﻿282 
  

  

  Prof. 
  W. 
  G. 
  Adams 
  on 
  the 
  Forms 
  of 
  [Feb. 
  25, 
  

  

  If 
  the 
  four 
  points 
  lie 
  on 
  a 
  circle, 
  and 
  the 
  complete 
  quadrilateral 
  be 
  drawn 
  

   through 
  them, 
  the 
  circles 
  which 
  have 
  their 
  centres 
  at 
  the 
  intersections 
  of 
  

   opposite 
  sides 
  of 
  the 
  quadrilateral, 
  and 
  which 
  cut 
  the 
  first 
  circle 
  at 
  right 
  

   angles, 
  will 
  also 
  cut 
  one 
  another 
  at 
  right 
  angles. 
  One 
  of 
  these 
  circles 
  

   is 
  shown 
  to 
  be 
  an 
  equip 
  otential 
  curve 
  for 
  the 
  four 
  electrodes, 
  and 
  the 
  

   other 
  is 
  a 
  line 
  of 
  force. 
  

  

  Hence, 
  if 
  we 
  cut 
  the 
  unlimited 
  sheet 
  along 
  the 
  edge 
  of 
  this 
  latter 
  

   circle, 
  we 
  shall 
  not 
  alter 
  the 
  forms 
  of 
  the 
  equipotential 
  curves 
  ; 
  and 
  within 
  

   it 
  we 
  shall 
  have 
  one 
  electrode 
  of 
  each 
  kind, 
  the 
  others 
  being 
  their 
  electric 
  

   images, 
  the 
  product 
  of 
  the 
  distances 
  of 
  an 
  electrode 
  and 
  its 
  image 
  from 
  

   the 
  centre 
  being 
  equal 
  to 
  the 
  square 
  of 
  the 
  radius 
  of 
  the 
  disk. 
  If 
  an 
  

   electrode 
  is 
  at 
  the 
  edge 
  of 
  the 
  disk, 
  then 
  the 
  electrode 
  and 
  its 
  image 
  coin- 
  

   cide, 
  and 
  the 
  equation 
  to 
  the 
  equipotential 
  curve 
  is 
  j- 
  

  

  r 
  2 
  =o\r 
  2 
  . 
  

  

  When 
  one 
  pole 
  is 
  at 
  the 
  edge 
  and 
  the 
  other 
  is 
  at 
  the 
  centre 
  of 
  a 
  

   circular 
  disk, 
  since 
  the 
  electric 
  image 
  of 
  the 
  centre 
  is 
  at 
  an 
  infinite 
  

   distance, 
  the 
  equation 
  to 
  the 
  equipotential 
  curves 
  is 
  

  

  r 
  2 
  = 
  o\. 
  

  

  This 
  is 
  an 
  interesting 
  case, 
  as 
  showing 
  that 
  the 
  equipotential 
  curves 
  do 
  

   not 
  always 
  cut 
  the 
  edge 
  of 
  the 
  disk 
  at 
  right 
  angles. 
  The 
  curves 
  around 
  

   the 
  centre 
  of 
  the 
  disk 
  are 
  nearly 
  ellipses 
  of 
  small 
  eccentricity, 
  with 
  one 
  

   focus 
  in 
  the 
  centre 
  ; 
  but 
  on 
  placing 
  one 
  tracing 
  electrode 
  at 
  a 
  distance 
  

   from 
  the 
  centre 
  

  

  between 
  the 
  electrodes, 
  where 
  a 
  is 
  the 
  radius, 
  there 
  is 
  great 
  uncertainty 
  

   in 
  determining 
  the 
  form 
  of 
  the 
  curve 
  on 
  the 
  opposite 
  side 
  of 
  the 
  centre 
  

   of 
  the 
  disk. 
  

  

  This 
  is 
  explained 
  by 
  the 
  fact 
  that 
  the 
  electrodes 
  were 
  1 
  millim. 
  in 
  

   diameter, 
  and 
  a 
  difference 
  of 
  distance 
  of 
  1 
  millim. 
  between 
  the 
  electrodes 
  

   near 
  this 
  point 
  corresponds 
  to 
  a 
  large 
  portion 
  of 
  the 
  disk 
  on 
  the 
  other 
  

   side 
  of 
  the 
  centre 
  — 
  this 
  portion 
  including 
  an 
  area 
  of 
  about 
  500 
  square 
  

   millims. 
  in 
  a 
  circle 
  36 
  millims. 
  in 
  radius, 
  i. 
  e. 
  about 
  one 
  eighth 
  of 
  the 
  

   whole 
  area 
  of 
  the 
  circle. 
  On 
  placing 
  one 
  of 
  the 
  galvanometer-electrodes 
  

   at 
  the 
  extremity 
  of 
  the 
  diameter 
  through 
  the 
  battery-electrodes 
  and 
  

   tracing 
  with 
  the 
  other, 
  it 
  is 
  found 
  that 
  the 
  equipotential 
  curve 
  through 
  

   that 
  point 
  cuts 
  the 
  edge 
  of 
  the 
  disk 
  at 
  an 
  angle 
  of 
  45°, 
  and 
  that 
  there 
  

   are 
  two 
  branches 
  cutting 
  one 
  another 
  at 
  right 
  angles. 
  

  

  These 
  peculiarities 
  are 
  explained 
  on 
  tracing 
  the 
  curve 
  

  

  corresponding 
  to 
  this 
  case. 
  The 
  extremity 
  of 
  the 
  diameter 
  is 
  a 
  point 
  

   through 
  which 
  two 
  branches 
  of 
  the 
  curve 
  pass 
  at 
  right 
  angles 
  to 
  one 
  

   another. 
  

  

  The 
  forms 
  of 
  the 
  equipotential 
  surfaces 
  and 
  lines 
  of 
  force 
  in 
  space 
  may 
  

   be 
  determined 
  experimentally 
  by 
  taking 
  a 
  large 
  vessel 
  containing 
  a 
  con- 
  

  

  