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  449 
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  L. 
  Multiple 
  Transmission 
  Fixed-Arm 
  Spectroscopes. 
  By 
  

   W. 
  Cassie, 
  M.A., 
  Professor 
  of 
  Physics 
  in 
  the 
  Royal 
  

   Hollo 
  way 
  Coll 
  eye 
  *. 
  

  

  VARIOUS 
  forms 
  of 
  spectroscope 
  have 
  been 
  devised 
  to 
  

   diminish 
  the 
  number 
  of 
  prisms 
  required 
  for 
  great 
  dis- 
  

   persion 
  by 
  using 
  each 
  prism 
  more 
  than 
  once. 
  Contrivances 
  

   for 
  reflecting 
  the 
  beam 
  of 
  light 
  back 
  through 
  a 
  prism 
  or 
  train 
  

   of 
  prisms 
  a 
  second 
  time 
  by 
  means 
  of 
  a 
  mirror 
  or 
  a 
  reflecting 
  

   prism 
  have 
  been 
  used 
  by 
  many 
  observers. 
  An 
  instrument 
  has 
  

   been 
  devised 
  by 
  Prof. 
  Wadsworth 
  in 
  which 
  the 
  beam 
  is 
  sent 
  

   six 
  times 
  through 
  one 
  prism 
  by 
  the 
  use 
  of 
  seven 
  mirrors. 
  

  

  The 
  spectroscopes 
  described 
  in 
  the 
  present 
  paper 
  secure 
  

   many 
  transmissions 
  of 
  the 
  beam 
  through 
  one 
  or 
  two 
  prisms 
  

   by 
  the 
  use 
  of 
  a 
  principle 
  which 
  will 
  be 
  best 
  explained 
  by 
  

   describing 
  the 
  instruments 
  themselves. 
  

  

  I. 
  

  

  The 
  first 
  form 
  of 
  instrument 
  I 
  have 
  to 
  describe, 
  which 
  is 
  in 
  

   some 
  respects 
  the 
  most 
  satisfactory 
  of 
  the 
  first 
  three, 
  is 
  made 
  

   with 
  two 
  half-prisms 
  each 
  silvered 
  on 
  one 
  side. 
  Figs. 
  1 
  

   and 
  2 
  (p. 
  450) 
  show 
  the 
  essentials 
  of 
  the 
  instrument, 
  fig. 
  1 
  

   in 
  plan 
  and 
  fig. 
  2 
  in 
  elevation. 
  

  

  A 
  is 
  the 
  collimator, 
  B 
  the 
  telescope, 
  ah 
  c 
  and 
  d 
  ef 
  are 
  two 
  

   equal 
  half-prisms 
  silvered 
  on 
  the 
  faces 
  ac 
  and 
  c//and 
  placed 
  

   with 
  their 
  faces 
  vertical. 
  The 
  beam 
  of 
  light, 
  after 
  emerging 
  

   from 
  the 
  collimator 
  A, 
  passes 
  under 
  the 
  prism 
  a 
  b 
  c 
  and 
  strikes 
  

   the 
  prism 
  d 
  ef 
  near 
  the 
  lower 
  edge 
  of 
  the 
  face 
  d 
  e. 
  This 
  

   prism 
  is 
  so 
  placed 
  that 
  the 
  beam 
  entering 
  at 
  d 
  e 
  is 
  reflected 
  

   almost 
  normally 
  at 
  the 
  silvered 
  face 
  df 
  and 
  comes 
  out 
  again 
  

   at 
  the 
  face 
  d 
  e. 
  - 
  Now 
  this 
  beam 
  is 
  not 
  horizontal 
  in 
  direction, 
  

   but 
  is 
  slightly 
  inclined 
  upwards. 
  The 
  consequence 
  is 
  that 
  

   the 
  beam 
  returning 
  after 
  emergence 
  from 
  d 
  e 
  can 
  be 
  caused 
  

   to 
  strike 
  the 
  prism 
  a 
  b 
  c 
  on 
  the 
  lower 
  part 
  of 
  the 
  face 
  a 
  b. 
  

   This 
  prism 
  also 
  is 
  placed 
  so 
  that 
  the 
  beam 
  is 
  reflected 
  almost 
  

   normally 
  at 
  the 
  silvered 
  face 
  a 
  c, 
  and 
  after 
  emerging 
  from 
  

   a 
  b 
  again 
  strikes 
  d 
  e 
  at 
  a 
  place 
  higher 
  than 
  at 
  first 
  ; 
  and 
  so 
  

   travels 
  backwards 
  and 
  forwards 
  between 
  the 
  two 
  prisms, 
  

   gradually 
  climbing 
  upwards 
  until 
  at 
  last 
  the 
  beam 
  from 
  a 
  1> 
  

   passes 
  over 
  the 
  top 
  of 
  the 
  prism 
  d 
  ef 
  and 
  enters 
  the 
  telescope 
  B. 
  

   Each 
  reflexion 
  through 
  a 
  half-prism 
  is 
  equivalent 
  to 
  transmis- 
  

   sion 
  with 
  minimum 
  deviation 
  through 
  a 
  prism 
  whose 
  refracting 
  

   anole 
  is 
  twice 
  that 
  of 
  the 
  half-prism. 
  So 
  that 
  this 
  arrange- 
  

   ment 
  is 
  equivalent 
  to 
  a 
  train 
  of 
  as 
  many 
  prisms 
  as 
  there 
  are 
  

  

  * 
  Communicated 
  by 
  the 
  Physical 
  Society 
  : 
  read 
  November 
  22, 
  1901. 
  

  

  