﻿736 
  Mr. 
  Taudin 
  Chabot: 
  Gyrodynamical 
  Solution 
  of 
  the 
  

  

  either 
  of 
  the 
  rolling 
  and 
  pitching 
  of 
  the 
  ship 
  (see 
  Poggen- 
  

   dorff^s 
  falling 
  machine 
  *, 
  of 
  date 
  1854), 
  or 
  else 
  horizontal 
  as 
  

   a 
  result 
  of 
  rectilinear 
  accelerations 
  on 
  her 
  way 
  and 
  their 
  

   variations; 
  they 
  have 
  no 
  influence 
  on 
  the 
  position 
  for 
  the 
  

   time 
  being 
  of 
  the 
  balanced 
  gyrostat. 
  Translatory 
  forces 
  

   along 
  an 
  arc 
  (or 
  circular 
  translatory 
  forces) 
  in 
  consequence 
  

   of 
  the 
  rotation 
  of 
  y 
  round 
  x, 
  which 
  tend 
  to 
  give 
  the 
  bearings 
  

   of 
  the 
  gyrostat 
  a 
  rotation 
  — 
  tWx, 
  exist 
  only 
  whilst 
  the 
  gyrostat 
  

   is 
  started 
  and 
  soon 
  vanish; 
  they 
  are 
  of 
  no 
  further 
  importance. 
  

  

  Rotary 
  forces 
  enter 
  in 
  two 
  ways 
  into 
  the 
  phenomena; 
  the 
  in- 
  

   termittently 
  acting 
  deflecting 
  force, 
  already 
  considered, 
  arising 
  

   in 
  consequence 
  of 
  the 
  rotation 
  round 
  the 
  planet's 
  axis 
  F, 
  and 
  

   the 
  permanent 
  directing 
  force, 
  likewise 
  referred 
  to, 
  resulting 
  

   from 
  spring 
  tension 
  or 
  from 
  rotation 
  round 
  x. 
  In 
  the 
  last 
  

   is 
  also 
  merged 
  any 
  disturbance, 
  arising 
  from 
  an 
  alteration 
  

   of 
  the 
  ship's 
  way, 
  which, 
  taking 
  place 
  in 
  a 
  horizontal 
  plane, 
  

   has 
  the 
  same 
  character 
  as 
  a 
  rotation 
  about 
  a 
  vertical 
  axis, 
  that 
  

   is 
  round 
  x. 
  or, 
  what 
  means 
  the 
  same 
  thing, 
  round 
  an 
  axis 
  

   parallel 
  to 
  x 
  ; 
  therefore, 
  an 
  increase 
  of 
  Wx 
  only 
  can 
  influence 
  

   the 
  directing 
  force 
  dependent 
  on 
  and 
  proportional 
  to 
  it 
  — 
  viz. 
  

   to 
  a 
  vanishingly 
  small 
  extent 
  — 
  what 
  solely 
  means 
  a 
  variation 
  

   (of 
  practically 
  unassignable 
  value) 
  of 
  the 
  maximum 
  elongation 
  

   of 
  the 
  gyrostatic 
  oscillation 
  and 
  in 
  no 
  way 
  will 
  disturb 
  the 
  

   frequency 
  of 
  the 
  pendulum-motion. 
  

  

  And 
  this 
  frequency 
  only 
  is 
  of 
  importance 
  to 
  us;. 
  it 
  is 
  

   equal 
  to 
  that 
  of 
  the 
  rotary 
  motion 
  of 
  the 
  forked-bearing, 
  

   and 
  necessarily 
  goes 
  through 
  a 
  to-and-fro 
  motion 
  round 
  y 
  

   during 
  each 
  rotation 
  round 
  x. 
  If 
  now 
  the 
  rotations 
  on 
  

   board 
  ship 
  are 
  counted 
  by 
  reading 
  a 
  mark, 
  fixed 
  rigidly 
  

   to 
  the 
  ship, 
  it 
  will 
  happen^ 
  that 
  apparently 
  less 
  or 
  more, 
  

   than 
  a 
  complete 
  pendulum 
  oscillation 
  about 
  y 
  corresponds 
  

   to 
  a 
  single 
  rotation 
  round 
  x. 
  This 
  phenomenon 
  is 
  easily 
  ex- 
  

   plained 
  : 
  the 
  ship 
  altering 
  her 
  course, 
  she 
  alters 
  her 
  angular 
  

   position 
  to 
  the 
  same 
  extent 
  as 
  the 
  phase-change 
  between 
  the 
  

   oscillation 
  and 
  the 
  rotation 
  of 
  the 
  gyrostat. 
  Indications 
  of 
  

   this 
  phase-change 
  imply 
  then 
  indications 
  of 
  the 
  variation 
  of 
  

   the 
  ship's 
  way, 
  or 
  rather 
  of 
  the 
  way 
  in 
  general, 
  in 
  so 
  far 
  as 
  

   only 
  the 
  passing 
  of 
  the 
  y-axis 
  through 
  definite 
  azimuths 
  at 
  

   the 
  planet's 
  surface 
  affects 
  the 
  oscillation, 
  and 
  these 
  indi- 
  

   cations 
  can 
  easily 
  be 
  obtained 
  by 
  any 
  stroboscopic 
  method, 
  

   with 
  the 
  help 
  of 
  electromagnetic 
  sending- 
  or 
  contact- 
  

   contrivances, 
  which 
  would 
  be 
  controlled 
  by 
  the 
  rotation 
  or 
  

   by 
  the 
  oscillation. 
  

  

  The 
  last 
  one 
  is 
  allowed 
  to 
  arise 
  not 
  with 
  the 
  largest 
  

  

  * 
  PoggendorfFo 
  Falling 
  Machine, 
  Annalen 
  der 
  Phys. 
  u. 
  Chem. 
  vol. 
  xcii., 
  

   1854. 
  

  

  