﻿1875.] 
  Observations 
  made 
  in 
  Little 
  Namaqualand. 
  555 
  

  

  o£ 
  the 
  magnet 
  was 
  found 
  as 
  follows 
  : 
  — 
  The 
  passage 
  of 
  the 
  line 
  of 
  reference 
  

   in 
  the 
  needle 
  oyer 
  the 
  wire 
  of 
  the 
  observing-telescope 
  was 
  noted 
  at 
  every 
  

   tenth 
  complete 
  vibration 
  passing 
  right 
  and 
  passing 
  left. 
  If 
  t 
  v 
  t 
  2 
  , 
  t 
  3 
  , 
  and 
  

   £ 
  4 
  are 
  n 
  observed 
  times 
  of 
  these 
  passages 
  right, 
  we 
  have 
  for 
  the 
  time 
  of 
  

   a 
  semivibration 
  

  

  10ft+l 
  [n(n 
  — 
  1) 
  J 
  

  

  and 
  a 
  similar 
  expression 
  for 
  the 
  time 
  from 
  the 
  passages 
  left. 
  

  

  The 
  probable 
  error 
  of 
  the 
  mean 
  of 
  these 
  two 
  determinations 
  can 
  be 
  

   shown 
  to 
  be 
  

  

  ± 
  /3 
  1 
  

  

  ioV 
  2 
  0-l>0+l)' 
  

  

  where 
  e 
  is 
  the 
  probable 
  error 
  of 
  a 
  single 
  time 
  determination. 
  

  

  In 
  the 
  Namaqualand 
  observations 
  n 
  was 
  usually 
  6. 
  If, 
  therefore, 
  

   e 
  = 
  S, 
  3, 
  we 
  have 
  for 
  the 
  probable 
  error 
  in 
  the 
  times 
  of 
  vibration 
  

  

  0-0025. 
  

  

  I 
  think 
  this 
  error 
  rather 
  in 
  excess 
  than 
  defect. 
  

  

  The 
  Dip 
  Observations 
  consisted 
  of 
  a 
  bisection 
  of 
  the 
  upper 
  and 
  lower 
  

   ends 
  of 
  the 
  needle 
  after 
  each 
  lift 
  of 
  the 
  needle 
  ; 
  both 
  microscopes 
  were 
  

   read 
  each 
  time. 
  There 
  were 
  never 
  less 
  than 
  four 
  of 
  these 
  independent 
  

   lifts 
  in 
  each 
  position 
  ; 
  a 
  complete 
  dip 
  therefore 
  consisted 
  of 
  at 
  least 
  sixty- 
  

   four 
  independent 
  bisections 
  of 
  the 
  ends 
  of 
  the 
  needle 
  and 
  of 
  thirty-two 
  

   independent 
  lifts 
  of 
  the 
  needle 
  from 
  the 
  agate 
  planes. 
  A 
  great 
  deal 
  of 
  

   time 
  was 
  consumed 
  in 
  making 
  one 
  of 
  these 
  dips 
  in 
  the 
  open 
  air, 
  on 
  

   account 
  of 
  the 
  disturbances 
  of 
  the 
  instrument 
  by 
  the 
  wind. 
  In 
  the 
  

   zenith-distance 
  observations 
  of 
  the 
  sun 
  for 
  local 
  time, 
  and 
  azimuth 
  obser- 
  

   vations 
  for 
  the 
  determination 
  of 
  the 
  absolute 
  azimuths 
  of 
  the 
  marks, 
  both 
  

   limbs 
  of 
  the 
  sun 
  in 
  reversed 
  positions 
  of 
  the 
  theodolite 
  were 
  always 
  taken. 
  

   The 
  differences 
  between 
  the 
  azimuths 
  of 
  these 
  marks, 
  usually 
  two, 
  and 
  the 
  

   azimuthal 
  reading 
  for 
  the 
  magnetic 
  meridian 
  were 
  taken 
  with 
  the 
  Elliott 
  

   instrument. 
  The 
  means 
  of 
  the 
  results 
  obtained 
  from 
  the 
  variation-needle, 
  

   which 
  allows 
  of 
  reversed 
  suspension, 
  were 
  alone 
  used 
  ; 
  but 
  the 
  reading 
  

   for 
  the 
  magnetic 
  axis 
  of 
  the 
  vibration-magnet, 
  which 
  is 
  well 
  adjusted, 
  

   was 
  usually 
  taken 
  as 
  a 
  check. 
  To 
  save 
  time 
  the 
  deflection 
  observations 
  

   were 
  only 
  made 
  at 
  the 
  distance 
  of 
  one 
  foot, 
  except 
  for 
  the 
  Port 
  Nolloth 
  

   station. 
  The 
  small 
  correction 
  to 
  the 
  results 
  thus 
  found, 
  usually 
  deter- 
  

   mined 
  by 
  a 
  second 
  set 
  of 
  deflections 
  at 
  1*3 
  foot, 
  has 
  been 
  obtained 
  from 
  

   the 
  Port 
  Nolloth 
  observations 
  and 
  other 
  determinations 
  at 
  the 
  obser- 
  

   vatory. 
  The 
  longitudes 
  of 
  the 
  stations 
  are 
  only 
  very 
  rough 
  approxima- 
  

   tions. 
  No 
  attempt 
  was 
  made 
  to 
  fix 
  them 
  with 
  any 
  greater 
  accuracy 
  than 
  

  

  