﻿730 
  Mr. 
  Taudin 
  Chabot: 
  Gyrodynamical 
  Solution 
  of 
  the 
  

  

  only 
  one 
  point 
  fixed, 
  so 
  that 
  since 
  then 
  we 
  distinguish 
  apart 
  

   from 
  a 
  theoretical 
  dynamics 
  of 
  rotation 
  still 
  a 
  kinematics 
  of 
  

   rotation 
  of 
  a 
  more 
  experimental 
  kind, 
  and 
  treatises 
  by 
  Ampere, 
  

   Poinsot, 
  Thomson 
  (Lord 
  Kelvin) 
  , 
  &c. 
  on 
  the 
  one 
  side, 
  as 
  well 
  

   as 
  such 
  by 
  Sang, 
  Foucault, 
  Sire, 
  &c. 
  on 
  the 
  other. 
  

  

  We 
  must 
  throughout 
  take 
  note 
  as 
  to 
  whether 
  the 
  axis 
  of 
  

   rotation 
  is 
  fixed 
  at 
  one 
  point 
  only, 
  viz., 
  the 
  centre 
  of 
  mass 
  

   of 
  the 
  rotating 
  system, 
  so 
  that 
  it 
  can 
  take 
  up 
  any 
  position 
  in 
  

   space, 
  or 
  is 
  fixed 
  in 
  one 
  plane, 
  wherein, 
  it 
  is 
  true, 
  it 
  may 
  

   take 
  up 
  any 
  azimuth, 
  but 
  which 
  it 
  does 
  not 
  leave. 
  

  

  The 
  first 
  case 
  indicates 
  the 
  way 
  to 
  obtain 
  an 
  axis 
  of 
  rotation 
  

   of 
  unchangeable 
  direction 
  in 
  absolute 
  space, 
  like 
  a 
  finger 
  (so 
  to 
  

   speak) 
  of 
  the 
  great 
  clock, 
  that 
  is 
  Earth. 
  Here, 
  however, 
  we 
  are 
  

   not 
  able 
  to 
  succeed 
  on 
  account 
  of 
  the 
  unavoidable 
  friction 
  on 
  

   the 
  pivot 
  — 
  in 
  default 
  of 
  a 
  directing 
  force 
  to 
  overcome 
  this. 
  

  

  But 
  there 
  is 
  fortunately 
  a 
  directing 
  force 
  to 
  hand 
  on 
  the 
  

   earth's 
  surface, 
  where 
  it 
  is 
  of 
  value 
  in 
  practical 
  arrangements 
  

   made 
  according 
  to 
  the 
  second 
  mode, 
  whereby 
  to 
  overcome 
  

   the 
  bearing-friction 
  ; 
  and 
  a 
  definite 
  direction 
  can 
  be 
  secured 
  

   of 
  the 
  axis 
  of 
  rotation, 
  which 
  is 
  no 
  longer 
  unvariable 
  in 
  

   relation 
  to 
  absolute 
  space, 
  but 
  in 
  relation 
  to 
  the 
  earth 
  alone. 
  

  

  Accordingly 
  the 
  conditions 
  appear 
  to 
  be 
  given, 
  by 
  which 
  

   we 
  may 
  succeed 
  in 
  setting 
  up 
  an 
  amagnetic 
  compass, 
  as 
  

   one 
  has 
  endeavoured 
  to 
  do 
  in 
  very 
  many 
  ways 
  by 
  gyro- 
  

   scopic 
  * 
  contrivances 
  for 
  nautical 
  use, 
  trying 
  to 
  determine 
  

   the 
  meridian 
  on 
  board 
  ship 
  by 
  means 
  of 
  the 
  axis 
  of 
  rotation 
  

   of 
  a 
  gyrostat 
  *, 
  held 
  horizontally 
  in 
  Cardani 
  suspensions. 
  

  

  The 
  whole 
  group 
  of 
  previous 
  investigators 
  have 
  endeavoured 
  

   to 
  succeed 
  in 
  this 
  manner, 
  but 
  evidence 
  is 
  forthcoming, 
  that 
  

   no 
  experimentalist 
  has 
  given 
  a 
  general 
  and 
  rigorous 
  account 
  

   of 
  the 
  actual 
  behaviour 
  and 
  the 
  necessary 
  conditions. 
  And 
  

   yet 
  for 
  this 
  it 
  is 
  only 
  necessary 
  to 
  analyse 
  the 
  system 
  of 
  forces, 
  

   which 
  enters 
  into 
  the 
  performance 
  of 
  a 
  gyrostat 
  mounted 
  on 
  

   board 
  ship 
  in 
  the 
  manner 
  described. 
  

  

  It 
  appears 
  then, 
  first 
  of 
  all, 
  that 
  the 
  vertical 
  axis, 
  round 
  

   which 
  the 
  turning 
  into 
  the 
  meridian 
  should 
  take 
  place, 
  is 
  

   only 
  an 
  imaginary 
  one. 
  In 
  practice 
  we 
  have 
  to 
  deal 
  with 
  

   an 
  axis, 
  which 
  moves 
  over 
  the 
  surface 
  of 
  a 
  cone 
  ; 
  and 
  

   the 
  axis 
  of 
  this 
  cone 
  only 
  is 
  the 
  ideal 
  vertical 
  axis, 
  round 
  

   which 
  constructors 
  have 
  hitherto 
  considered 
  their 
  gyrostats 
  

   to 
  rotate. 
  Now 
  we 
  can 
  make 
  the 
  apex 
  of 
  the 
  cone 
  small, 
  

   very 
  small 
  indeed, 
  but 
  never 
  zero, 
  a 
  certain 
  amount 
  of 
  

  

  * 
  A 
  gyroscope 
  means 
  the 
  whole 
  of 
  the 
  aiTangement 
  iDcluding 
  the 
  

   device 
  for 
  observation 
  (hand, 
  microscope, 
  or 
  the 
  like), 
  whilst 
  gyrostat 
  is 
  

   the 
  rotating 
  mass 
  in 
  its 
  frame 
  alone. 
  So 
  the 
  gyrostat 
  can 
  be 
  called 
  

   a 
  gyroscope 
  (as 
  is 
  generally 
  done 
  by 
  French 
  and 
  German 
  authors) 
  with 
  

   no 
  more 
  sense 
  than, 
  for 
  instance, 
  a 
  spectrum 
  can 
  be 
  called 
  a 
  spectroscope. 
  

  

  