﻿764 
  Mr. 
  W. 
  A. 
  Jenkins 
  : 
  N 
  etc 
  Method 
  of 
  Determining 
  tlie 
  

  

  yet 
  certain 
  individual 
  threads 
  might 
  be 
  displaced. 
  The 
  

   number 
  of 
  threads 
  per 
  cm. 
  is 
  about 
  19, 
  and 
  as 
  the 
  cutting 
  

   of 
  the 
  thread 
  was 
  done 
  by 
  a 
  good 
  machine 
  it 
  is 
  certain 
  that 
  

   no 
  thread 
  will 
  be 
  displaced 
  from 
  its 
  true 
  position 
  by 
  more 
  

   than 
  *1 
  mm., 
  that 
  is 
  £ 
  of 
  the 
  distance 
  between 
  any 
  two 
  

   consecutive 
  threads. 
  Suppose 
  such 
  a 
  deviation 
  to 
  occur 
  in 
  

   the 
  thread 
  at 
  the 
  centre^ 
  i. 
  e. 
  at 
  the 
  point 
  where 
  it 
  will 
  

   have 
  the 
  greatest 
  effect. 
  

  

  The 
  field 
  due 
  to 
  a 
  circular 
  current 
  at 
  a 
  point 
  P 
  on 
  its 
  

   axis 
  is 
  given 
  by 
  

  

  H 
  = 
  27rCr 
  2 
  /(V 
  2 
  +d 
  2 
  )f, 
  

  

  where 
  r 
  is 
  the 
  radius 
  of 
  the 
  circle 
  and 
  d 
  is 
  the 
  distance 
  of 
  

   the 
  point 
  P 
  from 
  the 
  centre 
  of 
  the 
  circle. 
  

  

  Hence 
  the 
  field 
  due 
  to 
  a 
  single 
  turn 
  of 
  the 
  solenoid 
  at 
  the 
  

   centre 
  of 
  the 
  solenoid 
  is 
  given 
  by 
  

  

  H 
  = 
  2tt0 
  2 
  /^. 
  

  

  If 
  the 
  deviation 
  is 
  '01 
  cm. 
  then 
  we 
  have 
  

  

  H 
  = 
  27rCr 
  2 
  /{^ 
  2 
  +(-01) 
  2 
  }^ 
  

  

  and 
  the 
  error 
  is 
  given 
  by 
  

  

  27r0 
  2 
  

  

  r 
  = 
  3*13 
  cm., 
  the 
  thick 
  copper 
  tube 
  and 
  ebonite 
  coating 
  

   making 
  the 
  external 
  diameter 
  much 
  greater 
  than 
  the 
  

   internal 
  ; 
  and 
  working 
  this 
  formula 
  out 
  we 
  get 
  

  

  S 
  H=^{l7xlO-} 
  

  

  or 
  an 
  error 
  of 
  17 
  parts 
  in 
  10 
  7 
  . 
  

  

  Thus 
  we 
  see 
  that 
  if 
  each 
  thread 
  were 
  displaced 
  by 
  *1 
  mm. 
  

   the 
  maximum 
  possible 
  error 
  would 
  be 
  much 
  less 
  than 
  17 
  

   parts 
  in 
  10 
  7 
  , 
  as 
  the 
  effects 
  of 
  many 
  of 
  the 
  displacements 
  

   would 
  cancel 
  each 
  other. 
  The 
  error 
  caused 
  by 
  inaccurate 
  

   winding 
  is 
  therefore 
  a 
  negligible 
  quantity, 
  as 
  the 
  wire 
  was 
  

   wound 
  on 
  when 
  hot 
  and 
  therefore 
  grips 
  tightly 
  in 
  the 
  screw- 
  

   threads. 
  

  

  