﻿442 
  Scientific 
  Intelligence. 
  

  

  By 
  means 
  of 
  vector 
  analysis 
  the 
  author 
  first 
  proves 
  that 
  ' 
  ' 
  the 
  

   resultant 
  action 
  of 
  all 
  doublets 
  in 
  an 
  unlimited 
  diamond 
  lattice 
  

   is 
  nil." 
  It 
  then 
  follows 
  at 
  once 
  that 
  y? 
  = 
  1 
  + 
  iVe 
  2 
  /m 
  (y 
  -y), 
  

   where 
  fi 
  = 
  refractive 
  index, 
  N 
  = 
  number 
  of 
  carbon 
  atoms 
  per 
  

   unit 
  volume 
  of 
  diamond, 
  e 
  = 
  electronic 
  charge, 
  m 
  = 
  electronic 
  

   mass, 
  y 
  = 
  4tt 
  2 
  c 
  2 
  /A 
  2 
  , 
  A 
  = 
  4tt 
  2 
  c 
  2 
  /A 
  2 
  , 
  y 
  = 
  incident 
  wave-length 
  (in 
  

   vacuo), 
  A 
  = 
  f 
  ree 
  wave-length 
  belonging 
  to 
  the 
  electron 
  of 
  the 
  

   carbon 
  atom, 
  and 
  c 
  = 
  velocity 
  of 
  the 
  light 
  in 
  free 
  space. 
  Put- 
  

   ting 
  u 
  = 
  1/A 
  2 
  and 
  a 
  = 
  Ne 
  2 
  /4nr 
  2 
  c 
  2 
  m, 
  the 
  final 
  formula 
  reduces 
  to 
  

  

  2 
  i 
  _i_ 
  a 
  

   P 
  =1 
  + 
  7. 
  --> 
  

  

  that 
  is, 
  the 
  simplest, 
  two-constant 
  formula 
  of 
  the 
  common 
  type. 
  

   When 
  this 
  formula 
  was 
  tested 
  on 
  the 
  thirteen 
  values 
  of 
  n 
  given 
  

   by 
  Martens 
  and 
  others, 
  for 
  values 
  of 
  A 
  varying 
  from 
  0-3133 
  

   micron 
  to 
  0-7604 
  micron, 
  it 
  was 
  found 
  to 
  agree 
  almost 
  exactly 
  

   with 
  the 
  experimental 
  data. 
  The 
  greatest 
  deviation 
  was 
  — 
  0-0009, 
  

   corresponding 
  to 
  fi 
  = 
  2-4410. 
  In 
  this 
  calculation 
  a 
  = 
  357-40 
  

   micr. 
  -2 
  and 
  fx 
  = 
  76-691 
  micr. 
  -2 
  . 
  The 
  free 
  wave-length 
  A 
  comes 
  

   out 
  1142 
  A. 
  IL, 
  which 
  is 
  quite 
  plausible. 
  The 
  empirical 
  formula 
  

   used 
  by 
  Martens 
  involved 
  three 
  constants, 
  hence 
  Silberstein's 
  

   equation 
  is 
  better 
  from 
  all 
  points 
  of 
  view. 
  There 
  remain 
  a 
  few 
  

   more 
  interesting 
  deductions 
  in 
  the 
  latter 
  part 
  of 
  the 
  paper, 
  but 
  

   these 
  cannot 
  be 
  entered 
  into 
  in 
  this 
  abstract. 
  — 
  Phil. 
  Mag., 
  37, 
  

   396, 
  1919. 
  h. 
  s. 
  u. 
  

  

  6. 
  Resonance 
  Radiation 
  of 
  Sodium 
  Vapor. 
  — 
  In 
  collaboration 
  

   with 
  F. 
  L. 
  Mohler, 
  R. 
  W. 
  Wood 
  has 
  repeated 
  and 
  extended 
  his 
  

   earlier 
  experiments 
  on 
  the 
  resonance 
  radiation 
  of 
  sodium 
  vapor 
  

   excited 
  by 
  either 
  one 
  of 
  the 
  D 
  lines. 
  The 
  apparatus 
  used 
  in 
  the 
  

   recent 
  work 
  was 
  more 
  powerful 
  and 
  efficient 
  than 
  that 
  employed 
  

   in 
  the 
  preceding 
  investigation 
  of 
  the 
  same 
  phenomenon. 
  For 
  

   example, 
  the 
  spectrograph 
  was 
  built 
  up 
  with 
  two 
  large 
  portrait 
  

   objectives 
  of 
  3 
  in. 
  aperture 
  and 
  24 
  in. 
  focal 
  length, 
  and 
  two 
  5 
  

   in. 
  prisms 
  of 
  flint 
  glass. 
  Larger 
  polarizing 
  prisms 
  were 
  used, 
  

   and 
  the 
  thick 
  quartz 
  plate 
  was 
  re-figured 
  and 
  polished. 
  The 
  

   entire 
  polarizing 
  system 
  was 
  kept 
  at 
  constant 
  temperature 
  by 
  

   a 
  thermostat. 
  "A 
  very 
  great 
  advance 
  resulted 
  from 
  the 
  dis- 
  

   covery 
  that 
  the 
  new 
  'pyrex' 
  glass 
  made 
  by 
  the 
  Corning 
  Co. 
  

   (Corning, 
  N. 
  Y.) 
  resists 
  the 
  action 
  of 
  sodium 
  vapour 
  far 
  better 
  

   than 
  any 
  other 
  glass 
  in 
  the 
  market. 
  Bulbs 
  blown 
  from 
  tubes 
  of 
  

   this 
  glass 
  showed 
  scarcely 
  any 
  discoloration 
  after 
  ten 
  hours' 
  

   heating, 
  which 
  is 
  sufficient 
  to 
  colour 
  bulbs 
  of 
  soft-glass 
  a 
  dark 
  

   brown." 
  Elaborate 
  precautions 
  were 
  taken 
  to 
  eliminate 
  all 
  

   known 
  sources 
  of 
  error. 
  In 
  particular, 
  special 
  attention 
  was 
  

   given 
  to 
  the 
  removal 
  of 
  hydrogen 
  from 
  the 
  sodium. 
  "We 
  found 
  

   that 
  even 
  after 
  the 
  sodium 
  deposit 
  had 
  been 
  driven 
  across 
  the 
  

   bulb 
  170 
  times, 
  the 
  McLeod 
  gauge 
  still 
  showed 
  a 
  small 
  trace 
  of 
  

   hydrogen." 
  

  

  