﻿436 
  Mr. 
  R. 
  Hargreaves 
  on 
  a 
  

  

  known 
  Jamin 
  refractometer. 
  It 
  is 
  perhaps 
  worthy 
  o£ 
  note 
  

   how 
  comparatively 
  simple 
  it 
  is 
  to 
  obtain 
  the 
  fringes 
  and 
  

   practically 
  construct 
  a 
  refractometer 
  out 
  of 
  ordinary 
  plate- 
  

   glass. 
  All 
  that 
  is 
  necessary 
  is 
  to 
  cut 
  two 
  pieces 
  from 
  the 
  

   same 
  sheet 
  so 
  as 
  to 
  include 
  the 
  same 
  contour-line. 
  They 
  

   then 
  necessarily 
  show 
  the 
  fringes 
  with 
  white 
  light, 
  and 
  the 
  

   width 
  of 
  the 
  fringes 
  can 
  he 
  made 
  as 
  great 
  as 
  desired 
  by 
  

   rotating 
  one 
  piece 
  on 
  the 
  other. 
  

  

  Multiple 
  Reflexion 
  in 
  Sodium 
  Liglit. 
  — 
  The 
  various 
  systems 
  

   due 
  to 
  multiple 
  reflexion 
  of 
  course 
  exist 
  with 
  sodium 
  light, 
  

   but 
  in 
  consequence 
  of 
  the 
  large 
  number 
  of 
  fringes 
  then 
  

   visible 
  the 
  systems 
  always 
  overlap, 
  and 
  it 
  is 
  the 
  resultant 
  

   effect 
  only 
  which 
  is 
  seen. 
  This 
  accounts 
  for 
  the 
  curious 
  

   behaviour 
  of 
  the 
  fringes 
  which 
  is 
  observed 
  when 
  one 
  plate 
  is 
  

   slightly 
  tilted 
  on 
  the 
  other. 
  Each 
  fringe, 
  instead 
  of 
  keeping 
  

   quite 
  fixed 
  to 
  the 
  glass 
  as 
  the 
  tilting 
  occurs, 
  appears 
  to 
  vibrate 
  

   rapidly 
  from 
  side 
  to 
  side 
  through 
  half 
  a 
  fringe 
  width. 
  It 
  

   suddenly 
  disappears, 
  reappears 
  half 
  a 
  fringe 
  width 
  away, 
  

   disappears, 
  and 
  reappears 
  in 
  its 
  original 
  position 
  again. 
  This 
  

   is 
  exactly 
  the 
  effect 
  that 
  the 
  superposition 
  of 
  individual 
  systems 
  

   of 
  fringes 
  moving 
  in 
  opposite 
  directions 
  across 
  the 
  field 
  would 
  

   produce. 
  

  

  The 
  same 
  effect 
  shows 
  itself 
  in 
  another 
  way 
  in 
  the 
  photo- 
  

   graph 
  of 
  the 
  fringes 
  (fig. 
  3). 
  The 
  fringes 
  have 
  disappeared 
  

   in 
  certain 
  regions 
  of 
  the 
  shadowed 
  space 
  which 
  bear 
  a 
  close 
  

   relation 
  to 
  those 
  where, 
  under 
  ordinary 
  conditions 
  of 
  illumi- 
  

   nation, 
  Newton's 
  rings 
  would 
  be 
  seen, 
  and 
  on 
  each 
  side 
  of 
  

   these 
  regions 
  the 
  fringes 
  are 
  displaced 
  through 
  half 
  a 
  fringe 
  

   width. 
  This 
  behaviour 
  of 
  the 
  fringes 
  introduces 
  an 
  occasional 
  

   uncertainty 
  of 
  half 
  a 
  fringe 
  width 
  in 
  testing 
  a 
  piece 
  of 
  glass 
  

   in 
  the 
  way 
  described 
  above. 
  The 
  uncertainty 
  need 
  notarise 
  

   with 
  a 
  little 
  care 
  ; 
  but 
  even 
  if 
  it 
  does, 
  for 
  the 
  purposes 
  for 
  

   which 
  plate-glass 
  would 
  be 
  used 
  the 
  resulting 
  error 
  is 
  usually 
  

   of 
  little 
  importance. 
  

  

  XXXVII. 
  A 
  Pressure-integral 
  as 
  Kinetic 
  Potential. 
  

   By 
  R. 
  Hargreaves*. 
  

  

  PRESSURE 
  is 
  usually 
  introduced 
  into 
  the 
  equations 
  of 
  

   hydrodynamics 
  in 
  the 
  character 
  of 
  a 
  normal 
  stress. 
  

   To 
  that 
  meaning 
  corresponds 
  the 
  use 
  of 
  surface-integrals 
  

   of 
  the 
  components 
  of 
  pressure, 
  to 
  determine 
  the 
  force 
  

   exerted 
  by 
  the 
  liquid 
  on 
  solids 
  immersed 
  in 
  it. 
  But 
  where 
  

   there 
  is 
  no 
  vorticity, 
  an 
  integral 
  

  

  ^ 
  P 
  ^f 
  + 
  2\^\ 
  + 
  ^\ 
  + 
  ^\r 
  f(t) 
  ' 
  ' 
  (1) 
  

   * 
  Communicated 
  by 
  the 
  Author. 
  

  

  