﻿306 
  

  

  Mr. 
  J. 
  Y. 
  Buchanan 
  on 
  the 
  [Mar. 
  4, 
  

  

  Let 
  the 
  specific 
  gravity 
  of 
  a 
  sea-water 
  be 
  found 
  to 
  be 
  y', 
  at 
  a 
  tempera- 
  

   ture 
  t, 
  and 
  let 
  v 
  be 
  the 
  volume 
  found 
  in 
  the 
  above 
  Table 
  corresponding 
  

   to 
  t°. 
  Then 
  we 
  shall 
  have, 
  for 
  the 
  value 
  of 
  the 
  specific 
  gravity 
  reduced 
  

   to 
  15°-56 
  C* 
  

  

  £c'=vy'. 
  

  

  Similarly, 
  any 
  other 
  observed 
  specific 
  gravity 
  y", 
  at 
  the 
  same 
  tempera- 
  

   ture 
  t, 
  becomes 
  at 
  15°*56 
  C, 
  

  

  oc" 
  =vy" 
  . 
  

  

  In 
  a 
  system 
  of 
  rectangular 
  coordinates, 
  let 
  observed 
  specific 
  gravities 
  be 
  

   measured 
  along 
  the 
  axis 
  of 
  y, 
  and 
  reduced 
  ones, 
  on 
  the 
  same 
  scale, 
  along 
  

   the 
  axis 
  of 
  sc. 
  We 
  have 
  then 
  two 
  points 
  (yy 
  , 
  y') 
  and 
  (vy", 
  y"), 
  and 
  the 
  

   equation 
  to 
  the 
  straight 
  line 
  passing 
  through 
  them 
  is 
  

  

  This 
  line 
  passes 
  through 
  the 
  origin 
  and 
  makes 
  an 
  angle 
  tan 
  ~- 
  

  

  v 
  

  

  with 
  the 
  axis 
  of 
  oc. 
  By 
  giving 
  to 
  v 
  the 
  successive 
  values 
  found 
  in 
  the 
  

   above 
  Table 
  for 
  different 
  temperatures, 
  we 
  can 
  draw 
  a 
  system 
  of 
  lines 
  

   all 
  branching 
  from 
  the 
  origin, 
  and 
  each 
  one 
  representing 
  the 
  relation 
  

   between 
  the 
  specific 
  gravity 
  of 
  different 
  sea- 
  waters 
  at 
  15°- 
  5 
  6 
  0. 
  and 
  at 
  

   same 
  temperature 
  of 
  observation 
  t. 
  If 
  the 
  values 
  of 
  v 
  have 
  been 
  taken 
  

   for 
  every 
  degree 
  Centigrade 
  within 
  the 
  limits 
  of 
  the 
  above 
  Table, 
  then 
  

   we 
  have 
  the 
  isothermals 
  for 
  every 
  degree 
  Centigrade. 
  In 
  the 
  extended 
  

   paper 
  an 
  isothermal 
  chart 
  of 
  this 
  kind 
  is 
  given 
  in 
  Plate 
  II. 
  In 
  it 
  ten 
  

   lines 
  are 
  drawn 
  for 
  every 
  two 
  degrees 
  Fahrenheit, 
  and 
  the 
  origin 
  has 
  been 
  

   shifted 
  from 
  the 
  point 
  of 
  zero 
  specific 
  gravity 
  to 
  a 
  point 
  (a, 
  a), 
  where 
  

   a 
  =1*02000; 
  so 
  that 
  the 
  general 
  equation 
  to 
  the 
  lines 
  is 
  

  

  y= 
  . 
  x 
  + 
  a 
  (1) 
  

  

  By 
  means 
  of 
  a 
  chart 
  of 
  this 
  kind 
  the 
  work 
  of 
  reducing 
  observed 
  specific 
  

   gravities 
  to 
  their 
  value 
  at 
  any 
  other 
  temperature 
  becomes 
  a 
  mere 
  me- 
  

   chanical 
  operation. 
  The 
  observed 
  specific 
  gravity 
  is 
  laid 
  off 
  on 
  the 
  axis 
  

   of 
  y, 
  and, 
  through 
  the 
  point 
  so 
  found, 
  a 
  hue 
  is 
  drawn 
  parallel 
  to 
  the 
  

   axis 
  of 
  oc. 
  Through 
  the 
  point 
  of 
  intersection 
  of 
  this 
  line 
  with 
  the 
  iso- 
  

   thermal 
  for 
  the 
  temperature 
  of 
  observation, 
  a 
  line 
  is 
  drawn 
  parallel 
  to 
  

   the 
  axis 
  of 
  y. 
  This 
  line 
  cuts 
  all 
  the 
  isothermals, 
  and 
  the 
  ordinates 
  of 
  the 
  

   points 
  of 
  intersection 
  are 
  the 
  specific 
  gravities 
  of 
  the 
  sea-water 
  in 
  ques- 
  

   tion 
  at 
  these 
  different 
  temperatures. 
  The 
  specific 
  gravity 
  at 
  15°-56 
  C. 
  

   (60° 
  F.) 
  is 
  given 
  by 
  the 
  intersections 
  — 
  namely, 
  where 
  the 
  line 
  cuts 
  the 
  

   isothermal 
  for 
  15°-56, 
  whose 
  equation 
  is 
  y 
  = 
  oc, 
  and 
  where 
  it 
  cuts 
  the 
  axis 
  

   of 
  x 
  ; 
  the 
  two 
  intersections 
  give, 
  of 
  course, 
  identical 
  values. 
  

  

  In 
  all 
  these 
  reductions 
  the 
  unit 
  remains 
  the 
  same 
  — 
  namely, 
  the 
  specific 
  

   gravity 
  of 
  distilled 
  water 
  at 
  4° 
  C. 
  In 
  hitherto 
  published 
  observations 
  on 
  

   the 
  specific 
  gravity 
  of 
  sea-water, 
  the 
  unit, 
  where 
  mentioned 
  at 
  all, 
  is 
  fre- 
  

   quently 
  the 
  specific 
  gravity 
  of 
  distilled 
  water 
  at 
  other 
  temperatures, 
  such 
  

  

  