﻿F. 
  H. 
  Bigelow 
  — 
  International 
  Cloud 
  Work. 
  437 
  

  

  transformation 
  the 
  formula 
  is 
  available 
  for 
  reduction 
  upwards 
  ; 
  

   this 
  may 
  take 
  place 
  between 
  any 
  two 
  fixed 
  points 
  whatsoever; 
  

   the 
  set 
  of 
  special 
  tables 
  to 
  determine 
  the 
  heights 
  by 
  the 
  baro- 
  

   metric 
  pressure 
  is 
  dispensed 
  with 
  entirely, 
  since 
  the 
  m 
  table 
  

   is 
  arranged 
  for 
  double 
  entry 
  with 
  the 
  arguments, 
  A 
  = 
  height, 
  

   t= 
  temperature; 
  with 
  A. 
  t. 
  m. 
  any 
  two 
  being 
  given, 
  the 
  other 
  

   follows. 
  These 
  new 
  tables 
  give 
  identical 
  results 
  with 
  the 
  

   others 
  for 
  special 
  cases 
  ; 
  they 
  work 
  rapidly 
  in 
  practice 
  ; 
  one 
  

   can 
  compute 
  with 
  accuracy 
  to 
  the 
  one-thousandth 
  of 
  a 
  milli- 
  

   meter, 
  so 
  far 
  as 
  the 
  data 
  are 
  concerned. 
  

  

  The 
  second 
  in)portant 
  group 
  of 
  tables 
  contains 
  the 
  four 
  

   thermodynamic 
  processes, 
  which 
  take 
  place 
  in 
  the 
  formation 
  of 
  

   clouds, 
  the 
  unsaturated, 
  the 
  saturated, 
  the 
  freezing 
  and 
  the 
  

   frozen 
  stages, 
  designated 
  as 
  the 
  a, 
  /9. 
  7, 
  S, 
  stages, 
  respectively. 
  

   This 
  subject 
  has 
  been 
  discussed 
  by 
  Ferrel, 
  Hann, 
  Lord 
  Kelvin 
  

   and 
  others 
  along 
  one 
  line, 
  and 
  by 
  Hertz 
  and 
  von 
  Bezold 
  along 
  

   another 
  line, 
  though 
  both 
  came 
  to 
  the 
  same 
  conclusion 
  so 
  far 
  

   as 
  the 
  results 
  are 
  concerned. 
  Plertz 
  has 
  constructed 
  a 
  diagram 
  

   which 
  graphically 
  deals 
  with 
  the 
  four 
  stages, 
  but 
  it 
  was 
  neces- 
  

   sary 
  for 
  him 
  to 
  neglect 
  in 
  part 
  the 
  vapor 
  contents, 
  so 
  that 
  

   although 
  the 
  divergence 
  is 
  no 
  more 
  than 
  7"""" 
  of 
  pressure 
  

   between 
  the 
  rigorous 
  and 
  the 
  approximate 
  solutions, 
  yet 
  all 
  the 
  

   tine 
  accuracy 
  which 
  should 
  pertain 
  to 
  good 
  cloud 
  computa- 
  

   tions 
  is 
  sacrificed. 
  The 
  direct 
  application 
  of 
  the 
  rigorous 
  

   formulae, 
  which 
  are 
  very 
  complex, 
  would 
  require 
  an 
  excessive 
  

   amount 
  of 
  labor 
  to 
  use 
  them, 
  and 
  they 
  are 
  never 
  utilized 
  by 
  

   meteorologists. 
  But 
  it 
  seemed 
  to 
  me 
  essential 
  to 
  overcome 
  this 
  . 
  

   obstacle, 
  and 
  accordingly 
  the 
  formulae 
  were 
  transformed 
  so 
  as 
  

  

  to 
  depend 
  upon 
  three 
  arguments, 
  namely, 
  B. 
  ^^. 
  -77. 
  pressure, 
  

  

  temperature, 
  and 
  the 
  ratio 
  of 
  the 
  vapor 
  pressure 
  to 
  the 
  baro- 
  

   metric 
  pressure. 
  The 
  tables 
  are 
  simple 
  in 
  structure, 
  and 
  

   involve 
  only 
  moderate 
  interpolations. 
  They 
  work 
  rapidly 
  and 
  

   have 
  proven 
  to 
  be 
  perfectly 
  satisfactory 
  by 
  use 
  in 
  the 
  actual 
  

   reductions. 
  The 
  results 
  of 
  this 
  discussion 
  have 
  led 
  to 
  much 
  

   definite 
  information 
  regarding 
  the 
  physics 
  of 
  clouds 
  in 
  many 
  

   connections, 
  but 
  only 
  a 
  few 
  of 
  them 
  can 
  be 
  mentioned 
  here. 
  

  

  (1) 
  In 
  the 
  case 
  of 
  air 
  rising 
  from 
  the 
  lower 
  strata 
  to 
  form 
  

   cumulus 
  clouds 
  there 
  exists 
  a 
  definite 
  level 
  at 
  which 
  satura- 
  

   tion 
  takes 
  place, 
  namely 
  the 
  base 
  of 
  the 
  cloud. 
  It 
  is 
  necessary 
  

   to 
  clearly 
  distinguish 
  between 
  true 
  adiabatic 
  saturation, 
  and 
  the 
  

   saturation 
  as 
  it 
  takes 
  place 
  in 
  the 
  actual 
  atmosphere. 
  The 
  

   formulae 
  of 
  the 
  tables 
  as 
  they 
  stand 
  deal 
  only 
  with 
  adiabatic 
  

   processes, 
  but 
  in 
  order 
  to 
  apply 
  them 
  to 
  the 
  atmosphere 
  the 
  

  

  value 
  of 
  the 
  ratio 
  — 
  must 
  be 
  observed 
  at 
  the 
  base 
  of 
  the 
  

  

  