﻿[ 
  802 
  ] 
  

  

  LXXXIV. 
  An 
  Electromagnetic 
  Method 
  of 
  Studying 
  the 
  

   Theory 
  of 
  and 
  Solving 
  Algebraical 
  Equations 
  of 
  any 
  

   Degree, 
  By 
  Alexander 
  Russell, 
  M.A.^ 
  B.Sc.^ 
  and 
  

   J. 
  N. 
  Alty,' 
  A.I.E.E., 
  Faraday 
  House^ 
  London 
  *. 
  

  

  Contents. 
  

  

  1. 
  Introduction. 
  

  

  2. 
  The 
  Electromagnetic 
  Method. 
  

  

  3. 
  Quadratic 
  Equations. 
  

  

  4. 
  The 
  Equation 
  to 
  Curves 
  passing 
  through 
  the 
  Neutral 
  Points. 
  

  

  5. 
  Cubic 
  Equations. 
  

  

  6. 
  Finding 
  the 
  Boots 
  of 
  an 
  Equation. 
  

  

  7. 
  Description 
  of 
  Apparatus. 
  

  

  1. 
  Introduction. 
  

  

  THE 
  electrical 
  device 
  recently 
  invented 
  by 
  Mr. 
  Arthur 
  

   Wright 
  enables 
  us 
  to 
  find 
  approximate 
  values 
  o£ 
  the 
  

   real 
  roots 
  of 
  an 
  equation 
  at 
  once 
  by 
  simple 
  mechanical 
  and 
  

   electrical 
  operations. 
  In 
  order, 
  however, 
  to 
  find 
  approximate 
  

   values 
  o£ 
  the 
  imaginary 
  roots 
  it 
  is 
  necessary 
  to 
  perform 
  

   certain 
  analytical 
  operations, 
  and 
  then 
  apply 
  the 
  device 
  to 
  

   find 
  the 
  roots 
  of 
  an 
  equation 
  of 
  a 
  higher 
  degree. 
  The 
  method 
  

   described 
  in 
  this 
  paper 
  has 
  the 
  great 
  merit 
  of 
  giving 
  approxi- 
  

   mate 
  values 
  of 
  all 
  the 
  imaginary 
  roots 
  as 
  well 
  as 
  all 
  the 
  real 
  

   roots. 
  It 
  is 
  not 
  capable 
  of 
  such 
  high 
  accuracy 
  as 
  the 
  Arthur 
  

   Wright 
  device, 
  and 
  it 
  cannot 
  be 
  directly 
  applied 
  when 
  the 
  

   indices 
  of 
  the 
  powers 
  of 
  the 
  unknown 
  quantity 
  are 
  fractional. 
  

   On 
  the 
  other 
  hand, 
  it 
  is 
  exceedingly 
  instructive, 
  as 
  it 
  shows 
  

   how 
  the 
  numerical 
  values 
  of 
  both 
  the 
  real 
  and 
  imaginary 
  

   roots 
  vary 
  as 
  the 
  coefficient 
  of 
  any 
  power 
  of 
  the 
  unknown 
  

   quantity 
  in 
  the 
  equation 
  is 
  varied. 
  The 
  apparatus 
  required 
  

   is 
  exceedingly 
  simple, 
  and 
  is 
  to 
  be 
  found 
  in 
  practically 
  every 
  

   physical 
  laboratory. 
  We 
  have 
  found 
  it 
  quite 
  a 
  suitable 
  

   experiment 
  to 
  include 
  in 
  a 
  laboratory 
  course 
  for 
  first 
  year 
  

   students. 
  

  

  The 
  method 
  suggested 
  itself 
  to 
  one 
  of 
  the 
  authors 
  when 
  

   studying 
  a 
  series 
  of 
  papers 
  by 
  Mr. 
  F. 
  Lucas 
  which 
  are 
  pub- 
  

   lished 
  in 
  the 
  Comptes 
  Rendus^ 
  i, 
  106 
  (1888). 
  The 
  final 
  

   electrical 
  method 
  (p. 
  1072) 
  devised 
  by 
  Mr. 
  Lucas 
  is 
  a 
  practical 
  

   one. 
  A 
  sheet 
  of 
  tinfoil 
  is 
  spread 
  over 
  a 
  large 
  fiat 
  plate 
  of 
  

   glass 
  or 
  other 
  insulating 
  material. 
  If 
  the 
  equation 
  is 
  of 
  the 
  

   ^th 
  degree 
  n 
  + 
  2 
  sources 
  and 
  sinks 
  for 
  electrical 
  current 
  are 
  

   provided. 
  These 
  are 
  arranged 
  on 
  a 
  line 
  at 
  equal 
  distances 
  

   apart. 
  The 
  currents 
  in 
  n 
  + 
  2 
  wires 
  touching 
  at 
  the 
  sources 
  

   and 
  sinks 
  are 
  adjusted 
  so 
  that 
  they 
  have 
  certain 
  definite 
  

   values. 
  The 
  method 
  of 
  calculating 
  these 
  values 
  is 
  practically 
  

  

  * 
  Communicated 
  by 
  the 
  Physical 
  Society 
  : 
  read 
  June 
  25, 
  1909. 
  

  

  