﻿Problem 
  of 
  the 
  Amagnetic 
  Mariner* 
  s 
  Compass, 
  73i^ 
  

  

  bearing 
  of 
  a 
  gyrostat, 
  perfectly 
  balanced 
  about 
  an 
  axis 
  ?/, 
  

   normal 
  to 
  the 
  axis 
  .r, 
  and 
  having 
  an 
  axis 
  of 
  rotation 
  7, 
  

   perpendicular 
  to 
  ?/. 
  Rotations 
  can 
  take 
  place 
  round 
  the 
  

   axis 
  r, 
  the 
  axis 
  x, 
  and 
  the 
  axis 
  7 
  ; 
  and 
  that 
  too 
  in 
  this 
  order, 
  

   in 
  general, 
  -with 
  increasing 
  angular 
  velocity: 
  cOj.<co^<(Oy 
  ; 
  

   correspondingly, 
  the 
  slowest 
  rotation, 
  round 
  the 
  axis 
  Y, 
  can 
  

   be 
  excited 
  perhaps 
  by 
  hand 
  ; 
  that 
  roand 
  the 
  axis 
  x 
  by 
  means 
  

   of 
  the 
  clockwork 
  C; 
  the 
  most 
  rapid 
  rotation, 
  round 
  the 
  axis 
  7, 
  

   by 
  means 
  of 
  a 
  cord, 
  wheelwork, 
  or 
  electromotor. 
  Further 
  

   possibilities, 
  that 
  the 
  model 
  may 
  be 
  arranged 
  to 
  exhibit 
  — 
  viz. 
  

   velocities 
  graded 
  otherwise 
  as 
  co 
  >(o^>(Dp 
  — 
  will 
  here 
  remain 
  

   undescribed. 
  

  

  By 
  observations 
  is 
  obtained 
  the 
  state 
  of 
  equilibrium 
  of 
  the 
  

   gyrostat, 
  i. 
  e. 
  of 
  the 
  system 
  round 
  the 
  axis 
  ?/, 
  while 
  none, 
  one, 
  

   or 
  more 
  of 
  the 
  rotations 
  round 
  the 
  axis 
  F, 
  round 
  x^ 
  or 
  round 
  

   7 
  are 
  excited. 
  Thereby 
  we 
  distinguish 
  between 
  8 
  principal 
  

   cases, 
  partially 
  subdivided, 
  according 
  to 
  the 
  given 
  azimuth 
  

   of 
  7/ 
  or 
  7: 
  

  

  Ascording 
  as 
  the 
  system 
  

  

  1 
  round 
  round 
  round 
  

  

  Axis 
  r 
  Axis 
  X 
  Axis 
  7 
  

  

  and 
  th 
  

   between 
  

   Axis 
  2/ 
  (t 
  Plane 
  r:r 
  

  

  e 
  angle 
  

  

  between 
  

  

  Axes 
  y 
  & 
  r 
  

  

  will 
  be 
  the 
  system 
  

   round 
  

   Axisy 
  

  

  1. 
  

  

  rests 
  

  

  rests 
  rests 
  

  

  

  astatic 
  

  

  2 
  

  

  turns 
  

  

  n 
  

  

  . 
  1 
  

  

  ,. 
  

  

  3. 
  

  

  re?ts 
  

  

  turns 
  

  

  ,. 
  

  

  .' 
  

  

  4. 
  

   5. 
  

  

  turns 
  

  

  

  " 
  

  

  .. 
  

  

  re.sts 
  

  

  rests 
  

  

  turns 
  

  

  >' 
  

  

  6. 
  

  

  turns 
  

  

  ^^ 
  

  

  

  = 
  0= 
  

  

  

  " 
  

  

  =90° 
  

  

  =0° 
  

   (syntropic 
  motions) 
  

  

  stable 
  

  

  1^0° 
  & 
  9^:180° 
  

  

  negatively 
  stable 
  

  

  = 
  180'^ 
  

   (antitropic 
  motions) 
  

  

  unstable 
  

   stable 
  

  

  7. 
  

  

  8. 
  

  

  rests 
  

  

  turns 
  

  

  " 
  

  

  = 
  (9O-0)° 
  

  

  9fc(90-</.)° 
  & 
  

   =7^(270-0)° 
  

  

  negatively 
  stable 
  

  

  =(270-^)" 
  

  

  unstable 
  

  

  turns 
  

  

  

  " 
  

  

  

  oscillating 
  

  

  