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  Pref. 
  A, 
  Anderson 
  on 
  the 
  Coefficients 
  of 
  

  

  Application 
  of 
  the 
  Curves. 
  

  

  (f.) 
  To 
  find 
  the 
  velocity 
  coefficient 
  k. 
  

  

  When 
  the 
  order 
  of 
  the 
  reaction 
  and 
  the 
  initial 
  concen- 
  

   trations 
  are 
  known 
  we 
  have 
  only 
  to 
  measure 
  the 
  fraction 
  

   (X) 
  changed 
  in 
  a 
  given 
  time 
  t 
  in 
  order 
  to 
  find 
  K£ 
  from 
  the 
  

   curve 
  and 
  therefore 
  k. 
  

  

  (ii.) 
  To 
  find 
  the 
  fraction 
  (X) 
  changed 
  in 
  a 
  given 
  time 
  t. 
  

  

  This 
  requires 
  a 
  knowledge 
  of 
  k, 
  the 
  order 
  of 
  the 
  reaction, 
  

   and 
  the 
  initial 
  concentrations. 
  Then 
  X 
  for 
  a 
  given 
  t 
  can 
  be 
  

   read 
  straight 
  from 
  the 
  curve. 
  

  

  (iii.) 
  To 
  find 
  the 
  Order 
  of 
  a 
  reaction. 
  

  

  Two 
  or 
  more 
  determinations 
  of 
  X 
  and 
  t 
  are 
  needed 
  together 
  

   with 
  a 
  knowledge 
  of 
  the 
  initial 
  concentrations. 
  The 
  

   particular 
  curve 
  on 
  which 
  the 
  points 
  (X, 
  t) 
  best 
  lie, 
  determines 
  

   the 
  order 
  of 
  the 
  reaction. 
  

   London, 
  

  

  December 
  1917. 
  

  

  XXXII. 
  On 
  the 
  Coefficients 
  of 
  Potential 
  of 
  Two 
  Conducting 
  

   Spheres. 
  By 
  Prof. 
  A. 
  Anderson 
  *. 
  

  

  IT 
  may 
  be 
  of 
  interest 
  to 
  show 
  how 
  the 
  coefficients 
  of 
  

   potential 
  of 
  two 
  conducting 
  spheres 
  may 
  be 
  obtained 
  

   directly 
  without 
  a 
  previous 
  determination 
  of 
  the 
  coefficients 
  

   of 
  capacity 
  and 
  induction, 
  and 
  without 
  making 
  use 
  of 
  electric 
  

   images. 
  For 
  this 
  purpose 
  the 
  following 
  elementary 
  pro- 
  

   position, 
  which 
  is 
  easily 
  seen 
  to 
  be 
  true, 
  may 
  be 
  used. 
  

  

  If 
  a 
  conducting 
  sphere 
  whose 
  radius 
  is 
  a 
  have 
  a 
  charge 
  E, 
  

   and 
  if 
  other 
  charged 
  bodies 
  be 
  brought 
  into 
  the 
  field, 
  the 
  

   potential 
  V 
  of 
  the 
  charge 
  E 
  at 
  an 
  external 
  point 
  P 
  whose 
  

   distance 
  from 
  the 
  centre 
  of 
  the 
  sphere 
  is 
  r 
  wilJ 
  be 
  given 
  by 
  

   the 
  equation 
  

  

  rV 
  = 
  E 
  + 
  a(U-U'), 
  

   where 
  U 
  is 
  the 
  potential 
  at 
  the 
  centre 
  of 
  the 
  sphere 
  of 
  the 
  

   introduced 
  charges, 
  and 
  U' 
  their 
  potential 
  at 
  P', 
  the 
  inverse 
  

   point 
  of 
  P 
  in 
  ihe 
  sphere. 
  

  

  Let 
  A 
  and 
  B 
  be 
  the 
  centres 
  of 
  two 
  spheres 
  whose 
  radii 
  

   are 
  a 
  and 
  b, 
  the 
  distance 
  AB 
  being 
  c. 
  Let 
  Ij 
  be 
  the 
  inverse 
  

   point 
  of 
  A 
  in 
  the 
  sphere 
  B, 
  I 
  2 
  the 
  inverse 
  of 
  I 
  x 
  in 
  A, 
  I 
  3 
  the 
  

   inverse 
  of 
  I 
  2 
  in 
  B, 
  and 
  so 
  on. 
  Also, 
  let 
  J 
  2 
  be 
  the 
  inverse 
  

   of 
  B 
  in 
  the 
  sphere 
  A, 
  J 
  2 
  the 
  inverse 
  of 
  Jj 
  in 
  B, 
  J 
  3 
  the 
  inverse 
  

   of 
  J 
  2 
  in 
  A, 
  and 
  so 
  on. 
  

  

  Let 
  U 
  be 
  the 
  potential 
  of 
  the 
  sphere 
  A 
  at 
  B, 
  Ui, 
  U 
  2J 
  U 
  3 
  , 
  

  

  &c. 
  its 
  potentials 
  at 
  I 
  b 
  I 
  2 
  , 
  I 
  3 
  , 
  &c, 
  and 
  U/, 
  U 
  2 
  ', 
  U 
  3 
  ', 
  &c. 
  its 
  

  

  potentials 
  at 
  J 
  l5 
  J 
  2 
  , 
  J 
  3 
  , 
  &c. 
  Also, 
  let 
  V 
  be 
  the 
  potential 
  of 
  

  

  the 
  sphere 
  B 
  at 
  A, 
  V 
  x 
  , 
  V 
  2 
  , 
  ~V 
  3 
  , 
  &c. 
  its 
  potentials 
  at 
  I 
  1? 
  I 
  2) 
  I 
  3; 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  