﻿Geological 
  Society. 
  549 
  

  

  the 
  rotation 
  round 
  CP 
  ; 
  then 
  if 
  these 
  circles 
  intersect 
  in 
  the 
  

   point 
  M, 
  the 
  resultant 
  of 
  the 
  two 
  successive 
  rotations 
  is 
  a 
  

   rotation 
  round 
  CM 
  through 
  an 
  angle 
  equal 
  to 
  2A!MP. 
  

   Now 
  since 
  A 
  1 
  P 
  = 
  7r/2, 
  we 
  have 
  

  

  O 
  7T 
  O 
  7T 
  

  

  tan 
  PM 
  = 
  tan 
  s 
  cosec 
  - 
  or 
  PM= 
  s 
  cosec 
  — 
  , 
  

   2 
  p 
  2 
  p 
  

  

  if 
  8 
  be 
  small 
  : 
  also 
  

  

  cos 
  AjMP 
  = 
  cos 
  - 
  cos 
  - 
  , 
  

  

  2 
  p 
  

  

  whence, 
  if 
  A 
  1 
  MP=7r/p 
  + 
  a), 
  we 
  have, 
  neglecting 
  co 
  2 
  , 
  

  

  S 
  2 
  L 
  TT 
  

  

  (0= 
  -r- 
  cot 
  — 
  , 
  

   o 
  p 
  

  

  and 
  the 
  resultant 
  rotation 
  (A 
  1 
  S_ 
  p 
  ) 
  p 
  is 
  a 
  rotation 
  round 
  CM 
  

   through 
  an 
  angle 
  

  

  { 
  

  

  27T 
  8 
  2 
  . 
  7lO 
  _ 
  , 
  »S 
  2 
  . 
  7T 
  

  

  — 
  + 
  — 
  COt- 
  > 
  Xp 
  = 
  27T+±—- 
  COt-. 
  

  

  p 
  4 
  p 
  ) 
  r 
  4 
  jo 
  

  

  Hence, 
  if 
  8 
  be 
  very 
  small, 
  the 
  effect 
  of 
  the 
  packet 
  is 
  very 
  

   nearly 
  to 
  move 
  the 
  representative 
  point 
  along 
  a 
  parallel 
  of 
  

   latitude 
  to 
  a 
  meridian 
  differing 
  from 
  the 
  original 
  meridian 
  by 
  

   an 
  angle 
  

  

  OD 
  P& 
  2 
  ,7T 
  

  

  2U= 
  — 
  - 
  cot 
  -, 
  

   4 
  p 
  

  

  the 
  rotation 
  being 
  in 
  a 
  direction 
  opposite 
  to 
  that 
  in 
  which 
  the 
  

   angle 
  of 
  combination 
  of 
  the 
  plates 
  is 
  measured. 
  

  

  Thus, 
  in 
  traversing 
  the 
  packet, 
  the 
  plane 
  of 
  maximum 
  

   polarization 
  of 
  the 
  stream 
  is 
  turned 
  through 
  an 
  angle 
  R, 
  the 
  

   form 
  of 
  the 
  vibrations 
  of 
  the 
  extremity 
  of 
  the 
  polarization- 
  

   vector 
  remaining 
  unchanged. 
  

  

  LXIV. 
  Proceedings 
  of 
  Learned 
  Societies. 
  

  

  GEOLOGICAL 
  SOCIETY. 
  

  

  [Continued 
  from 
  p. 
  460.] 
  

  

  December 
  4th, 
  1902.— 
  J. 
  J. 
  H. 
  Teall, 
  Esq., 
  M.A., 
  Y.P.R.S., 
  

   President, 
  in 
  the 
  Chair. 
  

   f 
  PHE 
  following 
  communications 
  were 
  read: 
  — 
  

   -■- 
  1. 
  'On 
  a 
  New 
  Genus 
  belonging 
  to 
  the 
  Leperditiadas, 
  from 
  the 
  

   Cambrian 
  Shales 
  of 
  Malvern.' 
  By 
  Prof. 
  Theodore 
  Thomas 
  Groom, 
  

   M.A., 
  D.Sc, 
  F.G.S. 
  

  

  