﻿68 
  Prof. 
  H. 
  A. 
  Rowland 
  on 
  Electrical 
  

  

  Connecting 
  them 
  in 
  pairs, 
  we 
  have 
  the 
  self-inductances 
  

  

  L 
  1 
  + 
  L 
  2 
  + 
  2M 
  12 
  L 
  1 
  + 
  L 
  3 
  + 
  2M 
  13 
  L 
  2 
  + 
  L 
  3 
  + 
  2M 
  23 
  

   L 
  1 
  + 
  L 
  2 
  ~2M 
  12 
  L 
  1 
  + 
  L 
  8 
  -2M 
  13 
  L 
  2 
  + 
  L 
  3 
  -2M 
  23 
  

  

  There 
  are 
  many 
  advantages 
  in 
  twisting 
  the 
  wires 
  of 
  the 
  

   standard 
  inductance 
  together, 
  but 
  it 
  certainly 
  increases 
  the 
  

   electrostatic 
  action 
  between 
  the 
  coils. 
  This 
  latter 
  source 
  of 
  

   error 
  must 
  be 
  constantly 
  in 
  mind, 
  however, 
  and, 
  for 
  great 
  

   accuracy, 
  calculated 
  and 
  corrected 
  for. 
  But 
  by 
  proper 
  choice 
  

   of 
  method 
  we 
  may 
  sometimes 
  eliminate 
  it. 
  

  

  For 
  the 
  most 
  accurate 
  standards, 
  I 
  am 
  rather 
  doubtful 
  

   about 
  the 
  use 
  of 
  twisted 
  wire 
  coils, 
  at 
  least 
  without 
  great 
  

   caution. 
  But 
  for 
  many 
  purposes 
  it 
  certainly 
  is 
  a 
  great 
  con- 
  

   venience, 
  especially 
  where 
  only 
  an 
  accuracy 
  of 
  one 
  per 
  

   cent, 
  is 
  desired. 
  In 
  some 
  calculations 
  I 
  have 
  made, 
  I 
  have 
  

   obtained 
  corrections 
  of 
  from 
  one 
  to 
  one-tenth 
  per 
  cent, 
  from 
  

   this 
  cause. 
  

  

  For 
  twisted 
  wires 
  the 
  above 
  results 
  reduce 
  to 
  3L 
  + 
  6M, 
  

   3L 
  — 
  2M. 
  Similar 
  equations 
  can 
  be 
  obtained 
  for 
  a 
  larger 
  

   number 
  of 
  wires. 
  For 
  twisted 
  wire 
  coils, 
  n 
  wires 
  joined 
  

  

  abreast, 
  the 
  self-induction 
  is 
  — 
  , 
  which 
  is 
  practically 
  

  

  equal 
  to 
  L 
  or 
  M. 
  The 
  resistance 
  is 
  R/n. 
  

  

  When 
  we 
  have 
  n=p 
  + 
  m 
  wires 
  twisted 
  and 
  wound 
  in 
  a 
  

   coil 
  and 
  we 
  connect 
  them 
  p 
  direct 
  and 
  m 
  reverse, 
  the 
  resist- 
  

   ance 
  and 
  self-induction 
  will 
  be 
  

  

  92R 
  3 
  + 
  5 
  2 
  R[AC 
  + 
  BC-»AB] 
  R 
  2 
  [n(A 
  f 
  B)-C]+& 
  2 
  ABC 
  

  

  (nR) 
  a 
  + 
  (6C) 
  a 
  ' 
  (nR) 
  2 
  +{bOf 
  

  

  where 
  R 
  is 
  the 
  resistance 
  of 
  one 
  coil 
  and 
  

  

  A=L+(n-l)M 
  

   B 
  = 
  L-M 
  

  

  G 
  = 
  nL+ 
  (4:mp 
  — 
  n)M. 
  

  

  This 
  gives 
  self 
  -inductances 
  and 
  resistances 
  equal 
  to 
  or 
  less 
  than 
  

   L 
  and 
  R. 
  The 
  correction 
  for 
  electrostatic 
  induction 
  remains 
  

   to 
  be 
  put 
  in. 
  For 
  the 
  general 
  case, 
  the 
  equation 
  is 
  very 
  

   complicated 
  for 
  coils 
  abreast, 
  with 
  mutual 
  inductances. 
  

  

  The 
  number 
  of 
  mutual 
  inductances 
  to 
  be 
  obtained 
  is 
  M 
  for 
  

   two 
  wires, 
  0, 
  M, 
  2M 
  for 
  three 
  wires, 
  0, 
  M, 
  2M, 
  3M 
  for 
  four 
  

   wires, 
  &c. 
  From 
  these 
  results 
  we 
  see 
  that 
  we 
  are 
  always 
  

   able 
  to 
  reduce 
  mutual 
  to 
  self- 
  inductance. 
  Measuring 
  the 
  

   self-inductance 
  of 
  a 
  coil 
  connected 
  in 
  different 
  ways, 
  we 
  can 
  

   always 
  determine 
  the 
  mutual 
  inductances 
  in 
  terms 
  of 
  the 
  

   self-inductances. 
  

  

  