﻿810 
  Dr. 
  Russell 
  and 
  Mr. 
  Alty 
  : 
  Electromagnetic 
  Method 
  

  

  positive 
  real 
  roots. 
  When 
  h 
  is 
  negligibly 
  small 
  we 
  see 
  by 
  

   (14) 
  that 
  the 
  locus 
  o£ 
  the 
  neutral 
  points 
  is 
  the 
  two 
  straight 
  

   lines 
  represented 
  by 
  

  

  Hence 
  the 
  imaginary 
  roots 
  are 
  o£ 
  the 
  form 
  .'?-i 
  + 
  .Ti\/3\/ 
  — 
  1 
  

   where 
  —2x1 
  is 
  the 
  value 
  of 
  the 
  real 
  negative 
  root. 
  

   Similarly 
  we 
  can 
  discuss 
  the 
  roots 
  of 
  the 
  equation 
  

  

  In 
  this 
  case 
  it 
  will 
  be 
  found 
  that 
  the 
  currents 
  in 
  the 
  wires 
  

   through 
  Bi 
  and 
  Bg 
  are 
  unequal, 
  and 
  that 
  the 
  equation 
  has 
  

   always 
  two 
  imaginary 
  roots, 
  the 
  neutral 
  points 
  lying 
  on 
  the 
  

   hyperbola 
  y^ 
  — 
  ?>x^ 
  = 
  P^ 
  which 
  is 
  conjugate 
  to 
  the 
  hyperbola 
  

   shown 
  in 
  iig. 
  3. 
  

  

  Equations 
  of 
  the 
  fourth 
  and 
  higher 
  degrees 
  can 
  be 
  dis- 
  

   cussed 
  in 
  like 
  manner. 
  To 
  get 
  the 
  most 
  instructive 
  results 
  

   care 
  has 
  to 
  be 
  taken 
  to 
  choose 
  the 
  distances 
  between 
  the 
  

   wires 
  so 
  that 
  the 
  analytical 
  expressions 
  for 
  the 
  required 
  

   currents 
  may 
  be 
  as 
  simple 
  as 
  possible. 
  If 
  this 
  be 
  not 
  done 
  

   analytical 
  difficulties 
  will 
  often 
  be 
  encountered 
  in 
  interpreting 
  

   the 
  results. 
  

  

  6. 
  Finding 
  the 
  Roots 
  of 
  an 
  Equation, 
  

  

  The 
  great 
  and 
  so 
  far 
  as 
  we 
  know 
  the 
  unique 
  advantage 
  of 
  

   this 
  method 
  is 
  that 
  it 
  enables 
  us 
  to 
  find 
  the 
  imaginary 
  as 
  

   well 
  as 
  the 
  real 
  roots 
  of 
  an 
  equation 
  almost 
  at 
  once. 
  In 
  

   equations 
  occurring 
  in 
  many 
  j)hysical 
  problems 
  it 
  is 
  the 
  

   latter 
  roots 
  which 
  we 
  desire 
  to 
  find, 
  and 
  this 
  method 
  enables 
  

   the 
  physicist 
  to 
  find 
  quickly 
  approximate 
  values 
  of 
  these 
  

   roots. 
  

  

  If 
  due 
  precautions 
  are 
  taken 
  the 
  maximum 
  inaccuracy 
  of 
  

   this 
  method 
  need 
  not 
  exceed 
  one 
  per 
  cent. 
  This 
  is 
  the 
  

   accuracy 
  obtainable 
  by 
  careful 
  students, 
  who 
  need 
  have 
  no 
  

   previous 
  experimental 
  training, 
  in 
  finding 
  H 
  by 
  measuring 
  

   the 
  distance 
  of 
  the 
  neutral 
  point 
  from 
  a 
  long 
  vertical 
  wire 
  

   carrying 
  a 
  known 
  current. 
  

  

  7. 
  Descriptio7i 
  of 
  Apparatus. 
  

  

  We 
  shall 
  now 
  describe 
  the 
  simple 
  apparatus 
  we 
  use 
  for 
  

   teaching 
  purposes. 
  In 
  fig. 
  4 
  the 
  arrangement 
  of 
  the 
  apparatus 
  

   for 
  solving 
  a 
  cubic 
  equation 
  is 
  shown. 
  S, 
  S 
  represent 
  springs 
  

  

  