﻿138 
  Dr. 
  Drysdale 
  on 
  the 
  Use 
  of 
  Shunts 
  and 
  Transformers 
  

   Hence 
  

  

  / 
  M+rA 
  2 
  M+#2 
  \ 
  2 
  

  

  W 
  _ 
  A 
  /_________ 
  A/ 
  V 
  *» 
  / 
  V 
  ^ 
  / 
  

  

  But 
  the 
  multiplying 
  power 
  of 
  the 
  shunt 
  for 
  direct 
  currents 
  

  

  M 
  = 
  T 
  ±±^ 
  from 
  which 
  n 
  = 
  (M-l)^. 
  In 
  addition 
  ^ 
  =Ttf>, 
  

  

  where 
  Tj 
  is 
  the 
  time 
  constant 
  of 
  the 
  instrument 
  and 
  p 
  is 
  2-7T 
  

  

  times 
  the 
  frequency 
  as 
  usual. 
  Similarly 
  l 
  -2 
  = 
  T 
  2 
  p, 
  where 
  T 
  2 
  

   is 
  the 
  time 
  constant 
  of 
  the 
  shunt. 
  r 
  2 
  

  

  Putting 
  these 
  values 
  in 
  the 
  expression 
  above 
  we 
  have 
  

  

  / 
  M* 
  + 
  {(M-1)T 
  1 
  + 
  T 
  2 
  }y 
  

  

  iVi 
  - 
  V 
  i+T 
  2 
  y~ 
  ~ 
  5 
  

  

  which 
  after 
  a 
  little 
  further 
  simplification 
  reduces 
  to 
  

  

  This 
  formula 
  at 
  once 
  shows 
  that 
  if 
  T 
  X 
  = 
  T 
  2 
  the 
  shunt 
  has 
  

   the 
  same 
  multiplying 
  power 
  for 
  both 
  direct 
  and 
  alternate 
  

   currents,, 
  as 
  is 
  well 
  known. 
  It 
  further 
  shows 
  that 
  if 
  

  

  (M-l)T 
  l+ 
  (M 
  + 
  l)T 
  2 
  = 
  or 
  ±? 
  = 
  - 
  j^-i 
  

  

  the 
  shunt 
  is 
  again 
  correct. 
  This 
  would 
  be 
  the 
  case 
  if 
  the 
  

   instrument 
  is 
  shunted 
  with 
  a 
  resistance 
  r 
  2 
  and 
  capacity 
  K 
  

  

  M 
  — 
  1 
  

   such 
  that 
  K> 
  2 
  = 
  ^ 
  -, 
  1\*. 
  

  

  If 
  the 
  instrument 
  is 
  inductive, 
  and 
  is 
  shunted 
  with 
  a 
  non- 
  

   inductive 
  resistance, 
  T 
  2 
  = 
  and 
  the 
  formula 
  reduces 
  to 
  

  

  w 
  = 
  M^/i+(^)\y. 
  ... 
  (4) 
  

  

  As 
  an 
  example, 
  a 
  Kelvin 
  centiampere 
  balance 
  was 
  found 
  

   on 
  test 
  to 
  have 
  a 
  resistance 
  of 
  62*4 
  ohms 
  and 
  an 
  inductance 
  

  

  (by 
  secohmmeter) 
  of 
  1(51 
  millihenry's. 
  The 
  time 
  constant 
  of 
  

   this 
  instrument 
  wag 
  therefore 
  '00258 
  second. 
  The 
  instrument 
  

  

  * 
  Mr. 
  Alexander 
  Russell 
  has 
  cast 
  doubts 
  on 
  this 
  formula, 
  and 
  I 
  have 
  

   found 
  that 
  it 
  is 
  only 
  true 
  in 
  special 
  cases. 
  It 
  was 
  based 
  on 
  the 
  assumption 
  

   that 
  a 
  shunted 
  condenser 
  could 
  be 
  treated 
  as 
  an 
  impedance 
  with 
  negative 
  

   time 
  constant, 
  which 
  is 
  not 
  strictly 
  true. 
  

  

  