﻿On 
  the 
  Two-Dimensional 
  Motion 
  of 
  Infinite 
  Liquid. 
  119 
  

  

  intensities 
  at 
  corresponding 
  points 
  have 
  been 
  made 
  with 
  

   reflecting 
  surfaces 
  of 
  rectangular 
  form 
  or 
  consisting 
  of 
  either 
  

   two 
  or 
  three 
  elements 
  in 
  the 
  same 
  plane 
  for 
  various 
  angles 
  

   of 
  incidence; 
  the 
  results 
  show 
  that 
  the 
  expression 
  for 
  the 
  

   illumination 
  at 
  any 
  point 
  of 
  the 
  diffraction 
  pattern 
  contains 
  

   a 
  factor 
  proportional 
  to 
  the 
  square 
  of 
  the 
  cosine 
  of 
  the 
  obli- 
  

   quity 
  at 
  such 
  point. 
  

  

  The 
  experiments 
  and 
  observations 
  described 
  in 
  the 
  note 
  

   were 
  carried 
  out 
  in 
  the 
  Palit 
  Laboratory 
  of 
  Physics. 
  The 
  

   writer 
  hopes 
  to 
  carry 
  out 
  further 
  work 
  on 
  the 
  subject 
  of 
  

   oblique 
  diffraction 
  by 
  various 
  forms 
  of 
  aperture, 
  and 
  parti- 
  

   cularly 
  in 
  regard 
  to 
  the 
  positions 
  of 
  the 
  points 
  of 
  maximum 
  

   intensity 
  in 
  the 
  pattern, 
  which 
  would 
  no 
  doubt 
  differ 
  from 
  

   those 
  given 
  by 
  the 
  usual 
  formulae 
  owing 
  to 
  the 
  asymmetry 
  

   of 
  the 
  illumination 
  curves. 
  

  

  Calcutta, 
  

  

  XII. 
  On 
  the 
  Two-Dimensional 
  Motion 
  of 
  Infinite 
  Liquid 
  

   produced 
  by 
  the 
  Translation 
  or 
  Rotation 
  of 
  a 
  Contained 
  

   Solid. 
  By 
  J. 
  Gr. 
  Leathem, 
  M.A., 
  D.Sc, 
  Fellow 
  of 
  

   St. 
  Johns 
  College, 
  Cambridge*. 
  

  

  1. 
  TJERIODIC 
  conformal 
  transformations 
  — 
  that 
  is, 
  trans- 
  

   XT 
  formations 
  by 
  which 
  doubly 
  connected 
  regions 
  in 
  

   the 
  plane 
  of 
  a 
  variable 
  z 
  = 
  x-\-iy, 
  externally 
  unbounded 
  and 
  

   bounded 
  internally 
  by 
  a 
  closed 
  polygon 
  or 
  curve, 
  may 
  be 
  

   represented 
  conformally 
  and 
  repeatedly 
  upon 
  successive 
  

   semi-infinite 
  strips 
  of 
  width 
  \ 
  in 
  the 
  half-plane 
  77 
  >0 
  of 
  a 
  

   variable 
  f= 
  %-\-ir) 
  — 
  have 
  been 
  studied 
  by 
  the 
  present 
  writer 
  

   in 
  a 
  previous 
  paper 
  f 
  . 
  It 
  has 
  there 
  been 
  shown 
  how 
  the 
  

   knowledge 
  of 
  such 
  a 
  transformation 
  for 
  any 
  particular 
  curve 
  

   makes 
  possible 
  the 
  specification 
  of 
  a 
  field 
  of 
  circulatory 
  

   liquid 
  flow 
  (with 
  or 
  without 
  logarithmic 
  singularities) 
  round 
  

   a 
  fixed 
  solid 
  body 
  bounded 
  by 
  the 
  curve. 
  

  

  It 
  is 
  now 
  propose 
  1 
  to 
  show 
  that 
  such 
  knowledge 
  makes 
  

   possible 
  also 
  the 
  determination 
  of 
  the 
  field 
  of 
  irrotational 
  

   motion 
  due 
  to 
  any 
  translation 
  or 
  rotation 
  of 
  the 
  same 
  solid 
  

   in 
  surrounding 
  infinite 
  liquid. 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  t 
  J. 
  G. 
  Leathem, 
  " 
  On 
  Periodic 
  Conformal 
  Curve-Factors 
  and 
  Corner- 
  

   Factors," 
  Proc. 
  Royal 
  Irish 
  Academy, 
  vol. 
  xxxiii. 
  Sec. 
  A, 
  August 
  

   1916. 
  

  

  