﻿1875.] 
  Specific 
  Gravity 
  of 
  Sea 
  -water. 
  307 
  

  

  as 
  14° 
  C, 
  16° 
  C, 
  and 
  so 
  forth. 
  In 
  order 
  to 
  reduce 
  results 
  from 
  their 
  

   value, 
  the 
  unit 
  being 
  water 
  at 
  4° 
  C, 
  to 
  their 
  value 
  the 
  specific 
  gravity 
  of 
  

   distilled 
  water 
  at 
  any 
  other 
  temperature 
  being 
  unity, 
  it 
  is 
  only 
  necessary 
  

   to 
  divide 
  the 
  result 
  by 
  the 
  specific 
  gravity 
  of 
  distilled 
  water 
  at 
  this 
  tem- 
  

   perature, 
  the 
  unit 
  being 
  water 
  at 
  4° 
  C. 
  Let 
  oc' 
  be 
  the 
  specific 
  gravity 
  of 
  

   a 
  sea-water 
  reduced 
  to 
  15°*56, 
  and 
  let 
  it 
  be 
  required 
  to 
  convert 
  it 
  into 
  its 
  

   value 
  when 
  the 
  unit 
  is 
  water 
  at 
  t°. 
  Let 
  c 
  be 
  the 
  specific 
  gravity 
  of 
  dis- 
  

   tilled 
  water 
  at 
  t, 
  that 
  at 
  4° 
  C. 
  being 
  unity, 
  we 
  have 
  then 
  for 
  the 
  specific 
  

   gravity 
  with 
  new 
  unit 
  

  

  y' 
  =- 
  oc' 
  or 
  oc' 
  = 
  cy'. 
  

  

  Similarly, 
  if 
  any 
  other 
  water 
  be 
  taken 
  of 
  the 
  specific 
  gravity 
  oc" 
  at 
  15°- 
  56, 
  

   its 
  value 
  at 
  15°*56 
  C, 
  water 
  at 
  *° 
  being 
  unity, 
  will 
  be 
  

  

  y"= 
  -oc" 
  or 
  cv" 
  = 
  cy". 
  

  

  And, 
  just 
  as 
  before, 
  we 
  get 
  the 
  general 
  equation 
  to 
  a 
  system 
  of 
  lines, 
  

   which, 
  when 
  the 
  origin 
  is 
  the 
  point 
  (a, 
  a), 
  is 
  

  

  y= 
  (2) 
  

  

  c 
  c 
  

  

  Now 
  in 
  Table 
  I. 
  the 
  extreme 
  values 
  of 
  v 
  are 
  0-99792 
  and 
  1*00420, 
  and 
  

   for 
  temperatures 
  below 
  22° 
  C. 
  the 
  extreme 
  values 
  of 
  c 
  are 
  0*99789 
  and 
  1. 
  

   For 
  any 
  value 
  of 
  c, 
  between 
  those 
  extremes, 
  the 
  line 
  expressed 
  by 
  equa- 
  

   tion 
  (2) 
  must 
  coincide 
  with 
  one 
  represented 
  by 
  equation 
  (1). 
  By 
  com- 
  

   paring, 
  then, 
  the 
  values 
  of 
  v 
  in 
  Table 
  I. 
  with 
  those 
  of 
  c 
  in 
  any 
  Table 
  of 
  

   the 
  expansion 
  of 
  distilled 
  water, 
  the 
  lines 
  which 
  represent 
  specific 
  

   gravities 
  at 
  15°*56, 
  their 
  unit 
  being 
  water 
  at 
  any 
  temperature 
  t, 
  may 
  be 
  

   found 
  which 
  correspond 
  to 
  isothermals 
  represented 
  by 
  equation 
  (1). 
  For 
  

   instance, 
  the 
  value 
  of 
  c 
  for 
  15°*56 
  is 
  0*99910, 
  and 
  in 
  Table 
  I. 
  the 
  value 
  of 
  

   v 
  for 
  11° 
  C. 
  is 
  also 
  0*99910. 
  For 
  these 
  values, 
  then, 
  equations 
  (1) 
  and 
  (2) 
  

   represent 
  identical 
  lines. 
  Hence, 
  to 
  reduce 
  any 
  observed 
  specific 
  gravity 
  

   to 
  its 
  value 
  at 
  15°*56 
  C, 
  water 
  

   at 
  15°*56 
  C. 
  being 
  unity, 
  the 
  same 
  

   construction 
  is 
  made 
  as 
  for 
  re- 
  

   ducing 
  to 
  11° 
  C, 
  the 
  unit 
  remain- 
  

   ing 
  the 
  same 
  ; 
  only 
  the 
  intersec- 
  

   tion 
  of 
  the 
  Hue 
  parallel 
  to 
  the 
  

   axis 
  of 
  y 
  with 
  the 
  isothermal 
  to 
  

   11° 
  C. 
  is 
  taken, 
  and 
  the 
  ordinate 
  

   of 
  the 
  point 
  is 
  the 
  specific 
  gravity 
  

   at 
  15°*56 
  C, 
  water 
  at 
  15°*56 
  C. 
  

   being 
  unity. 
  

  

  In 
  a 
  precisely 
  similar 
  manner 
  

   we 
  find 
  the 
  equation 
  to 
  the 
  iso- 
  

   thermal 
  for 
  specific 
  gravities 
  re- 
  

   duced 
  to 
  any 
  temperature 
  t, 
  water 
  

  

  