﻿Device 
  for 
  evaluating 
  FormulcB 
  and 
  solving 
  Equations. 
  305 
  

  

  Theoretically 
  we 
  can 
  always 
  obtain 
  approximate 
  values 
  of 
  

   all 
  the 
  roots 
  real 
  or 
  imaginary 
  of 
  an 
  equation 
  of 
  the 
  nth. 
  

   degree 
  by 
  the 
  device, 
  as 
  ?/^ 
  can 
  always 
  be 
  easily 
  eliminated 
  

   from 
  the 
  equations 
  corresponding 
  to 
  (a) 
  and 
  (h) 
  by 
  Sylvester's 
  

   method^ 
  . 
  

  

  XI. 
  Solution 
  of 
  Equations 
  containing 
  Miscellaneous 
  Functions. 
  

   For 
  this 
  purpose 
  some 
  of 
  the 
  contact-fingers 
  are 
  made 
  

   from 
  wires 
  bent 
  into 
  the 
  shape 
  of 
  certain 
  curves. 
  Suppose, 
  

   for 
  example, 
  we 
  desire 
  to 
  find 
  the 
  roots 
  of 
  the 
  equation 
  

  

  where 
  the 
  values 
  of 
  f{x) 
  and 
  ¥{x) 
  have 
  been 
  computed, 
  or 
  

   found 
  experimentally, 
  for 
  values 
  of 
  x. 
  

  

  Fi-. 
  9. 
  

  

  The 
  wire 
  passing 
  through 
  the 
  point 
  N/- 
  (fig. 
  9) 
  is'bent 
  so 
  

   * 
  Burnside 
  and 
  Panton, 
  * 
  Theory 
  of 
  Equations,' 
  p. 
  296. 
  

  

  