﻿1875.] 
  On 
  the 
  Specific 
  Gravity 
  of 
  Sea-water. 
  301 
  

  

  is 
  that 
  in 
  which 
  one 
  of 
  these 
  quantities 
  is 
  even 
  and 
  the 
  other 
  odd. 
  Put, 
  

   then, 
  2m 
  for 
  m, 
  and 
  2n 
  — 
  1 
  for 
  n 
  ; 
  thus 
  we 
  have 
  

  

  {2m(2m 
  + 
  1) 
  - 
  (2n 
  - 
  l)2n} 
  J* 
  V 
  2m 
  (x) 
  V 
  2n 
  _ 
  x 
  {x)dx 
  

  

  Then 
  by 
  (1) 
  we 
  obtain 
  finally 
  

  

  { 
  2m(2m 
  + 
  1) 
  - 
  (2n 
  - 
  l)2n} 
  J* 
  ¥ 
  2 
  Jx) 
  V^{sc)dx 
  

  

  1 
  ^ 
  w 
  1.3.5..(2m-l) 
  1.3... 
  (2n-l) 
  

   ; 
  2. 
  4.. 
  2m 
  ' 
  2.4..(2n-2) 
  " 
  

  

  This 
  formula 
  will 
  be 
  found 
  to 
  include 
  the 
  results 
  which 
  are 
  given 
  in 
  

   the 
  Philosophical 
  Transactions 
  for 
  1870, 
  pages 
  579-587. 
  

   February 
  11, 
  1875. 
  

  

  III. 
  " 
  On 
  the 
  Determination, 
  at 
  Sea, 
  of 
  the 
  Specific 
  Gravity 
  of 
  

   Sea-water." 
  By 
  J. 
  Y. 
  Buchanan, 
  Chemist 
  on 
  board 
  H.M.S. 
  

   ( 
  Challenger.' 
  Communicated 
  by 
  Prof. 
  Wyville 
  Thomson, 
  

   F.B.S. 
  Received 
  January 
  22, 
  1875. 
  

  

  (Abstract.) 
  

  

  In 
  the 
  investigation 
  of 
  the 
  physical 
  condition 
  of 
  the 
  ocean 
  the 
  accu- 
  

   rate 
  determination 
  of 
  the 
  specific 
  gravity 
  of 
  the 
  water 
  holds 
  a 
  first 
  place. 
  

   The 
  tolerably 
  numerous 
  observations 
  which 
  have 
  been 
  made 
  in 
  this 
  

   direction, 
  in 
  a 
  more 
  or 
  less 
  connected 
  manner, 
  are 
  sufficient 
  to 
  prove 
  that 
  

   the 
  density 
  of 
  the 
  water 
  varies, 
  not 
  only 
  with 
  the 
  latitude 
  and 
  longitude, 
  

   but 
  also 
  with 
  the 
  distance 
  from 
  the 
  surface 
  of 
  the 
  source 
  from 
  which 
  it 
  

   is 
  taken. 
  This 
  difference 
  of 
  density 
  depends 
  partly 
  on 
  an 
  actual 
  differ- 
  

   ence 
  in 
  saltness, 
  and 
  partly 
  on 
  a 
  difference 
  in 
  temperature 
  of 
  the 
  water. 
  

   The 
  amount 
  of 
  effect 
  due 
  to 
  each 
  of 
  these 
  causes 
  can 
  be 
  precisely 
  stated 
  

   when 
  we 
  know 
  the 
  effect 
  of 
  one 
  of 
  them, 
  the 
  sum 
  of 
  the 
  effects 
  of 
  the 
  

   two 
  being 
  given 
  by 
  our 
  observations. 
  Hence, 
  to 
  determine 
  the 
  saltness, 
  

   we 
  eliminate 
  the 
  effect 
  of 
  temperature 
  by 
  reducing 
  the 
  results 
  to 
  their 
  

   value 
  at 
  one 
  common 
  temperature. 
  It 
  is 
  also 
  necessary 
  that 
  the 
  means 
  

   of 
  obtaining 
  the 
  water 
  should 
  be 
  of 
  a 
  reliable 
  character. 
  In 
  estimating, 
  

   therefore, 
  the 
  trustworthiness 
  of 
  the 
  results, 
  we 
  must 
  consider, 
  first, 
  the 
  

   means 
  used 
  for 
  collecting 
  the 
  water 
  ; 
  second, 
  those 
  used 
  for 
  determining 
  

   the 
  relation 
  between 
  its 
  weight 
  and 
  volume 
  ; 
  third, 
  the 
  determination 
  of 
  

  

  