﻿7L0 
  Prof. 
  Rutherford 
  and 
  Mr. 
  Nuttall 
  on 
  

  

  inverse 
  fourth 
  power 
  of 
  the 
  velocity. 
  This 
  is 
  the 
  law 
  of 
  

   scattering 
  with 
  velocity 
  found 
  by 
  Geiger 
  and 
  Marsden 
  in 
  

   their 
  experiments 
  on 
  " 
  single" 
  scattering. 
  

  

  Consideration 
  of 
  the 
  Results* 
  

  

  In 
  drawing 
  deductions 
  from 
  these 
  experiments, 
  it 
  is 
  of 
  

   importance 
  to 
  decide 
  whether 
  the 
  scattering 
  coefficient 
  ob- 
  

   served 
  is 
  to 
  be 
  ascribed 
  to 
  "single" 
  or 
  "compound" 
  scat- 
  

   tering. 
  If 
  the 
  reduction 
  in 
  the 
  number 
  of 
  a 
  particles 
  in 
  

   passing 
  between 
  the 
  glass 
  plates 
  is 
  due 
  mainly 
  to 
  " 
  single 
  " 
  

   scattering, 
  we 
  should 
  expect 
  the 
  scattering 
  to 
  vary 
  directly 
  

   as 
  the 
  pressure 
  of 
  the 
  gas 
  and 
  inversely 
  as 
  the 
  fourth 
  power 
  

   of 
  the 
  velocity 
  — 
  results 
  observed 
  experimentally. 
  On 
  the 
  

   other 
  hand, 
  if 
  the 
  reduction 
  in 
  number 
  is 
  due 
  mainly 
  to 
  

   " 
  compound" 
  scattering, 
  we 
  should 
  expect 
  that 
  the 
  scatter- 
  

   ing 
  should 
  be 
  proportional 
  to 
  the 
  square 
  root 
  of 
  the 
  pressure, 
  

   and 
  to 
  vary 
  as 
  the 
  inverse 
  square 
  of 
  the 
  velocity. 
  It 
  is 
  thus 
  

   clear 
  from 
  the 
  experiments 
  that 
  the 
  scattering 
  coefficient 
  

   observed 
  is 
  a 
  consequence 
  mainly 
  of 
  "single" 
  scattering. 
  

   This 
  conclusion 
  is 
  still 
  further 
  strengthened 
  by 
  the 
  rapid 
  

   variation 
  of 
  the 
  scattering 
  with 
  atomic 
  weight 
  between 
  

   carbon 
  and 
  sulphur. 
  No 
  doubt 
  "compound" 
  scattering 
  

   produces 
  some 
  effect, 
  but 
  the 
  main 
  part 
  of 
  the 
  scattering 
  is 
  

   to 
  be 
  ascribed 
  to 
  the 
  scattering 
  of 
  individual 
  atoms 
  resulting 
  

   from 
  the 
  passage 
  of 
  the 
  a 
  particle 
  through 
  the 
  intense 
  field 
  

   close 
  to 
  the 
  electrons 
  and 
  the 
  nucleus. 
  If 
  we 
  consider 
  the 
  

   atom 
  to 
  be 
  composed 
  of 
  a 
  nucleus 
  with 
  a 
  charge 
  ne 
  and 
  a 
  

   compensating 
  distribution 
  of 
  n 
  electrons, 
  the 
  scattering 
  due 
  

   to 
  the 
  n 
  electrons 
  is 
  proportional 
  to 
  n, 
  and 
  the 
  scattering 
  

   due 
  to 
  the 
  nucleus 
  is 
  proportional 
  to 
  n 
  2 
  . 
  Mr. 
  C. 
  Darwin 
  

   kindly 
  examined 
  this 
  question 
  mathematically 
  for 
  us, 
  and 
  

   concluded 
  that 
  if 
  the 
  electrons 
  and 
  the 
  nucleus 
  were 
  a 
  suf- 
  

   ficient 
  distance 
  apart 
  so 
  as 
  not 
  to 
  interfere 
  seriously 
  with 
  

   the 
  electric 
  fields 
  close 
  to 
  them, 
  the 
  scattering 
  for 
  simple 
  

   atoms 
  should 
  be 
  proportional 
  to 
  n-\-n 
  2 
  or 
  w(n 
  + 
  l), 
  where 
  ne 
  

   is 
  the 
  charge 
  on 
  the 
  atomic 
  nucleus. 
  For 
  deflexions 
  through 
  

   a 
  small 
  angle, 
  such 
  as 
  are 
  involved 
  in 
  the 
  experimental 
  

   arrangement 
  employed 
  in 
  this 
  paper, 
  we 
  should 
  expect 
  the 
  

   scattering 
  in 
  the 
  heavy 
  atoms 
  to 
  be 
  proportional 
  to 
  n 
  + 
  kn 
  2 
  , 
  

   where 
  k 
  is 
  less 
  than 
  unity. 
  This 
  is 
  borne 
  out 
  by 
  the 
  fact 
  

   that 
  under 
  the 
  experimental 
  conditions 
  the 
  scattering 
  due 
  to 
  

   heavy 
  atoms 
  like 
  bromine 
  and 
  iodine 
  was 
  found 
  to 
  be 
  less 
  

   than 
  the 
  theoretical 
  values 
  when 
  k 
  is 
  takeu 
  as 
  unit} 
  7- 
  . 
  As- 
  

   suming 
  the 
  simple 
  formula 
  found 
  by 
  Darwin 
  as 
  applicable 
  

   to 
  light 
  atoms, 
  the 
  scattering 
  coefficient 
  \ 
  is 
  proportional 
  to 
  

   n(n-\-l) 
  or 
  X=cw(n 
  + 
  1), 
  where 
  c 
  is 
  a 
  constant. 
  

  

  