﻿on 
  Electric 
  Waves 
  in 
  Short 
  Wire 
  Systems. 
  601 
  

  

  Calculation 
  of 
  the 
  Specific 
  Inductive 
  Capacity. 
  

  

  If 
  in 
  two 
  successive 
  experiments 
  the 
  deflexions 
  are 
  the 
  

   same, 
  it 
  is 
  assumed 
  that 
  the 
  capacities 
  in 
  the 
  condenser 
  circuits 
  

   are 
  equal. 
  The 
  condenser 
  circuit 
  has 
  been 
  carefully 
  arranged 
  

   so 
  that 
  when 
  the 
  distance 
  between 
  the 
  plates 
  is 
  altered, 
  the 
  

   only 
  capacity 
  change 
  is 
  that 
  of 
  the 
  plates. 
  In 
  these 
  experi- 
  

   ments 
  there 
  are 
  no 
  attachments 
  to 
  the 
  plates 
  except 
  the 
  central 
  

   lugs 
  on 
  their 
  outer 
  surfaces. 
  Whatever 
  may 
  be 
  the 
  capacity 
  

   of 
  these 
  lugs, 
  it 
  may 
  be 
  considered 
  not 
  to 
  change 
  when 
  the 
  

   distance 
  between 
  the 
  plates 
  alters 
  by 
  a 
  small 
  amount. 
  The 
  

   total 
  capacity 
  in 
  the 
  condenser 
  circuit 
  is, 
  for 
  the 
  present 
  pur- 
  

   pose, 
  a 
  matter 
  of 
  no 
  concern. 
  The 
  change 
  in 
  the 
  capacity 
  is 
  

   of 
  importance 
  alone, 
  and 
  this 
  may 
  be 
  accurately 
  determined 
  by 
  

   an 
  application 
  of 
  KirchhofFs 
  formula 
  (Abhandl. 
  p. 
  113). 
  

  

  Let 
  C 
  be 
  that 
  part 
  of 
  the 
  capacity 
  of 
  the 
  condenser 
  circuit 
  

   which 
  does 
  not 
  change 
  when 
  the 
  distance 
  between 
  the 
  plates 
  

   is 
  altered. 
  With 
  air 
  between 
  the 
  plates 
  the 
  capacity 
  of 
  the 
  

   circuit 
  is 
  : 
  — 
  

  

  S 
  , 
  r 
  f 
  . 
  i 
  167rr(a 
  + 
  d) 
  ■ 
  ,, 
  a 
  + 
  d~\ 
  n 
  

  

  la 
  

  

  r 
  being 
  the 
  radius 
  of 
  the 
  plates, 
  d 
  their 
  thickness, 
  and 
  a 
  the 
  

   distance 
  between 
  them. 
  

  

  Professor 
  Bragg, 
  to 
  whom 
  we 
  are 
  indebted 
  for 
  much 
  help 
  

   in 
  this 
  matter, 
  pointed 
  out 
  to 
  us 
  that 
  under 
  certain 
  conditions 
  

   the 
  capacity 
  of 
  a 
  circular 
  plate 
  condenser 
  with 
  a 
  slab 
  of 
  

   material 
  between 
  the 
  plates 
  can 
  be 
  accurately 
  calculated. 
  If, 
  

   for 
  instance, 
  a 
  cylindrical 
  disk 
  of 
  glass 
  considerably 
  smaller 
  

   in 
  diameter 
  than 
  the 
  condenser-plates 
  is 
  placed 
  coaxially 
  with 
  

   them, 
  the 
  plates 
  touching 
  the 
  glass 
  on 
  either 
  side, 
  the 
  edge 
  

   of 
  the 
  glass 
  disk 
  may 
  be 
  considered 
  everywhere 
  parallel 
  to 
  

   the 
  tubes 
  of 
  force 
  touching 
  it, 
  and 
  no 
  disturbance 
  of 
  the 
  

   external 
  field 
  takes 
  place. 
  This 
  condition 
  has 
  been 
  carefully 
  

   kept 
  in 
  view 
  in 
  these 
  experiments. 
  With 
  the 
  glass 
  between 
  

   the 
  condenser-plates 
  the 
  capacity 
  of 
  the 
  circuit 
  is 
  therefore 
  : 
  — 
  

  

  K 
  being 
  the 
  specific 
  inductive 
  capacity 
  of 
  the 
  glass, 
  r 
  x 
  the 
  

   radius 
  of 
  the 
  glass 
  disk, 
  and 
  a 
  x 
  its 
  thickness 
  ( 
  = 
  the 
  distance 
  

   between 
  the 
  plates), 
  the 
  other 
  symbols 
  being 
  as 
  just 
  mentioned. 
  

   If 
  a 
  value 
  of 
  a 
  can 
  be 
  found 
  which 
  makes 
  the 
  capacity 
  

   in 
  the 
  two 
  cases 
  equal, 
  equating 
  the 
  two 
  expressions 
  enables 
  

   the 
  value 
  of 
  K 
  to 
  be 
  calculated. 
  Calculating 
  K 
  with 
  the 
  

  

  