
  of 
  the 
  green- 
  

   house 
  roof 
  is 
  supposed 
  to 
  let 
  in 
  rays 
  which 
  are 
  transformed 
  

   at 
  the 
  surface 
  into 
  others 
  which 
  cannot 
  get 
  out, 
  or 
  can 
  get 
  

   out 
  only 
  in 
  small 
  part, 
  a 
  fraction 
  of 
  the 
  heat 
  from 
  inward 
  

   radiation 
  must 
  be 
  added 
  to 
  the 
  heat 
  of 
  the 
  infinitesimal 
  layer 
  

   at 
  each 
  radiant 
  transfer 
  from 
  solid 
  to 
  glass 
  and 
  back, 
  until 
  

   the 
  temperature 
  of 
  the 
  superficial 
  layer 
  of 
  the 
  solid 
  background 
  

   is 
  raised 
  so 
  high 
  that 
  it 
  either 
  begins 
  to 
  give 
  out 
  radiations 
  

   which 
  will 
  penetrate 
  glass, 
  or 
  until 
  the 
  glass 
  emits 
  an 
  equal 
  

   radiation. 
  If 
  the 
  layer 
  is 
  really 
  nonconducting, 
  or 
  what 
  is 
  

   the 
  same 
  thing 
  thermally, 
  if 
  its 
  thickness 
  is 
  infinitesimal 
  and 
  

   its 
  radiation 
  one-sided, 
  or 
  again, 
  if 
  the 
  background 
  conducts 
  

   but 
  has 
  been 
  exposed 
  to 
  insolation 
  so 
  long 
  that 
  the 
  interior 
  

   temperature 
  gradient 
  is 
  zero 
  at 
  the 
  surface, 
  a 
  second 
  is 
  long 
  

   enough 
  for 
  the 
  entire 
  process 
  ; 
  or 
  if 
  the 
  glass 
  transmits 
  a 
  

   little 
  of 
  the 
  infra-red, 
  and 
  a 
  single 
  layer 
  of 
  glass 
  is 
  insufficient 
  

   to 
  give 
  the 
  maximum 
  effect, 
  additional 
  ones 
  will 
  complete 
  the 
  

   realization 
  of 
  the 
  maximum 
  temperature 
  in 
  static 
  equilibrium. 
  

  

  Now, 
  as 
  we 
  are 
  not 
  making 
  a 
  world, 
  but 
  only 
  an 
  ideal, 
  or 
  

   perhaps 
  I 
  should 
  say 
  a 
  transcendental 
  greenhouse, 
  there 
  is 
  

   nothing 
  to 
  hinder 
  us 
  from 
  piling 
  story 
  on 
  story 
  until 
  we 
  get 
  a 
  

   greenhouse, 
  let 
  us 
  say, 
  fifty 
  stories 
  high. 
  At 
  first 
  each 
  added 
  

   story 
  will 
  capture 
  a 
  little 
  extra 
  heat, 
  and 
  this 
  will 
  also 
  go 
  on 
  ac- 
  

   cumulating 
  until 
  the 
  absorption 
  of 
  the 
  additional 
  sheets 
  of 
  glass 
  

   for 
  the 
  solar 
  rays 
  is 
  greater 
  than 
  their 
  power 
  to 
  obstruct 
  the 
  

   passage 
  of 
  radiation 
  of 
  long 
  wave-length, 
  and 
  thus 
  to 
  increase 
  

   the 
  amount 
  of 
  heat 
  trapped. 
  By 
  making 
  our 
  glass 
  thin 
  

   enough, 
  however, 
  we 
  can 
  entirely 
  obviate 
  this 
  difficulty; 
  for 
  

   by 
  making 
  a 
  greenhouse 
  of 
  one 
  thousand 
  stories, 
  each 
  covered 
  

   with 
  glass 
  one 
  one-thousandth 
  as 
  thick 
  as 
  that 
  of 
  the 
  ordinary 
  

   greenhouse, 
  the 
  absorption 
  will 
  be 
  no 
  greater, 
  but 
  the 
  heat- 
  

   trapping 
  will 
  increase 
  up 
  to 
  a 
  certain 
  point 
  in 
  proportion 
  to 
  

   the 
  number 
  of 
  chambers 
  traversed. 
  Such 
  a 
  structure 
  will 
  

   have 
  a 
  cumulative 
  action 
  resembling 
  that 
  of 
  a 
  bundle 
  of 
  im- 
  

   perfectly 
  reflecting 
  mirrors, 
  which, 
  if 
  numerous 
  enough,. 
  

  

  