﻿302 
  MR 
  J. 
  DALMAHOY 
  ON 
  THE 
  WEIGHT 
  OF 
  AQUEOUS 
  VAPOUR 
  

  

  At 
  York, 
  during 
  the 
  winter 
  quarters 
  of 
  the 
  years 
  1832-33, 
  1833-34, 
  1834-35. 
  

   a 
  rain-gauge 
  placed 
  on 
  the 
  ground 
  received 
  17*32 
  inches 
  of 
  rain, 
  and 
  a 
  similar 
  

   gauge 
  placed 
  at 
  the 
  height 
  of 
  43'7 
  feet 
  received 
  only 
  12*17 
  inches 
  of 
  rain. 
  

  

  In 
  this 
  case, 
  according 
  to 
  the 
  hypothesis, 
  a 
  rain-drop, 
  while 
  falling 
  through 
  

   the 
  height 
  of 
  43*7 
  feet 
  condensed 
  on 
  its 
  surface 
  a 
  quantity 
  of 
  moisture, 
  the 
  weight 
  

   of 
  which 
  was 
  to 
  the 
  weight 
  of 
  the 
  drop, 
  before 
  the 
  condensation 
  began, 
  in 
  the 
  

   ratio 
  of 
  -42 
  to 
  1. 
  

  

  In 
  order 
  to 
  make 
  a 
  fair 
  comparison 
  between 
  this 
  assumed 
  rate 
  of 
  condensation 
  

   and 
  the 
  rate 
  deduced 
  from 
  experiment, 
  it 
  would 
  be 
  necessary 
  to 
  know 
  the 
  mean 
  

   temperature 
  of 
  the 
  rain, 
  the 
  mean 
  temperature 
  of 
  the 
  dew-point, 
  the 
  mean 
  size 
  of 
  

   the 
  drops 
  of 
  rain, 
  and 
  the 
  velocity 
  of 
  their 
  fall. 
  

  

  But 
  as 
  the 
  available 
  data 
  are 
  not 
  sufficient 
  to 
  furnish 
  mean 
  values 
  of 
  these 
  

   quantities, 
  it 
  is 
  necessary, 
  in 
  order 
  to 
  obviate 
  any 
  objection 
  on 
  this 
  ground 
  to 
  the 
  

   proposed 
  mode 
  of 
  comparison, 
  to 
  assume 
  for 
  the 
  temperature 
  of 
  the 
  rain, 
  the 
  

   temperature 
  of 
  the 
  dew-point, 
  and 
  the 
  size 
  of 
  the 
  rain-drops, 
  values 
  the 
  most 
  

   favourable 
  to 
  the 
  hypothesis 
  which 
  the 
  case 
  admits 
  of. 
  

  

  First, 
  therefore, 
  we 
  are 
  sure 
  that 
  in 
  assuming 
  the 
  temperature 
  of 
  the 
  rain 
  to 
  

   be 
  32°, 
  we 
  ascribe 
  to 
  the 
  condensing 
  surface 
  the 
  greatest 
  cold 
  compatible 
  with 
  its 
  

   being 
  a 
  surface 
  of 
  fluid 
  water. 
  

  

  Again, 
  since 
  the 
  mean 
  temperature 
  of 
  the 
  air 
  during 
  the 
  winter 
  months 
  of 
  the 
  

   three 
  years 
  of 
  observation 
  was 
  36 
  0- 
  3, 
  and 
  the 
  mean 
  range 
  of 
  temperature 
  was 
  equal 
  

   to 
  8*6 
  degrees, 
  it 
  follows 
  that 
  the 
  mean 
  maximum 
  temperature 
  of 
  the 
  air 
  was 
  

  

  36*3 
  +2 
  =40 
  o, 
  6. 
  The 
  temperature 
  of 
  the 
  dew-point, 
  therefore, 
  cannot 
  possibly 
  be 
  

  

  assumed 
  as 
  having 
  been 
  higher 
  than 
  40 
  o, 
  6. 
  

  

  Further, 
  as 
  Sir 
  John 
  Leslie 
  states 
  that 
  the 
  diameters 
  of 
  the 
  drops 
  of 
  rain 
  

   vary 
  from 
  '04 
  to 
  *25 
  of 
  an 
  inch 
  ; 
  and 
  as 
  it 
  is 
  more 
  favourable 
  to 
  the 
  hypothesis 
  to 
  

   suppose 
  them 
  small 
  than 
  great, 
  it 
  is 
  proposed 
  to 
  assume 
  that 
  the 
  diameter 
  of 
  each 
  

   drop 
  was 
  only 
  -05 
  of 
  an 
  inch. 
  The 
  weight 
  of 
  a 
  drop 
  of 
  rain 
  of 
  this 
  magnitude 
  is 
  

   •0165 
  of 
  a 
  grain, 
  and 
  the 
  area 
  of 
  its 
  surface 
  is 
  equal 
  to 
  '00786 
  of 
  a 
  square 
  inch. 
  

  

  Lastly, 
  since 
  a 
  drop 
  of 
  rain 
  having 
  its 
  diameter 
  equal 
  to 
  05 
  of 
  an 
  inch 
  would 
  

   soon 
  attain 
  its 
  terminal 
  velocity, 
  it 
  may 
  be 
  assumed 
  that 
  the 
  drops 
  fell 
  with 
  an 
  

  

  43-7 
  

   uniform 
  velocity 
  of 
  14-6 
  feet 
  per 
  second, 
  and 
  consequently 
  occupied 
  j^ng 
  =3 
  seconds 
  

  

  in 
  falling 
  through 
  the 
  height 
  of 
  43 
  '7 
  feet. 
  

  

  It 
  now 
  remains 
  to 
  ascertain 
  what 
  rate 
  of 
  condensation 
  is 
  deducible 
  from 
  these 
  

   data, 
  as 
  compared 
  with 
  the 
  rate 
  assumed 
  by 
  the 
  hypothesis. 
  

  

  In 
  order 
  to 
  do 
  this, 
  let/"=-27, 
  the 
  tension 
  of 
  vapour 
  at 
  40 
  o, 
  6; 
  /'"=-2, 
  the 
  

   tension 
  at 
  32° 
  ; 
  m=39'7, 
  the 
  coefficient 
  due 
  to 
  a 
  current 
  of 
  air 
  having 
  a 
  velocity 
  

   of 
  14- 
  8 
  feet 
  per 
  second, 
  which 
  is 
  nearly 
  the 
  same 
  as 
  the 
  terminal 
  velocity 
  with 
  

   which 
  the 
  drops 
  of 
  rain 
  have 
  been 
  supposed 
  to 
  fall. 
  

  

  