﻿Chemistry 
  and 
  Physics. 
  73 
  

  

  d 
  = 
  density 
  of 
  liquid, 
  and 
  b 
  = 
  horizontal 
  distance 
  from 
  the 
  cen- 
  

   tral 
  knife 
  edges 
  to 
  the 
  plane 
  of 
  the 
  loop. 
  Consequently 
  

  

  V.D.a 
  = 
  V 
  (D 
  — 
  d)borD 
  = 
  [b/(b 
  — 
  a)]d. 
  

  

  By 
  taking 
  values 
  of 
  D 
  which 
  increase 
  in 
  arithmetical 
  progression 
  

   and 
  d 
  = 
  1 
  (for 
  water, 
  say) 
  the 
  scale 
  can 
  be 
  graduated 
  from 
  the 
  

   values 
  of 
  b 
  derived 
  from 
  the 
  last 
  equation. 
  After 
  the 
  beam- 
  

   extension 
  has 
  been 
  thus 
  calibrated 
  the 
  unknown 
  density 
  of 
  a 
  

   given 
  solid 
  may 
  be 
  read 
  off 
  directly 
  from 
  the 
  scale. 
  Obviously, 
  

   the 
  scale 
  divisions 
  will 
  be 
  smaller 
  near 
  one 
  end 
  of 
  the 
  range 
  of 
  

   feasible 
  densities 
  than 
  the 
  other. 
  In 
  general, 
  however, 
  the 
  same 
  

   lack 
  of 
  uniformity 
  affects 
  hydrometers. 
  The 
  average 
  time 
  

   required 
  for 
  the 
  determination 
  of 
  the 
  density 
  of 
  a 
  single 
  sample 
  

   is 
  said 
  1o 
  be 
  about 
  two 
  minutes. 
  For 
  lack 
  of 
  space 
  the 
  preceding 
  

   account 
  is 
  intended 
  to 
  be 
  suggestive 
  rather 
  than 
  complete. 
  — 
  

   Jour. 
  d. 
  Phys., 
  6, 
  291, 
  1916. 
  h. 
  s. 
  u. 
  

  

  8. 
  Influence 
  of 
  the 
  Finite 
  Volume 
  of 
  Molecules 
  on 
  the 
  Equa- 
  

   tion 
  of 
  State. 
  — 
  The 
  fact 
  that 
  the 
  simple 
  equation 
  pv 
  = 
  NK6 
  does 
  

   not 
  represent 
  accurately 
  the 
  behavior 
  of 
  real 
  gases 
  is 
  explained 
  

   on 
  the 
  grounds 
  that 
  the 
  theoretical 
  derivation 
  of 
  the 
  ideal 
  gas 
  

   equation 
  takes 
  into 
  account 
  neither 
  the 
  forces 
  of 
  cohesion 
  between 
  

   the 
  particles 
  nor 
  the 
  finiteness 
  of 
  the 
  volume 
  of 
  the 
  molecules. 
  

   Although 
  the 
  equation 
  of 
  van 
  der 
  "Waals 
  involves 
  both 
  of 
  these 
  

   factors, 
  nevertheless 
  it 
  does 
  not 
  represent 
  the 
  observed 
  phenom- 
  

   ena 
  to 
  a 
  sufficiently 
  high 
  degree 
  of 
  accuracy. 
  ' 
  ' 
  In 
  all 
  subsequent 
  

   modifications 
  of 
  this 
  equation 
  (Clausius, 
  Dieterici, 
  or 
  D. 
  Berthe- 
  

   lot), 
  the 
  changes 
  which 
  have 
  been 
  proposed 
  all 
  relate 
  to 
  the 
  

   influence 
  of 
  the 
  cohesive 
  forces 
  ; 
  the 
  part 
  of 
  the 
  argument 
  deal- 
  

   ing 
  with 
  the 
  finiteness 
  of 
  the 
  molecular 
  volumes 
  is 
  generally 
  left 
  

   untouched." 
  Accordingly 
  the 
  authors 
  of 
  the 
  last 
  sentence, 
  

   Megh 
  Nad 
  Shaha 
  and 
  Satyendra 
  Nath 
  Basu, 
  have 
  published 
  a 
  

   paper 
  in 
  which 
  an 
  attempt 
  is 
  made 
  to 
  correct 
  for 
  the 
  volume 
  of 
  

   the 
  molecules. 
  

  

  Boltzmann's 
  equation 
  S 
  = 
  K 
  log 
  W 
  + 
  C 
  is 
  taken 
  as 
  funda- 
  

   mental. 
  S 
  = 
  entropy, 
  E 
  = 
  Boltzmann's 
  gas-constant, 
  and 
  W 
  == 
  

   probability 
  of 
  the 
  state. 
  Neglecting 
  (for 
  the 
  time 
  being) 
  the 
  

   influence 
  of 
  internal 
  forces, 
  it 
  is 
  shown 
  that 
  the 
  probability 
  that 
  

   & 
  number 
  N 
  of 
  molecules, 
  originally 
  confined 
  within 
  the 
  volume 
  

   v 
  and 
  possessing 
  finite 
  volumes, 
  shall 
  be 
  contained 
  in 
  a 
  volume 
  Y 
  

   is 
  given 
  by 
  

  

  w= 
  V 
  V-fi 
  V-2J3 
  •■■ 
  y-(JY-i)p 
  

   ■v 
  v 
  - 
  (3 
  v-zp 
  v-(JSr-l)p' 
  

  

  where 
  p 
  = 
  8 
  X 
  (volume 
  of 
  a 
  single 
  molecule). 
  Combining 
  the 
  

   preceding 
  equations 
  with 
  the 
  constant-energy 
  relation 
  

  

  Q8_ 
  p_ 
  

  

  9V~ 
  

  

  