﻿Diamagnetic 
  and 
  Weakly 
  Magnetic 
  Substances. 
  439 
  

  

  The 
  difference 
  in 
  these 
  two 
  values 
  gives 
  us 
  the 
  total 
  force 
  

   acting 
  upon 
  the 
  surface 
  considered. 
  If 
  P 
  x 
  denote 
  its 
  value 
  

   in 
  grams-weight, 
  we 
  have 
  

  

  5'P 
  1 
  =^{» 
  2 
  H 
  2 
  -» 
  1 
  H 
  1 
  }. 
  

  

  07T 
  

  

  But 
  since 
  H 
  near 
  the 
  surface 
  is 
  the 
  same 
  in 
  both 
  media, 
  

   we 
  have 
  

  

  9*i= 
  LUhZi'-lhB-i*)- 
  

  

  o7T 
  

  

  Since 
  #21 
  the 
  relative 
  susceptibility 
  is 
  by 
  definition 
  

  

  Now 
  a 
  similar 
  treatment 
  of 
  the 
  forces 
  acting 
  at 
  the 
  top 
  

   surface 
  of 
  the 
  slab 
  will 
  give 
  for 
  the 
  resultant 
  force 
  there 
  

  

  where 
  W 
  is 
  the 
  magnetic 
  force 
  at 
  the 
  top 
  surface. 
  

  

  The 
  difference 
  between 
  P 
  x 
  and 
  P 
  / 
  times 
  the 
  area 
  of 
  the 
  

   Z-face 
  will 
  give 
  us 
  the 
  total 
  force 
  acting 
  in 
  the 
  line 
  of 
  sus- 
  

   pension. 
  If 
  A 
  is 
  the 
  area 
  of 
  the 
  Z-face, 
  then 
  P, 
  the 
  total 
  

   vertical 
  force, 
  is 
  given 
  by 
  

  

  P=^|A(H 
  1 
  2 
  -H 
  /2 
  ). 
  

  

  Now 
  experiment 
  shows 
  that 
  H 
  /2 
  is 
  negligible 
  in 
  comparison 
  

   with 
  Hj 
  2 
  . 
  If 
  jju^ 
  the 
  permeability 
  of 
  air, 
  be 
  assumed 
  equal 
  

   to 
  unity, 
  we 
  have 
  

  

  so 
  that 
  2^/P 
  

  

  *~ZH 
  2 
  ' 
  

  

  where 
  H 
  is 
  put 
  for 
  H 
  l5 
  and 
  k 
  for 
  /c 
  21 
  . 
  

  

  For 
  the 
  determination 
  of 
  k. 
  it 
  is, 
  accordingly, 
  only 
  necessary 
  

   to 
  determine 
  P 
  the 
  mechanical 
  force 
  acting 
  on 
  the 
  slab, 
  H 
  

   the 
  magnetic 
  force 
  at 
  the 
  bottom 
  of 
  the 
  slab, 
  and 
  the 
  area 
  of 
  a 
  

   cross-section 
  of 
  the 
  slab. 
  In 
  determining 
  the 
  strength 
  of 
  the 
  

   field 
  the 
  balance 
  mentioned 
  above 
  was 
  used. 
  A 
  known 
  

   current 
  is 
  sent 
  through 
  a 
  conductor 
  placed 
  in 
  that 
  part 
  of 
  the 
  

   field 
  the 
  strength 
  of 
  which 
  we 
  wish 
  to 
  measure, 
  and 
  then 
  the 
  

  

  