﻿Boivland 
  and 
  Penniman 
  — 
  Electrical 
  Measurements. 
  49 
  

  

  The 
  third 
  class 
  were 
  those 
  wound 
  on 
  frames 
  whose 
  self- 
  

   inductances 
  were 
  calculated. 
  There 
  were 
  several 
  resistances 
  

   of 
  2000 
  ohms 
  each, 
  whose 
  self-inductances 
  were 
  -0000436 
  henry, 
  

   which 
  would 
  hardly 
  affect 
  the 
  phase 
  of 
  the 
  current 
  or 
  the 
  

   impedence 
  of 
  the 
  circuit. 
  

  

  These 
  coils 
  were 
  subdivided 
  into 
  resistances 
  of 
  various 
  

   amounts. 
  Another 
  frame 
  resistance 
  used 
  was 
  of 
  7463 
  ohms 
  

   divided 
  into 
  parts 
  of 
  about 
  250 
  ohms 
  each. 
  The 
  self-induc- 
  

   tance 
  of 
  the 
  entire 
  7463 
  ohms 
  was 
  '000105 
  henry. 
  

  

  As 
  the 
  open 
  resistances 
  were 
  not 
  divided 
  into 
  small 
  amounts 
  

   it 
  was 
  necessary 
  to 
  use 
  resistance 
  boxes 
  for 
  adjustment 
  ; 
  as 
  few 
  

   ohms 
  as 
  possible 
  were 
  used 
  in 
  each 
  case. 
  

  

  From 
  the 
  fact 
  that 
  the 
  coils 
  of 
  the 
  electrodynamometer 
  had 
  

   self-inductance 
  a 
  correction 
  was 
  introduced 
  in 
  order 
  that 
  the 
  

   ratio 
  of 
  the 
  resistances 
  should 
  give 
  the 
  ratio 
  of 
  the 
  self- 
  

   inductances 
  of 
  the 
  coils 
  direct. 
  

  

  The 
  value 
  of 
  this 
  correction 
  in 
  ohms 
  was 
  calculated 
  as 
  

   follows 
  : 
  

  

  Calculation 
  of 
  connection 
  due 
  to 
  fixed 
  and 
  hanqing 
  coils. 
  

  

  Self-inductance 
  of 
  fixed 
  coils 
  =yz= 
  -0164 
  henry 
  

   " 
  " 
  " 
  hanging 
  coil 
  = 
  A 
  = 
  -0007 
  " 
  

  

  Correction 
  due 
  to 
  fixed 
  coils. 
  From 
  an 
  inspection 
  of 
  the 
  

   tables 
  it 
  is 
  seen 
  that 
  

  

  L 
  R-l-r 
  L 
  R4-^ 
  

  

  or 
  

  

  B^-f/ 
  U" 
  ' 
  1-01G4 
  ~ 
  902 
  

  

  where 
  L 
  is 
  the 
  self-inductance 
  of 
  some 
  coil 
  and 
  R-f 
  ;' 
  is 
  the 
  

   corresponding 
  resistance. 
  B, 
  is 
  taken 
  as 
  equal 
  to 
  1 
  henry 
  

  

  L 
  _ 
  1-0164 
  

   ' 
  * 
  K+r 
  ~" 
  902 
  

   But 
  the 
  comparison 
  of 
  L 
  with 
  B, 
  = 
  1 
  is 
  wanted, 
  therefore 
  

  

  both 
  numerator 
  and 
  denominator 
  of 
  are 
  divided 
  by 
  

  

  902 
  -^ 
  

  

  1-0164 
  or 
  

  

  L 
  1 
  = 
  B, 
  

  

  R-fr 
  88'7-45 
  

  

  L 
  __ 
  R+r 
  

  

  ' 
  * 
  B 
  "" 
  887-45 
  

  

  That 
  is, 
  the 
  self-inductance 
  '0164 
  henry 
  of 
  the 
  fixed 
  coils 
  pro- 
  

   duced 
  a 
  correction 
  of 
  SS7'45 
  — 
  902 
  =—14-55 
  ohms, 
  which 
  must 
  

   be 
  applied 
  to 
  the 
  R" 
  circuit 
  if 
  the 
  self 
  -inductance 
  of 
  that 
  cir- 
  

   cuit 
  is 
  to 
  be 
  considered 
  as 
  1 
  henry. 
  

  

  Am. 
  Jour. 
  Sci. 
  — 
  Fourth 
  Series, 
  Vol. 
  YIII, 
  Xo. 
  43.— 
  Jult, 
  1899. 
  

   4 
  

  

  