﻿436 
  F. 
  11. 
  Bigelow 
  — 
  International 
  Cloud 
  Work. 
  

  

  an 
  elevation 
  of 
  at 
  least 
  15,000 
  meters, 
  wherein 
  the 
  pressure 
  B, 
  

   the 
  temperature 
  t. 
  and 
  the 
  vapor 
  pressure 
  e, 
  pass 
  through 
  great 
  

   changes, 
  it 
  was 
  found 
  that 
  the 
  existing 
  tables 
  were 
  wholly 
  inad- 
  

   equate 
  for 
  the 
  purpose. 
  The 
  International 
  and 
  the 
  Smith- 
  

   sonian 
  Barometric 
  Tables 
  extend 
  only 
  to 
  2,000 
  meters, 
  but 
  the 
  

   new 
  tables 
  are 
  computed 
  in 
  metric 
  measures 
  from 
  to 
  15,000 
  

   meters, 
  and 
  for 
  temperatures 
  ranging 
  from 
  —40° 
  C. 
  to 
  -f 
  40° 
  C. 
  

   for 
  A 
  = 
  to 
  5,000 
  meters, 
  from 
  -50° 
  to 
  +80° 
  for 
  A 
  = 
  5,000 
  to 
  

   10,000 
  meters, 
  and 
  from 
  -60° 
  to 
  +20° 
  for 
  h 
  = 
  10,000 
  to 
  15,000 
  

   meters 
  ; 
  similar 
  tables 
  have 
  been 
  made 
  in 
  English 
  measures 
  up 
  

   to 
  10,000 
  feet, 
  which 
  is 
  sufficient 
  for 
  our 
  weather 
  map 
  reduc- 
  

   tions. 
  There 
  are 
  certain 
  practical 
  difficulties 
  with 
  the 
  existing 
  

   tables 
  in 
  other 
  particulars. 
  The 
  formula 
  employed 
  by 
  them 
  is 
  

   of 
  the 
  form, 
  B,-B 
  = 
  B(10™-1), 
  where 
  B„ 
  > 
  B, 
  and 
  77i 
  is 
  a 
  

   function 
  of 
  the 
  temperature, 
  humidity, 
  gravity, 
  altitude, 
  and 
  

   surface 
  topography. 
  It 
  gives 
  the 
  correction 
  which, 
  added 
  to 
  

   the 
  pressure 
  B 
  at 
  a 
  given 
  altitude, 
  will 
  reduce 
  it 
  to 
  B^,, 
  the 
  

   pressure 
  at 
  sea 
  level. 
  It 
  is 
  perceived 
  that 
  this 
  is 
  a 
  very 
  special 
  

   case 
  of 
  reduction, 
  namely, 
  downward 
  to 
  sea 
  level, 
  whereas 
  in 
  

   cloud 
  work 
  we 
  must 
  be 
  prepared 
  to 
  reduce 
  upward 
  as 
  well 
  as 
  

   downward, 
  and 
  also 
  where 
  neither 
  pressure 
  is 
  that 
  at 
  sea 
  level. 
  

   If 
  by 
  the 
  above 
  formulse 
  we 
  wish 
  to 
  reduce 
  upward, 
  it 
  must 
  

   be 
  done 
  through 
  approxitnations, 
  because 
  the 
  value 
  of 
  B 
  at 
  the 
  

   upper 
  station 
  is 
  involved 
  in 
  the 
  formula, 
  and 
  not 
  the 
  value 
  

   of 
  Bq 
  with 
  which 
  we 
  begin. 
  There 
  is 
  trouble 
  with 
  the 
  

   humidity 
  term, 
  especially 
  in 
  the 
  Smithsonian 
  tables, 
  where 
  a 
  

   certain 
  average 
  value 
  of 
  the 
  vapor 
  pressure 
  is 
  included 
  perma- 
  

   nently 
  within 
  the 
  m, 
  so 
  that 
  the 
  humidity 
  does 
  not 
  stand 
  out 
  

   by 
  itself, 
  and 
  is, 
  therefore, 
  not 
  available 
  for 
  an 
  independent 
  

   discussion. 
  But 
  in 
  cloud 
  work 
  this 
  is 
  the 
  very 
  element 
  most 
  

   required, 
  and 
  it 
  is 
  not 
  proper 
  to 
  assume 
  either 
  an 
  invariable 
  

   law 
  of 
  variation 
  of 
  the 
  vapor 
  contents, 
  nor, 
  as 
  in 
  the 
  Interna- 
  

   tional 
  tables, 
  is 
  it 
  possible 
  to 
  measure 
  the 
  humidity 
  term 
  at 
  the 
  

   top 
  and 
  bottom 
  of 
  a 
  cohimn 
  which 
  is 
  not 
  in 
  contact 
  with 
  the 
  

   ground. 
  For 
  example, 
  in 
  reducing 
  from 
  the 
  bottom 
  to 
  the 
  top 
  

   of 
  a 
  cumulus 
  cloud, 
  I 
  have 
  taken 
  the 
  following 
  form 
  of 
  equa- 
  

   tion, 
  

  

  log. 
  Bg— 
  log. 
  B-i-77i 
  — 
  (3in 
  — 
  ym, 
  

  

  where 
  m 
  includes 
  the 
  temperature, 
  the 
  altitude, 
  and 
  the 
  topo- 
  

   graphic 
  terms, 
  /3 
  the 
  humidity 
  and 
  7 
  the 
  gravity. 
  What 
  is 
  

   wanted 
  is 
  the 
  value 
  of 
  B^, 
  and 
  not 
  the 
  correction 
  B^ 
  — 
  B, 
  which 
  

   involves 
  one 
  superfluous 
  operation 
  in 
  computing. 
  The 
  

   humidity 
  term 
  with 
  its 
  assumed 
  law 
  of 
  vertical 
  variation, 
  and 
  

   the 
  gravity 
  term 
  here 
  stand 
  out 
  distinctly 
  by 
  themselves, 
  and 
  

   the 
  whole 
  subject 
  of 
  humidity 
  is 
  easily 
  open 
  to 
  treatment, 
  and 
  

   even 
  to 
  employing 
  a 
  different 
  law 
  without 
  disturbing 
  the 
  main 
  

   term, 
  which 
  is 
  limited 
  to 
  the 
  dry 
  air 
  pressures. 
  By 
  simple 
  

  

  