﻿172 
  Prof. 
  Q. 
  Majorana 
  on 
  the 
  Second 
  

  

  in 
  this 
  manner 
  I 
  have 
  been 
  able 
  to 
  observe 
  with 
  the 
  tele- 
  

   scope 
  C, 
  with 
  sufficient 
  clearness, 
  countless 
  circular 
  fringes, 
  

   even 
  for 
  Z 
  = 
  32 
  cm. 
  But 
  for 
  these 
  researches 
  I 
  have 
  limited 
  

   the 
  difference 
  of 
  path 
  to 
  1=1'6 
  cm., 
  or 
  still 
  less. 
  

  

  The 
  disposition 
  described 
  above 
  is 
  particularly 
  suitable 
  

   for 
  detecting 
  very 
  small 
  differences 
  in 
  the 
  value 
  of 
  the 
  

   incident 
  wave-length 
  ; 
  in 
  fact, 
  the 
  value 
  of 
  I 
  being 
  large 
  a 
  

   very 
  great 
  number 
  of 
  wave-lengths 
  is 
  comprised 
  in 
  this 
  length 
  

   (e.g., 
  200,000 
  if 
  A 
  = 
  0*5//., 
  and 
  1 
  = 
  10 
  cm.), 
  and 
  correspond- 
  

   ingly 
  for 
  the 
  same 
  variations 
  very 
  sensible 
  displacements 
  

   can 
  be 
  observed 
  in 
  the 
  position 
  of 
  a 
  fringe. 
  

  

  With 
  the 
  apparatus 
  disposed 
  as 
  above, 
  let 
  us 
  note 
  with 
  

   the 
  micrometer 
  wire 
  of 
  the 
  telescope 
  the 
  position 
  of 
  a 
  fringe, 
  

   for 
  instance 
  the 
  first 
  central 
  bright 
  one, 
  when 
  R 
  is 
  in 
  the 
  

   position 
  shown 
  in 
  the 
  figure, 
  or, 
  still 
  better, 
  when 
  it 
  revolves 
  

   with 
  a 
  negligible 
  velocity 
  (one 
  turn 
  per 
  second). 
  If, 
  now, 
  

   this 
  velocity 
  be 
  increased 
  to 
  sixty 
  turns 
  per 
  second 
  a 
  displace- 
  

   ment 
  of 
  the 
  fringe 
  under 
  observation 
  is 
  distinctly 
  visible 
  ; 
  if 
  

   the 
  mirrors 
  are 
  moving 
  against 
  the 
  incident 
  ray 
  this 
  dis- 
  

   placement 
  indicates 
  a 
  diminution 
  of 
  \ 
  and 
  it 
  changes 
  sign 
  

   when 
  the 
  direction 
  of 
  rotation 
  of 
  the 
  wheel 
  is 
  reversed, 
  and 
  

   this 
  indicates 
  an 
  increase 
  of 
  X. 
  In 
  order 
  to 
  define 
  the 
  sense 
  

   of 
  the 
  displacement, 
  I 
  will 
  say 
  that 
  on 
  examining 
  the 
  system 
  of 
  

   circular 
  fringes 
  with 
  the 
  telescope 
  focussed 
  for 
  infinite 
  distance 
  

   the 
  diameter 
  of 
  each 
  of 
  these 
  increases 
  when 
  the 
  mirrors 
  

   move 
  against 
  the 
  incident 
  ray, 
  and 
  the 
  fringes 
  themselves 
  

   crowd 
  together 
  as 
  those 
  of 
  large 
  diameter 
  are 
  very 
  little 
  

   displaced 
  ; 
  at 
  the 
  same 
  time 
  some 
  new 
  fringes 
  come 
  out 
  

   from 
  the 
  centre 
  of 
  the 
  system. 
  On 
  the 
  other 
  hand, 
  when 
  

   the 
  mirrors 
  are 
  moving 
  in 
  the 
  sense 
  of 
  propagation 
  of 
  the 
  

   incident 
  light 
  the 
  diameter 
  of 
  each 
  fringe 
  diminishes 
  ; 
  they 
  

   become 
  more 
  widely 
  separated, 
  and 
  some 
  of 
  them 
  are 
  as 
  it 
  

   were 
  swallowed 
  up 
  by 
  the 
  centre. 
  

  

  Before 
  stating 
  the 
  measure 
  of 
  the 
  displacement 
  observed 
  

   we 
  will 
  see 
  what 
  it 
  should 
  amount 
  to, 
  making 
  the 
  hypothesis 
  

   that 
  the 
  velocity 
  of 
  the 
  light 
  reflected 
  from 
  a 
  mirror 
  is 
  the 
  

   same 
  as 
  that 
  of 
  the 
  incident 
  light. 
  Let 
  g 
  be 
  the 
  number 
  of 
  

   revolutions 
  of 
  R 
  per 
  second 
  and 
  d 
  its 
  diameter, 
  reckoned 
  

   between 
  the 
  centres 
  of 
  two 
  opposite 
  mirrors 
  M, 
  then 
  irdg 
  

   will 
  be 
  the 
  instantaneous 
  velocity 
  of 
  translation 
  of 
  the 
  latter. 
  

   Since 
  the 
  mirrors 
  are 
  inclined 
  at 
  an 
  angle 
  a 
  to 
  the 
  radius 
  of 
  

   the 
  wheel 
  passing 
  through 
  each 
  of 
  them, 
  the 
  component 
  

   of 
  the 
  given 
  velocity 
  in 
  the 
  direction 
  normal 
  to 
  the 
  plane 
  of 
  

   each 
  mirror 
  will 
  be 
  

  

  v 
  = 
  irdg 
  cos 
  a. 
  

  

  