﻿308 
  

  

  On 
  the 
  Specific 
  Gravity 
  of 
  Sea-water. 
  [Mar. 
  4, 
  

  

  at 
  any 
  temperature 
  t' 
  being 
  unity, 
  to 
  be 
  

  

  1 
  , 
  1 
  — 
  vc 
  /rs 
  < 
  

   y= 
  - 
  x+a 
  (3) 
  

  

  VC 
  VG 
  

  

  Thus 
  for 
  t=t' 
  = 
  ll° 
  C. 
  we 
  have 
  ^=0-99910, 
  c 
  = 
  0-99966, 
  whence 
  

   w=0-99876. 
  Now 
  in 
  Table 
  I. 
  0-99878 
  is 
  the 
  value 
  of 
  v 
  for 
  the 
  isothermal 
  

   for 
  9° 
  C. 
  Hence 
  to 
  reduce 
  observed 
  specific 
  gravities 
  to 
  their 
  values 
  at 
  

   11° 
  C, 
  water 
  at 
  11° 
  C. 
  being 
  unity, 
  is 
  equivalent 
  to 
  reducing 
  it 
  to 
  9° 
  C, 
  

   water 
  at 
  4° 
  C. 
  being 
  unity, 
  the 
  isothermal 
  for 
  which 
  is 
  given 
  in 
  the 
  chart. 
  

  

  To 
  take 
  an 
  example, 
  let 
  the 
  specific 
  gravity 
  of 
  a 
  water 
  be 
  observed 
  at 
  

   20° 
  0. 
  and 
  found 
  to 
  be 
  1-0247. 
  Finding 
  1-0247 
  on 
  the 
  axis 
  of 
  y, 
  we 
  

   draw 
  through 
  it 
  the 
  line 
  A 
  B 
  parallel 
  to 
  the 
  axis 
  of 
  x. 
  Through 
  the 
  

   intersection 
  of 
  A 
  B 
  with 
  the 
  isothermal 
  for 
  20° 
  C, 
  the 
  line 
  C 
  D 
  is 
  drawn 
  

   parallel 
  to 
  the 
  axis 
  of 
  y. 
  The 
  ordinates 
  of 
  its 
  points 
  of 
  intersection 
  with 
  

   the 
  other 
  isothermals 
  are 
  the 
  specific 
  gravities 
  at 
  these 
  temperatures, 
  

   water 
  at 
  4° 
  C. 
  being 
  unity 
  ; 
  they 
  are 
  at 
  15°*56 
  1-02575 
  (both 
  by 
  the 
  inter- 
  

   section 
  with 
  the 
  isothermal 
  and 
  with 
  the 
  axis 
  of 
  x\ 
  at 
  11° 
  1-02665, 
  and 
  

   at 
  9° 
  1-02685. 
  When 
  the 
  unit 
  is 
  the 
  specific 
  gravity 
  of 
  distilled 
  water 
  

   at 
  15°-56, 
  the 
  specific 
  gravity 
  at 
  15°-56 
  is 
  1*02665, 
  or 
  the 
  same 
  as 
  at 
  11°, 
  

   water 
  at 
  4° 
  C. 
  being 
  unity. 
  When 
  the 
  specific 
  gravity 
  of 
  distilled 
  water 
  

   at 
  11° 
  C. 
  is 
  unity, 
  the 
  specific 
  gravity 
  at 
  11° 
  C. 
  is 
  1-02685, 
  or 
  the 
  same 
  

   as 
  at 
  9° 
  0., 
  when 
  water 
  at 
  4° 
  is 
  unity. 
  

  

  During 
  the 
  course 
  of 
  the 
  cruise 
  a 
  considerable 
  number 
  of 
  waters 
  have 
  

   had 
  their 
  specific 
  gravities 
  determined 
  at 
  different 
  temperatures. 
  The 
  

   results 
  when 
  reduced 
  to 
  the 
  common 
  temperature 
  of 
  15°-56 
  C. 
  agree, 
  

   as 
  a 
  rule, 
  within 
  5 
  in 
  the 
  fifth 
  decimal 
  place, 
  the 
  greatest 
  difference 
  

   being 
  14. 
  

  

  When 
  the 
  specific 
  gravity 
  of 
  the 
  same 
  water 
  is 
  determined 
  with 
  the 
  

   same 
  hydrometer 
  and 
  table, 
  but 
  with 
  different 
  weights, 
  the 
  mean 
  dis- 
  

   crepancy 
  in 
  the 
  results 
  is 
  5, 
  and 
  the 
  maximum 
  10 
  in 
  the 
  fifth 
  decimal 
  

   place. 
  

  

  As 
  an 
  absolute 
  test 
  of 
  the 
  trustworthiness 
  of 
  the 
  results, 
  I 
  landed 
  my 
  

   balance, 
  and 
  determined 
  the 
  specific 
  gravity 
  of 
  the 
  water 
  of 
  Hong-Kong 
  

   harbour, 
  in 
  the 
  usual 
  way, 
  by 
  weighing 
  it 
  in 
  a 
  specific-gravity 
  tube, 
  and 
  

   reducing 
  it 
  to 
  its 
  value 
  at 
  15°- 
  56 
  both 
  by 
  the 
  graphical 
  method, 
  already 
  

   described, 
  and 
  arithmetically, 
  using 
  the 
  factors 
  found 
  in 
  the 
  two 
  Tables 
  

   of 
  expansion 
  of 
  sea 
  and 
  distilled 
  waters. 
  I 
  found 
  its 
  specific 
  gravity 
  

   reduced 
  arithmetically 
  to 
  be 
  1*02391, 
  reduced 
  graphically 
  1*02394. 
  De- 
  

   termined 
  on 
  board 
  by 
  means 
  of 
  the 
  hydrometer 
  and 
  reduced 
  graphically, 
  

   it 
  was 
  1*02397. 
  The 
  true 
  specific 
  gravity 
  must 
  therefore 
  lie 
  between 
  

   1*02391 
  and 
  1*02397. 
  Taking, 
  therefore, 
  into 
  account 
  the 
  results 
  of 
  the 
  

   application 
  of 
  those 
  different 
  tests 
  of 
  accuracy, 
  I 
  think 
  the 
  trustworthi- 
  

   ness 
  of 
  the 
  method 
  is 
  fully 
  established. 
  

  

  H.M.S. 
  ' 
  Challenger,' 
  Hong 
  Kong, 
  

   14th 
  December, 
  1874. 
  

  

  