﻿Pope. 
  — 
  A 
  Method 
  of 
  measuring 
  Position 
  of 
  Double 
  Stais. 
  143 
  

  

  and 
  firmly 
  held 
  there, 
  this 
  raises 
  the 
  valves 
  W, 
  and 
  water 
  flows 
  up 
  the 
  

   glass 
  tuhe 
  G, 
  which 
  has 
  previously 
  been 
  filled 
  up 
  to 
  the 
  zero 
  point 
  of 
  the 
  

   scale. 
  The 
  instant 
  that 
  the 
  second 
  star 
  is 
  bisected 
  by 
  the 
  wire 
  or 
  web 
  the 
  

   lever 
  is 
  released, 
  the 
  valves 
  are 
  immediately 
  closed, 
  and 
  the 
  flow 
  of 
  water 
  

   ceases. 
  The 
  height 
  of 
  the 
  column 
  of 
  water 
  is 
  then 
  accurately 
  measured 
  by 
  

   means 
  of 
  the 
  graduated 
  scale. 
  Then 
  the 
  water 
  is 
  allowed 
  to 
  escape 
  through 
  

   the 
  waste-tap 
  T", 
  and 
  the 
  operation 
  is 
  repeated. 
  A 
  mean 
  of 
  all 
  the 
  observa- 
  

   tions 
  gives 
  the 
  quantity 
  of 
  water 
  that 
  flows 
  into 
  the 
  glass-tube 
  during 
  the 
  

   interval 
  between 
  the 
  transits 
  of 
  the 
  two 
  stars. 
  Let 
  this 
  quantity 
  be 
  2-25 
  

   inches. 
  Then 
  an 
  observation 
  is 
  made, 
  by 
  means 
  of 
  a 
  watch, 
  of 
  the 
  time 
  

   required 
  to 
  fill 
  the 
  tube, 
  that 
  is 
  to 
  say 
  for 
  30 
  inches 
  of 
  water 
  to 
  run 
  into 
  it 
  ; 
  

   let 
  this 
  time 
  be 
  21-5 
  seconds. 
  A 
  rule 
  of 
  three 
  sum 
  shows 
  us 
  the 
  time 
  

   elapsing 
  between 
  the 
  transits 
  of 
  the 
  two 
  stars 
  : 
  — 
  

  

  inches, 
  inches. 
  sees. 
  sees. 
  

  

  30 
  : 
  2-25 
  : 
  : 
  21-5 
  : 
  1-612 
  

  

  1*612 
  seconds 
  of 
  time 
  is, 
  therefore, 
  the 
  interval 
  between 
  the 
  transits 
  of 
  the 
  

   two 
  stars. 
  

  

  Having 
  found 
  this 
  interval, 
  a 
  simple 
  trigonometrical 
  calculation 
  gives 
  us 
  

   the 
  distance 
  between 
  the 
  two 
  stars 
  : 
  — 
  

  

  Let 
  p 
  = 
  "the 
  North 
  Polar 
  distance 
  of 
  the 
  star. 
  

   a 
  = 
  angle 
  of 
  position 
  of 
  the 
  wire 
  ; 
  and 
  

   d 
  = 
  angle 
  of 
  position 
  of 
  the 
  line 
  joining 
  the 
  stars. 
  

   T 
  = 
  interval 
  between 
  the 
  two 
  transits 
  in 
  seconds 
  of 
  time. 
  

   A 
  = 
  distance 
  in 
  seconds 
  of 
  arc 
  between 
  the 
  two 
  stars. 
  

   T 
  X 
  15 
  . 
  sin^ 
  . 
  cos 
  a 
  • 
  

  

  Then 
  A 
  = 
  

  

  sin 
  (a 
  — 
  0). 
  

  

  These 
  calculations 
  are 
  not 
  very 
  troublesome. 
  A 
  very 
  little 
  practice 
  

   enables 
  one 
  to 
  do 
  them 
  very 
  rapidly. 
  It 
  may 
  be 
  as 
  well, 
  in 
  conclusion, 
  to 
  

   give 
  an 
  example 
  just 
  to 
  show 
  how 
  very 
  little 
  labour 
  is 
  really 
  involved 
  in 
  this 
  

   process. 
  

  

  On 
  April 
  5th, 
  1876, 
  twelve 
  oblique 
  transits 
  were 
  taken 
  of 
  the 
  star 
  4763 
  

   (of 
  Brisbane's 
  catalogue), 
  E.A. 
  14h. 
  Om., 
  Decl. 
  63° 
  6' 
  S. 
  The 
  average 
  

   duration 
  of 
  time 
  between 
  the 
  transits 
  of 
  the 
  component 
  stars 
  of 
  the 
  double 
  

   over 
  a 
  wire 
  inclined 
  78° 
  5' 
  to 
  the 
  meridian, 
  was 
  9'61 
  sees. 
  The 
  angle 
  of 
  

   position 
  had 
  been 
  found 
  to 
  be 
  22° 
  0'. 
  Then— 
  

  

  9-61 
  sees. 
  X 
  15 
  = 
  144-15 
  Log 
  2458814 
  

  

  Bin 
  P 
  (36° 
  54') 
  9-778465 
  

  

  cos 
  a 
  78° 
  5' 
  9-314897 
  

  

  oosec 
  (a-0) 
  56° 
  5' 
  10-081000 
  

  

  1-333166 
  

   The 
  natural 
  number 
  corresponding 
  to 
  this 
  is 
  21*53. 
  Hence 
  the 
  distance 
  

   between 
  the 
  stars 
  is 
  21J 
  seconds 
  of 
  arc. 
  This 
  measure 
  was 
  taken 
  befors 
  

   apparatus 
  described 
  in 
  this 
  paper 
  had 
  been 
  made 
  as 
  perfect 
  as 
  it 
  is 
  at 
  

  

  