﻿icitJi 
  Alternate 
  Current 
  Measuring 
  Instruments. 
  139 
  

  

  was 
  then 
  shunted 
  with 
  a 
  non-inductive 
  resistance, 
  and 
  it 
  was 
  

   found 
  that 
  a 
  current 
  of 
  *878 
  amp. 
  gave 
  a 
  reading 
  of 
  '17 
  amp. 
  

   on 
  the 
  balance 
  with 
  direct 
  current, 
  thus 
  giving 
  a 
  multiplying 
  

   power 
  M 
  of 
  5*16. 
  Hence 
  at 
  50 
  periods, 
  which 
  is 
  the 
  usual 
  

   frequency 
  of 
  the 
  supply, 
  M' 
  should 
  be 
  

  

  - 
  - 
  a 
  L 
  , 
  4-16 
  2 
  x-00258 
  2 
  x314* 
  a 
  - 
  7 
  

   o-16 
  \/ 
  1+ 
  ^^ 
  = 
  6*17 
  ; 
  

  

  while 
  on 
  testing 
  a 
  current 
  of 
  "927 
  amp. 
  gave 
  a 
  reading 
  of 
  

   •15 
  amp. 
  or 
  a 
  multiplying 
  power 
  of 
  6*18. 
  It 
  should 
  be 
  

   noticed 
  that 
  the 
  formula 
  may 
  be 
  expressed 
  in 
  the 
  form 
  

  

  Ti 
  = 
  ^Wv 
  — 
  tv 
  — 
  i 
  which 
  gives 
  us 
  a 
  convenient 
  method 
  of 
  

   1 
  (M 
  — 
  V)p 
  ' 
  fe 
  

  

  testing 
  the 
  inductances 
  of 
  ammeters, 
  &c. 
  

  

  For 
  commercial 
  work, 
  therefore, 
  we 
  see 
  that 
  the 
  only 
  

  

  legitimate 
  method 
  of 
  employing 
  shunts 
  is 
  to 
  make 
  the 
  time 
  

  

  constants 
  of 
  the 
  instruments 
  and 
  shunts 
  either 
  negligible 
  or 
  

  

  approximately 
  equal. 
  If 
  T 
  2 
  and 
  T 
  2 
  are 
  nearly 
  equal 
  since 
  

  

  v/l 
  + 
  A 
  = 
  1 
  + 
  9 
  nearly 
  when 
  h 
  is 
  small, 
  

  

  JM 
  

  

  ' 
  = 
  * 
  {i+w 
  (M 
  ^? 
  +1) 
  v 
  -M- 
  (5) 
  

  

  It 
  will 
  be 
  noticed 
  that 
  for 
  a 
  given 
  difference 
  in 
  the 
  time 
  

   constants 
  the 
  correcting 
  term 
  is 
  greater 
  the 
  greater 
  the 
  value 
  

   of 
  M 
  and 
  the 
  less 
  that 
  of 
  T 
  2 
  . 
  Consequently, 
  if 
  we 
  take 
  in 
  

   our 
  formula 
  M 
  so 
  large 
  that 
  M, 
  (M 
  + 
  l) 
  and 
  (M 
  — 
  1) 
  may 
  be 
  

   regarded 
  as 
  equal 
  and 
  at 
  the 
  same 
  time 
  neglect 
  T 
  2 
  p 
  in 
  com- 
  

   parison 
  with 
  unity, 
  we 
  have 
  : 
  

  

  M'=M 
  |l+ 
  ^^(Ti-T^l 
  =M{1 
  + 
  (T 
  1 
  -T 
  2 
  )T/}, 
  (6) 
  

  

  where 
  T 
  is 
  the 
  average 
  value 
  of 
  the 
  two 
  time 
  constants 
  

   Ti 
  and 
  T 
  2 
  . 
  

  

  This 
  may 
  be 
  written 
  in 
  the 
  form 
  —^r- 
  = 
  T 
  . 
  AT 
  . 
  p 
  2 
  , 
  and 
  

   finally 
  M 
  

  

  AM 
  AT 
  

  

  M 
  p 
  T 
  K 
  / 
  

  

  Consequently, 
  to 
  ensure 
  that 
  the 
  ratio 
  M 
  shall 
  not 
  be 
  altered 
  

   by 
  more 
  than 
  x 
  per 
  cent, 
  with 
  alternating 
  current 
  of 
  given 
  

   frequency, 
  the 
  time 
  constants 
  must 
  be 
  adjusted 
  to 
  equality 
  

  

  within 
  .-j^-g 
  per 
  cent. 
  

  

  