﻿114 
  Barus— 
  Trial 
  of 
  Interferential 
  Induction 
  balance. 
  

  

  One 
  helix 
  in 
  circuit. 
  

  

  Both 
  helices 
  in 
  circuit. 
  

  

  Fields 
  (maxima). 
  

  

  Fringes. 
  

  

  Fields 
  (maxima). 
  

  

  Fringes. 
  

  

  18 
  

  

  Hazy 
  

  

  16 
  

  

  all 
  clear. 
  

  

  22 
  

  

  Just 
  vanished 
  

  

  18 
  

  

  clear. 
  

  

  27 
  

  

  Vanished 
  

  

  21 
  

  

  clear. 
  

  

  36 
  

  

  do 
  

  

  26 
  

  

  f 
  of 
  face 
  clear. 
  

  

  57 
  

  

  do 
  

  

  34 
  

  

  do. 
  

  

  70 
  

  

  do 
  

  

  40 
  

  

  do. 
  

  

  100 
  

  

  do 
  

  

  49 
  

  

  vanishing. 
  

  

  Conformably 
  with 
  § 
  5 
  the 
  fringes 
  vanish 
  much 
  sooner 
  (i. 
  e. 
  

   for 
  smaller 
  fields) 
  when 
  only 
  one 
  helix 
  is 
  in 
  circuit 
  than 
  when 
  

   both 
  are 
  inserted. 
  Since 
  only 
  about 
  30 
  per 
  cent 
  of 
  the 
  full 
  

   current 
  is 
  effective, 
  the 
  minimum 
  field 
  producing 
  elongation 
  

   and, 
  therefore, 
  vibration 
  of 
  the 
  cores 
  is 
  about 
  of 
  the 
  same 
  

   value 
  as 
  before 
  (§ 
  5). 
  

  

  It 
  is 
  difficult 
  to 
  give 
  the 
  vanishing 
  point. 
  The 
  fringes 
  do 
  

   not 
  disappear 
  uniformly 
  over 
  the 
  whole 
  face, 
  but 
  parts 
  of 
  the 
  

   field 
  of 
  view 
  linger 
  longer 
  than 
  others. 
  This 
  again 
  points 
  to 
  

   rotation 
  of 
  fringes, 
  parts 
  nearer 
  the 
  axis 
  vanishing 
  last. 
  Many 
  

   other 
  experiments 
  of 
  a 
  similar 
  kind 
  were 
  made, 
  without, 
  how- 
  

   ever, 
  adding 
  essentially 
  to 
  the 
  above. 
  

  

  7. 
  The 
  question 
  finally 
  occurs 
  whether 
  the 
  above 
  arrange- 
  

   ment 
  is 
  sufficient 
  to 
  test 
  the 
  speed 
  of 
  transmission 
  of 
  an 
  elec- 
  

   tric 
  signal 
  or 
  impulse 
  from 
  helix 
  A 
  to 
  helix 
  B. 
  The 
  equations 
  

   for 
  this 
  case 
  were 
  originally 
  worked 
  out 
  by 
  Lord 
  Kelvin* 
  and 
  

   since 
  by 
  others; 
  but 
  I 
  do 
  not 
  know 
  that 
  much 
  direct 
  experi- 
  

   mentation 
  has 
  been 
  given 
  to 
  the 
  subject, 
  seeing 
  that 
  in 
  deep 
  

   sea 
  cables 
  the 
  leakage 
  obscures 
  the 
  law. 
  As 
  the 
  underlying 
  

   differential 
  equation 
  is 
  of 
  the 
  same 
  form 
  as 
  that 
  which 
  occurs 
  

   in 
  heat 
  conduction, 
  many 
  of 
  the 
  electrical 
  problems 
  have 
  vir- 
  

   tually 
  been 
  solved 
  in 
  the 
  analytic 
  theory 
  of 
  heat. 
  Thus 
  if 
  the 
  

   potential 
  at 
  the 
  initial 
  point 
  varies 
  as 
  sin 
  Scot, 
  the 
  distribution 
  

   of 
  potential 
  along 
  the 
  wire 
  is 
  given 
  by 
  

  

  E 
  " 
  w 
  sin(2<o£— 
  2V 
  o> 
  ) 
  

  

  where 
  z 
  = 
  x 
  V'kc 
  , 
  x 
  being 
  the 
  distance 
  of 
  transmission 
  from 
  the 
  

   initial 
  point, 
  c 
  the 
  electrostatic 
  capacity 
  per 
  unit 
  of 
  length, 
  Tc 
  

   the 
  electrostatic 
  resistance 
  per 
  unit 
  of 
  length. 
  Thus 
  the 
  speed 
  

   of 
  transmission 
  of 
  like 
  phases 
  is 
  2\/(o/kc, 
  increasing, 
  there- 
  

   fore, 
  as 
  the 
  square 
  root 
  of 
  the 
  frequency 
  of 
  vibration, 
  while 
  

  

  *See 
  Math, 
  and 
  Phys. 
  papers 
  of 
  Sir 
  William 
  Thomson, 
  p. 
  61 
  et 
  seq., 
  where 
  

   the 
  expression 
  for 
  capacity 
  is 
  also 
  given. 
  

  

  