﻿Problem 
  of 
  the 
  Amagnetic 
  Mariner 
  s 
  Compass. 
  735 
  

  

  conditions 
  to 
  be 
  realised 
  here 
  are 
  : 
  exact 
  balancing 
  about 
  

   the 
  axis 
  y, 
  by 
  adjusting 
  the 
  centre 
  of 
  the 
  rotating 
  mass 
  (and 
  

   not 
  by 
  an 
  additional 
  weight, 
  as 
  Gilbert 
  did 
  in 
  his 
  baro- 
  

   gyroscope 
  *), 
  and 
  practically 
  no 
  slack-motion 
  of 
  the 
  axis 
  y 
  

   in 
  its 
  bearings. 
  

  

  Let 
  us 
  now 
  identify 
  the 
  principal 
  axis 
  of 
  rotation, 
  F, 
  of 
  our 
  

   model 
  with 
  the 
  axis 
  of 
  rotation 
  of 
  the 
  planet, 
  so 
  that 
  as 
  

   tangible 
  of 
  the 
  whole 
  merely 
  remain 
  the 
  gyrostat, 
  lying 
  in 
  

   its 
  bearings, 
  with 
  the 
  clockwork, 
  C, 
  which 
  imparts 
  the 
  

   angular 
  velocity 
  w^, 
  syntropic 
  with 
  o)^ 
  ; 
  and 
  let 
  this 
  

   apparatus 
  be 
  mounted 
  with 
  the 
  .37-axis 
  in 
  suitable 
  Cardani- 
  

   suspensions 
  on 
  bpard 
  a 
  ship, 
  where 
  it, 
  when 
  in 
  the 
  geo- 
  

   graphical 
  latitude 
  </>, 
  takes 
  up 
  the 
  position, 
  indicated 
  in 
  the 
  

   figure 
  relative 
  to 
  the 
  earth^s 
  axis 
  F, 
  whenever 
  the 
  ?/-axis 
  

   passes 
  through 
  the 
  meridian. 
  At 
  this 
  moment 
  the 
  gyrostat 
  

   behaves 
  astatically 
  with 
  respect 
  to 
  the 
  simultaneous 
  rotation 
  

   round 
  F 
  (c/. 
  above, 
  No. 
  6 
  a), 
  and 
  responds 
  exclusively 
  to 
  

   the 
  directing 
  force, 
  due 
  to 
  the 
  rotation 
  round 
  ^, 
  or 
  else 
  to 
  an 
  

   elastic 
  device, 
  which 
  tends 
  to 
  turn 
  the 
  7-axis 
  into 
  the 
  vertical, 
  

   I. 
  e. 
  into 
  the 
  extension 
  of 
  the 
  axis 
  of 
  rotation 
  x. 
  But 
  at 
  the 
  

   next 
  instant 
  the 
  ?/-axis 
  has 
  passed 
  through 
  the 
  meridian, 
  ex- 
  

   periences 
  again 
  the 
  deflecting 
  force 
  of 
  the 
  rotation 
  round 
  F, 
  

   which 
  comes 
  into 
  play, 
  and 
  increases 
  with 
  the 
  sine 
  of 
  the 
  

   angle 
  of 
  rotation 
  up 
  to 
  a 
  maximum 
  for 
  90° 
  rotation 
  of 
  the 
  

   axis 
  y 
  round 
  x 
  {cf. 
  above, 
  No. 
  6 
  li). 
  Were 
  the 
  just-named 
  

   directing 
  force 
  not 
  available, 
  so 
  would 
  the 
  deflexion 
  of 
  the 
  

   y-axis 
  from 
  the 
  vertical 
  reach 
  the 
  value 
  (90 
  — 
  </>)°, 
  i.e. 
  the 
  

   7-axis 
  would 
  set 
  itself 
  parallel 
  to 
  the 
  planet's 
  axis, 
  but 
  as 
  the 
  

   directing 
  force 
  continues, 
  the 
  deviation 
  remains 
  in 
  general 
  

   less 
  than 
  (90 
  — 
  <^)°, 
  with 
  the 
  exception 
  of 
  the 
  case 
  (treated 
  

   further 
  later 
  on) 
  of 
  a 
  resonance 
  between 
  the 
  oscillations 
  

   round 
  y 
  and 
  the 
  rotation 
  round 
  x. 
  After 
  a 
  further 
  90° 
  

   rotation 
  of 
  the 
  y-axis 
  round 
  x 
  the 
  elongation 
  will 
  be 
  again 
  

   zero, 
  and 
  the 
  7-axis 
  again 
  stand 
  vertical 
  in 
  the 
  extension 
  of 
  

   the 
  axis 
  of 
  rotation 
  x. 
  A 
  model 
  allowing 
  to 
  observe 
  these 
  

   movements 
  most 
  beautifully 
  according 
  to 
  the 
  theory 
  — 
  built 
  

   by 
  Messrs. 
  Hartmann 
  & 
  Braun 
  — 
  is 
  shown 
  in 
  fig. 
  2, 
  PI. 
  XXI. 
  

  

  Of 
  special 
  importance, 
  as 
  already 
  emphasized 
  in 
  the 
  

   introduction, 
  is 
  now 
  an 
  analysis 
  of 
  the 
  system 
  of 
  forces, 
  

   acting 
  in 
  our 
  gyrostat. 
  Besides 
  the 
  practically 
  constant 
  

   gravitational 
  force, 
  the 
  remaining 
  inconstant 
  forces 
  may 
  be 
  

   classified 
  as 
  translatory- 
  and 
  rotatory-ones. 
  All 
  translatory 
  

   forces, 
  resulting 
  from 
  the 
  inertia-reaction, 
  can 
  be 
  separated 
  

   into 
  vertical 
  and 
  horizontal 
  components, 
  in 
  consequence 
  

  

  * 
  Karissima 
  avis 
  ! 
  I 
  saw 
  one 
  only 
  once, 
  and 
  of 
  average 
  worl?manship, 
  

   at 
  the 
  CoUep^e 
  de 
  France 
  in 
  Paris. 
  

  

  