﻿Problem 
  of 
  the 
  Amagnetic 
  Mariner 
  s 
  Compass. 
  737 
  

  

  possible 
  amplitudes, 
  but 
  playing 
  only 
  with 
  aii, 
  arm 
  o£ 
  

   the 
  pendulum-system 
  betv/een 
  'two 
  stops 
  placed 
  near 
  to- 
  

   gether, 
  and 
  the 
  breaking 
  of 
  an 
  electric 
  circuit 
  is 
  brought 
  

   about 
  by 
  the 
  motion 
  o£ 
  the 
  7-axis 
  through 
  the 
  vertical 
  in 
  (so 
  

   to 
  speak) 
  statu 
  nascenii. 
  I£ 
  we 
  keep 
  then, 
  for 
  example, 
  a 
  

   vacuum-tube 
  lighted 
  whilst 
  it 
  rotates 
  round 
  an 
  axis 
  normal 
  to 
  

   its 
  own 
  axis, 
  synchronously 
  with 
  the 
  axis 
  of 
  the 
  fork 
  x 
  (thus 
  

   at 
  the 
  same 
  time 
  with 
  angular 
  velocity 
  w^), 
  so 
  will 
  the 
  ship's 
  

   way 
  and 
  its 
  variations 
  be 
  indicated 
  by 
  the 
  position 
  and 
  the 
  

   angular 
  deviations 
  of 
  the 
  luminous 
  line 
  of 
  the 
  tube. 
  Thence 
  

   arises 
  obviously 
  the 
  possibility 
  also 
  of 
  indicating 
  it 
  at 
  a 
  dis- 
  

   tance 
  and 
  at 
  several 
  distant 
  points 
  of 
  the 
  ship 
  at 
  the 
  same 
  

   time, 
  — 
  not 
  only 
  by 
  means 
  of 
  vacuum-tubes 
  of 
  course, 
  but 
  

   also 
  by 
  means 
  of 
  indicator-plates 
  (scales) 
  or 
  of 
  the 
  ordinary 
  

   compass-cards. 
  

  

  The 
  basis 
  of 
  determining 
  the 
  numerical 
  relations 
  of 
  an 
  in- 
  

   strument 
  constructed 
  for 
  this 
  purpose, 
  is 
  obtained 
  as 
  follows: 
  — 
  

   AYe 
  take 
  two 
  planes 
  of 
  reference, 
  one 
  through 
  the 
  equator 
  of 
  

   the 
  rotating 
  planet, 
  and 
  one 
  through 
  the 
  meridian 
  of 
  the 
  point 
  

   in 
  question, 
  perpendicular 
  to 
  its 
  surface 
  and 
  normal 
  to 
  the 
  

   equatorial 
  plane. 
  At 
  this 
  point 
  the 
  axis 
  x 
  is 
  the 
  vertical. 
  

   The 
  deviation 
  of 
  the 
  axis 
  ./; 
  from 
  the 
  equatorial 
  plane, 
  i. 
  e. 
  the 
  

   geographical 
  latitude, 
  we 
  take 
  as 
  c^, 
  the 
  angle 
  between 
  the 
  

   now-horizontal 
  axis 
  y 
  and 
  the 
  meridian-plane 
  as 
  ;!^, 
  the 
  angle 
  

   between 
  the 
  axis 
  7 
  and 
  the 
  horizontal 
  plane 
  as 
  y^. 
  Further 
  

   we 
  denote 
  by 
  ly 
  the 
  moment 
  of 
  inertia 
  of 
  the 
  system 
  M 
  

   round 
  J/, 
  by 
  ly 
  that 
  of 
  the 
  rotating 
  mass 
  m 
  round 
  7 
  and 
  by 
  w,, 
  

   the 
  greatest 
  value 
  of 
  the 
  angular 
  velocity 
  of 
  an 
  alteration 
  

   of 
  the 
  ship's 
  way, 
  for 
  which 
  the 
  instrument 
  shall 
  be 
  required 
  

   to 
  perform, 
  wherefore 
  we 
  do 
  not 
  need 
  the 
  value 
  of 
  the 
  most 
  

   rapid 
  turning 
  as 
  the 
  largest 
  angular 
  velocity 
  in 
  general, 
  but 
  

   it 
  evidently 
  is 
  enough 
  to 
  insert 
  in 
  the 
  calculation 
  the 
  

   greatest 
  value 
  of 
  <o„ 
  for 
  which 
  at 
  any 
  time 
  will 
  be 
  steered 
  

   from 
  the 
  instrument 
  alone. 
  

  

  The 
  azimuths 
  % 
  = 
  0^ 
  and 
  ;i^ 
  = 
  180^ 
  of 
  the 
  y-axis 
  correspond 
  

   then 
  to 
  the 
  value 
  i|r 
  = 
  90°. 
  as 
  is 
  shown 
  in 
  the 
  figure 
  of 
  the 
  

   model, 
  whilst 
  for 
  ;^ 
  = 
  90° 
  and 
  ;;^ 
  = 
  270° 
  the 
  axis 
  7 
  shows 
  the 
  

   greatest 
  possible 
  deviation, 
  but 
  only, 
  in 
  general 
  (as 
  above 
  

   pointed 
  out), 
  without 
  -^^r 
  taking 
  up 
  its 
  theoretically 
  smallest 
  

   value 
  0. 
  

  

  At 
  the 
  instants 
  when 
  % 
  = 
  0° 
  and 
  ;)^ 
  = 
  180° 
  the 
  pendulum- 
  

   system 
  is 
  able 
  to 
  follow 
  unlessened 
  a 
  directing 
  force 
  F^, 
  

   called 
  into 
  play 
  by 
  the 
  rotation 
  round 
  .r 
  or 
  an 
  elastic 
  force 
  Fr, 
  

   which 
  one 
  will 
  have 
  adjusted 
  so 
  as 
  to 
  render 
  the 
  .r-axis 
  

   stable 
  in 
  the 
  vertical. 
  So 
  in 
  F^ 
  we 
  have 
  to 
  deal 
  with 
  an 
  

   independent 
  variable, 
  which 
  can 
  l)e 
  measured 
  as 
  circumstances 
  

  

  