﻿370 
  Notises 
  respecting 
  New 
  Boohs. 
  

  

  Since 
  F(0) 
  is 
  an 
  odd 
  function 
  o£ 
  6, 
  it 
  follows 
  that 
  </>(F) 
  is 
  

   expansible 
  in 
  a 
  series 
  of 
  ascending 
  powers 
  of 
  F$, 
  convergent 
  

   when 
  F 
  is 
  sufficiently 
  small, 
  in 
  which 
  the 
  first 
  two 
  terms 
  are 
  

   given 
  by 
  the 
  formula 
  

  

  0(F) 
  cv^tt- 
  2*3^/20, 
  

   and 
  hence 
  the 
  integral 
  of 
  3 
  n 
  (nx) 
  possesses 
  an 
  asymptotic 
  

   expansion 
  in 
  which 
  the 
  ratio 
  of 
  consecutive 
  terms 
  is 
  of 
  

   order 
  n 
  3 
  , 
  the 
  first 
  two 
  terms 
  being 
  given 
  by 
  the 
  formula 
  

  

  Jt 
  

  

  1 
  2*3* 
  

  

  i 
  

  

  cv>- 
  

  

  207T713 
  

  

  3n 
  3*5n*r(J)' 
  

  

  This 
  approximation 
  gives 
  the 
  value 
  of 
  the 
  integral 
  correct 
  

   to 
  four 
  places 
  of 
  decimals 
  when 
  ?i 
  = 
  23. 
  

  

  XLI. 
  Notices 
  respecting 
  New 
  Books. 
  

  

  The 
  Electron. 
  Its 
  isolation 
  and 
  measurement 
  and 
  the 
  determination 
  

   of 
  some 
  of 
  its 
  properties. 
  By 
  Eobert 
  Andrews 
  Millikan. 
  

   Pp. 
  xii+268. 
  The 
  University 
  of 
  Chicago 
  Press. 
  Price 
  7s. 
  net. 
  

  

  STARTING- 
  with 
  a 
  brief 
  historical 
  account 
  of 
  the 
  rise 
  of 
  the 
  

   ^ 
  electron 
  theory, 
  the 
  author 
  soon 
  reaches 
  the 
  question 
  of 
  the 
  

   determination 
  of 
  the 
  electronic 
  charge 
  e, 
  and, 
  after 
  describing 
  

   briefly 
  the 
  early 
  work 
  of 
  the 
  Cavendish 
  school, 
  and 
  the 
  difficulties 
  

   encountered, 
  he 
  devotes 
  special 
  attention 
  to 
  the 
  experiments 
  

   carried 
  out 
  by 
  himself 
  and 
  his 
  students 
  in 
  the 
  Ryerson 
  laboratory 
  

   of 
  the 
  University 
  of 
  Chicago. 
  In 
  these 
  experiments, 
  in 
  place 
  of 
  

   Wilson's 
  cloud, 
  a 
  single 
  oil 
  drop 
  was 
  observed 
  ; 
  and 
  Professor 
  

   Millikan 
  gives 
  a 
  most 
  interesting 
  account 
  of 
  the 
  method 
  by 
  which 
  the 
  

   capture 
  of 
  single 
  electrons 
  by 
  a 
  drop 
  was 
  observed, 
  the 
  corrections 
  

   to 
  Stokes' 
  law 
  necessitated 
  by 
  the 
  small 
  radii 
  of 
  some 
  of 
  the 
  drops, 
  

   and 
  the 
  final 
  determination 
  of 
  e 
  to 
  be 
  (4*774 
  + 
  -005) 
  x 
  10 
  -10 
  electro- 
  

   static 
  units, 
  and 
  N", 
  Avogadro's 
  constant, 
  to 
  be 
  (6*062 
  + 
  -006) 
  x 
  10 
  23 
  . 
  

   He 
  also 
  details 
  experiments 
  carried 
  out 
  on 
  the 
  Brownian 
  movement 
  

   in 
  gases 
  to 
  determine 
  N. 
  

  

  Not 
  long 
  before 
  the 
  war 
  Ehrenhaft 
  published 
  an 
  account 
  of 
  

   series 
  of 
  experiments 
  which 
  he 
  considered 
  to 
  demonstrate 
  the 
  

   existence 
  of 
  a 
  sub-electron, 
  or 
  charge 
  very 
  much 
  smaller 
  than 
  the 
  

   electron. 
  Few 
  English 
  physicists 
  found 
  the 
  work 
  convincing, 
  

   but, 
  nevertheless, 
  it 
  aroused 
  some 
  attention. 
  Professor 
  Millikan 
  

   devotes 
  a 
  chapter 
  of 
  his 
  book 
  to 
  discussing 
  this 
  question 
  of 
  a 
  

   sub-electron, 
  and 
  brings 
  forward 
  very 
  strong 
  arguments, 
  based 
  on 
  

   his 
  own 
  experience, 
  for 
  supposing 
  Ehrenhaft's 
  results 
  to 
  be 
  a 
  

   development 
  of 
  experimental 
  errors 
  and 
  uncertainties. 
  There 
  

   seems 
  no 
  doubt 
  that, 
  according 
  to 
  the 
  best 
  experimental 
  evidence 
  

   at 
  present 
  available, 
  the 
  electronic 
  charge 
  e 
  is 
  constant 
  and 
  indi- 
  

   visible, 
  as 
  was 
  universally 
  assumed. 
  

  

  