﻿with 
  Alternate 
  Current 
  Measuring 
  Instruments. 
  151 
  

  

  of 
  the 
  differential 
  wattmeter 
  previously 
  employed. 
  Figs. 
  7 
  

   and 
  8 
  (PI. 
  IV.) 
  show 
  the 
  current 
  ratio 
  and 
  phase-displacements 
  

   for 
  this 
  transformer, 
  while 
  figs. 
  9 
  and 
  10 
  give 
  the 
  P.D. 
  relations 
  

  

  Connexions 
  for 
  P.D. 
  Test. 
  

  

  which 
  have 
  heen 
  determined 
  over 
  a 
  greater 
  range 
  of 
  core 
  

   induction 
  than 
  before. 
  

  

  As 
  a 
  test 
  of 
  formulae 
  14 
  and 
  17 
  for 
  the 
  ratio 
  and 
  phase- 
  

   displacement 
  when 
  used 
  as 
  a 
  current 
  transformer, 
  we 
  will 
  take 
  

   case 
  VII., 
  where 
  the 
  coils 
  were 
  separated 
  and 
  a 
  secondary 
  

   load 
  of 
  5' 
  9 
  ohms 
  non-inductive 
  was 
  employed. 
  The 
  core 
  

   induction 
  was 
  then 
  found 
  from 
  the 
  voltages 
  in 
  the 
  unused 
  

   coils 
  and 
  was 
  taken 
  at 
  1565 
  for 
  a 
  secondary 
  load 
  of 
  5 
  amps. 
  

   On 
  measuring 
  the 
  equivalent 
  reactance 
  of 
  the 
  transformer 
  it 
  

   came 
  out 
  at 
  5" 
  12 
  co 
  or 
  2*56 
  <o 
  for 
  the 
  secondary 
  leakage 
  

   reactance. 
  From 
  this 
  we 
  get 
  a 
  total 
  secondary 
  resistance 
  of 
  

   7*1 
  co, 
  reactance 
  of 
  2*56 
  (o, 
  and 
  impedance 
  of 
  7*5 
  a> 
  approx. 
  

   cos 
  cj> 
  8 
  ='94: 
  and 
  sin 
  (/>/=* 
  34. 
  

  

  Formula 
  14 
  gives 
  us 
  as 
  the 
  loss 
  of 
  ratio 
  per 
  cent. 
  

  

  100 
  

  

  P* 
  — 
  Py 
  

  

  = 
  100 
  | 
  A 
  

  

  ^-cos$ 
  s 
  + 
  -j- 
  sin 
  </>*>-, 
  

  

  which 
  works 
  out 
  at 
  1*92 
  per 
  cent., 
  while 
  the 
  experimental 
  

   value 
  is 
  1*8 
  per 
  cent. 
  

  

  The 
  phase-displacement 
  in 
  the 
  same 
  case 
  may 
  be 
  taken 
  as 
  

  

  -^-cos0 
  s 
  — 
  j- 
  am<p 
  s 
  , 
  

  

  which 
  works 
  out 
  to 
  '58°, 
  the 
  experimental 
  value 
  being 
  *75°. 
  

  

  In 
  the 
  case 
  of 
  a 
  lagging 
  load 
  as 
  in 
  curve 
  VI. 
  but 
  with 
  the 
  

   coils 
  close 
  together, 
  the 
  calculated 
  loss 
  of 
  ratio 
  is 
  1*87 
  per 
  

  

  