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  On 
  the 
  Nodal-Slide 
  Method 
  of 
  Focometry. 
  21 
  

  

  is 
  difficult 
  to 
  calculate 
  and 
  almost 
  impossible 
  to 
  estimate 
  

   exactly. 
  There 
  may 
  be 
  other 
  methods 
  of 
  dispensing 
  with 
  

   astronomical 
  observations 
  in 
  gravity 
  measurements, 
  but 
  I 
  

   believe 
  that 
  the 
  method 
  of 
  current-balance 
  is 
  one 
  of 
  the 
  

   most 
  accurate 
  that 
  can 
  be 
  easily 
  brought 
  into 
  practice 
  with- 
  

   out 
  sacrificing 
  to 
  any 
  great 
  extent 
  the 
  degree 
  of 
  precision 
  

   usually 
  attainable 
  with 
  invariable 
  pendulums. 
  

  

  In 
  the 
  theory 
  of 
  atomic 
  constitution, 
  it 
  is 
  generally 
  as- 
  

   sumed 
  that 
  there 
  are 
  rings 
  of 
  electrons 
  in 
  rapid 
  rotation 
  : 
  

   these 
  are 
  no 
  doubt 
  equivalent 
  to 
  currents 
  and 
  must 
  exert 
  

   mutual 
  influence 
  upon 
  each 
  other. 
  When 
  such 
  atoms 
  com- 
  

   bine 
  into 
  a 
  molecule 
  and 
  are 
  in 
  such 
  a 
  position 
  that 
  the 
  

   planes 
  of 
  the 
  rings 
  are 
  parallel 
  to 
  each 
  other, 
  then 
  the 
  posi- 
  

   tion 
  of 
  maximum 
  force 
  between 
  two 
  circular 
  rings 
  here 
  

   discussed 
  will 
  be 
  of 
  some 
  significance 
  in 
  the 
  atomic 
  

   configuration 
  of 
  molecules. 
  

  

  III. 
  On 
  the 
  Nodal-Slide 
  Method 
  of 
  Focometry. 
  By 
  J. 
  A. 
  

   Tomkins, 
  A.R.C.S. 
  (Lond.), 
  Lecturer 
  in 
  Physics, 
  Technical 
  

   College, 
  Bradford*. 
  

  

  PROF. 
  A. 
  ANDERSON 
  has 
  recently 
  described 
  (Phil. 
  

   Mag. 
  Jan. 
  1917, 
  p. 
  157) 
  an 
  elegant 
  method 
  of 
  deter- 
  

   mining 
  the 
  focal 
  length, 
  and 
  other 
  constants, 
  of 
  a 
  lens 
  system 
  

   based 
  upon 
  a 
  general 
  theorem 
  of 
  which 
  the 
  ordinary 
  nodal- 
  

   slide 
  method 
  is 
  but 
  a 
  particular 
  application. 
  This 
  theorem 
  

   is 
  that 
  for 
  any 
  lens 
  system 
  there 
  is 
  always 
  one, 
  and 
  only 
  one, 
  

   point 
  on 
  the 
  optic 
  axis 
  such 
  that 
  a 
  small 
  rotation 
  of 
  the 
  system 
  

   about 
  a 
  perpendicular 
  axis 
  through 
  it 
  will 
  cause 
  no 
  lateral 
  

   displacement 
  of 
  the 
  image 
  of 
  an 
  object 
  in 
  a 
  given 
  position. 
  

   This 
  point 
  was 
  shown 
  by 
  Prof. 
  Anderson 
  to 
  divide 
  the 
  

   distance 
  between 
  the 
  object 
  and 
  image, 
  and 
  also 
  that 
  between 
  

   the 
  nodal 
  points, 
  externally 
  in 
  a 
  ratio 
  equal 
  to 
  the 
  value 
  of 
  

   the 
  magnification. 
  

  

  A 
  numerical 
  example 
  of 
  the 
  determination 
  of 
  the 
  focal 
  

   length 
  of 
  a 
  diverging 
  combination 
  by 
  this 
  method 
  was 
  given, 
  

   but 
  it 
  was 
  pointed 
  out 
  by 
  Mr. 
  R. 
  E. 
  Baynes 
  (Phil. 
  Mag. 
  

   April 
  1917, 
  p. 
  357) 
  that 
  these 
  data 
  yielded 
  very 
  different 
  

   results 
  for 
  the 
  focal 
  length 
  and 
  the 
  positions 
  of 
  the 
  nodal 
  

   points 
  when 
  calculated 
  in 
  different 
  ways. 
  These 
  discrepancies 
  

   were 
  explained 
  by 
  Prof. 
  Anderson 
  (Phil. 
  Mag. 
  July 
  1917, 
  

   p. 
  76), 
  who 
  discussed 
  the 
  effect 
  of 
  various 
  errors 
  and 
  showed 
  

   that, 
  while 
  the 
  method 
  gave 
  quite 
  satisfactory 
  values 
  for 
  

   the 
  focal 
  length, 
  it 
  failed 
  to 
  do 
  so 
  for 
  the 
  distance 
  between 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  