﻿J. 
  Trowbridge 
  — 
  Electrical 
  Oscillations 
  on 
  Iron 
  Wires. 
  229 
  

  

  resistance 
  of 
  the 
  short 
  connecting 
  lead 
  wires 
  and 
  of 
  the 
  spark 
  

   x. 
  Then 
  will 
  r 
  = 
  H 
  / 
  +x, 
  and 
  n 
  will 
  be 
  the 
  number 
  of 
  com- 
  

   plete 
  oscillations 
  visible. 
  

  

  Take 
  cases 
  (1) 
  and 
  (2), 
  large 
  copper 
  and 
  large 
  German 
  silver 
  

   wires 
  : 
  — 
  

  

  € 
  ni(R' 
  1 
  + 
  x)A 
  _ 
  £ 
  w 
  2 
  (R 
  / 
  2 
  + 
  x)A. 
  

  

  n 
  x 
  (R\+x) 
  = 
  n 
  2 
  (R' 
  2 
  + 
  a); 
  

   9*5 
  (0-66 
  + 
  x) 
  = 
  3 
  (9-2 
  +sc);- 
  

   x 
  = 
  3-4 
  ohms. 
  

  

  Taking 
  cases 
  (1) 
  and 
  (4) 
  similarly, 
  

  

  rc, 
  (R\+ 
  x) 
  = 
  7i 
  4 
  (R' 
  4 
  + 
  a;) 
  ; 
  

   9-5 
  (0-66 
  +x) 
  = 
  5 
  (3'5+cc); 
  

   x 
  = 
  2*6 
  ohms. 
  

  

  Experiments 
  with 
  other 
  copper 
  wires 
  having 
  B/ 
  equal 
  to 
  

   34 
  and 
  1*27 
  give 
  5 
  and 
  8 
  for 
  the 
  values 
  of 
  n 
  respectively, 
  or 
  

   x 
  = 
  2*4 
  ohms. 
  

  

  The 
  resistance 
  (R') 
  of 
  the 
  lead 
  wires 
  forming 
  part 
  of 
  x 
  was 
  

   0*8 
  ohm, 
  leaving 
  as 
  a 
  possible 
  value 
  for 
  the 
  resistance 
  of 
  the 
  

   spark 
  about 
  2 
  ohms. 
  

  

  If, 
  taking 
  this 
  value 
  of 
  x, 
  we 
  calculate 
  the 
  value 
  of 
  R' 
  neces- 
  

   sary 
  to 
  damp 
  out 
  the 
  oscillation 
  in 
  one 
  complete 
  double 
  dis- 
  

   charge 
  in 
  the 
  case 
  of 
  the 
  large 
  iron 
  wire, 
  we 
  shall 
  have 
  

  

  9'5 
  (0-66X3) 
  = 
  1 
  (R' 
  + 
  3); 
  

   R' 
  = 
  30 
  ohms. 
  

  

  But 
  neglecting 
  the 
  magnetic 
  property 
  of 
  the 
  iron, 
  its 
  calcu- 
  

   lated 
  resistance 
  to 
  alternating 
  currents 
  of 
  this 
  periodicity 
  was 
  

   R 
  / 
  = 
  2*78 
  ohms. 
  This 
  is 
  obviously 
  inadequate, 
  and 
  would 
  

   point 
  to 
  the 
  conclusion 
  that 
  the 
  oscillation 
  is 
  not, 
  as 
  sometimes 
  

   stated, 
  too 
  rapid 
  to 
  admit 
  of 
  the 
  magnetic 
  action 
  of 
  the 
  iron. 
  

  

  If 
  we 
  substitute 
  this 
  value 
  R'= 
  30 
  in 
  the 
  equation 
  

  

  R 
  = 
  ^/ipTJlB,, 
  

  

  we 
  have 
  for 
  the 
  resulting 
  value 
  of 
  the 
  magnetic 
  permeability 
  

   ^=230. 
  This 
  lies 
  between 
  the 
  limits 
  /z=103 
  and 
  //=1110, 
  

   found 
  by 
  taking 
  the 
  number 
  of 
  oscillations 
  one 
  and 
  a 
  half 
  and 
  

   one-half 
  respectively 
  for 
  the 
  case 
  of 
  the 
  iron 
  wire. 
  

  

  It 
  should 
  be 
  noticed 
  that 
  this 
  estimate 
  of 
  fi 
  necessitates 
  

   assuming 
  that 
  T 
  and 
  L 
  remain 
  the 
  same 
  within 
  broad 
  limits. 
  

   Measurements 
  of 
  the 
  single 
  oscillation 
  on 
  the 
  negatives 
  show 
  

   that 
  this 
  is 
  near 
  enough 
  the 
  case. 
  Part 
  of 
  the 
  more 
  rapid 
  

   decay 
  of 
  the 
  oscillation 
  in 
  the 
  iron 
  may 
  be 
  well 
  ascribed 
  to 
  the 
  

   dissipation 
  of 
  energy 
  by 
  hysteresis. 
  While 
  we 
  cannot 
  place 
  

   much 
  reliance 
  upon 
  an 
  estimate 
  of 
  its 
  value 
  in 
  such 
  a 
  case, 
  — 
  

   its 
  percentage 
  effect 
  probably 
  increasing 
  rapidly 
  with 
  the 
  decay 
  

  

  