﻿806 
  Dr. 
  Russell 
  and 
  Mr. 
  Alty: 
  Electromagnetic 
  MetJiod 
  

   and, 
  therefore, 
  

  

  TT 
  x^ 
  + 
  ^^'^' 
  + 
  ^ 
  __ 
  TT 
  , 
  (5Hc/^) 
  

  

  a;[x-\-h) 
  

  

  6x 
  

  

  (5Hc/6) 
  

   5(^ 
  + 
  6)' 
  

  

  (8) 
  

  

  In 
  fig. 
  2 
  let 
  us 
  suppose 
  that, 
  the 
  plane 
  of 
  the 
  paper 
  repre- 
  

   sents 
  a 
  horizontal 
  plane, 
  and 
  that 
  H 
  is 
  the 
  direction 
  of 
  the 
  

   earth's 
  magnetic 
  force. 
  Let 
  us 
  also 
  suppose 
  that 
  two 
  long 
  

  

  H 
  

  

  Fig. 
  2. 
  

  

  In; 
  

  

  Y 
  

  

  X' 
  

  

  B 
  J 
  N, 
  \P 
  /V> 
  

  

  X 
  

  

  

  vertical 
  wires 
  cut 
  the 
  plane 
  of 
  the 
  paper 
  perpendicularly 
  at 
  

   and 
  B 
  respectively, 
  the 
  length 
  of 
  BO 
  being 
  b 
  centimetres 
  and 
  

   the 
  magnitude 
  of 
  the 
  current 
  C, 
  in 
  amperes^ 
  in 
  the 
  wire 
  

   being 
  5Hc/5, 
  and 
  the 
  B 
  wire 
  carrying 
  the 
  return 
  current 
  

   — 
  5Hc/6. 
  If 
  the 
  direction 
  of 
  the 
  current 
  C 
  be 
  into 
  the 
  paper 
  

   at 
  B 
  and 
  out 
  of 
  it 
  at 
  0, 
  the 
  circtilar 
  lines 
  of 
  force 
  due 
  to 
  the 
  

   currents 
  in 
  each 
  wire 
  will 
  act 
  in 
  the 
  directions 
  of 
  the 
  curved 
  

   arrow-heads 
  shown 
  in 
  the 
  figure. 
  

  

  We 
  shall 
  now 
  consider 
  how 
  the 
  numerical 
  values 
  of 
  the 
  

   roots 
  of 
  the 
  quadratic 
  equation 
  alter 
  as 
  c, 
  and 
  therefore 
  also 
  

   C, 
  increases 
  from 
  zero 
  to 
  infinity, 
  h 
  which 
  w^e 
  suppose 
  to 
  be 
  

   positive 
  remaining 
  constant. 
  

  

  We 
  have 
  already 
  shown 
  that 
  the 
  coordinates 
  of 
  the 
  points 
  

   at 
  which 
  the 
  resultant 
  magnetic 
  force 
  is 
  zero, 
  that 
  is, 
  the 
  

   neutral 
  points, 
  determine 
  completely 
  the 
  numerical 
  values 
  of 
  

   both 
  the 
  real 
  and 
  imaginary 
  roots 
  of 
  the 
  equation. 
  

  

  When 
  c 
  is 
  very 
  small 
  and 
  positive 
  the 
  neutral 
  points 
  lie 
  

   between 
  B 
  and 
  0. 
  For 
  a 
  particular 
  value 
  of 
  c, 
  for 
  instance, 
  

   they 
  are 
  at 
  Ni 
  and 
  Ng 
  on 
  the 
  axis 
  of 
  X. 
  We 
  see 
  at 
  once 
  

   from 
  symmetry 
  that 
  0Ni 
  = 
  N2B. 
  If 
  the 
  length 
  of 
  ONi 
  on 
  

   the 
  same 
  scale 
  that 
  BO 
  is7> 
  be 
  — 
  .I'l, 
  the 
  roots 
  of 
  the 
  equation 
  

   for 
  this 
  value 
  of 
  c 
  are 
  both 
  real 
  and 
  equal 
  to 
  — 
  a^iand 
  —h 
  + 
  o!^ 
  

  

  