﻿APR. 
  4, 
  1922 
  HERSEY 
  : 
  PROPERTIES 
  OF 
  MATTER 
  1G9 
  

  

  the 
  unknown 
  function 
  will 
  be 
  numerically 
  the 
  same 
  in 
  the 
  two 
  

   experiments, 
  so 
  that 
  Equation 
  3 
  gives 
  

  

  - 
  = 
  - 
  (5) 
  

  

  Mo 
  "-"o 
  

  

  If 
  the 
  condition 
  for 
  dynamical 
  similarity 
  expressed 
  by 
  Equation 
  4 
  

   above 
  could 
  be 
  realized 
  at 
  the 
  first 
  trial, 
  then 
  a 
  single 
  experiment 
  on 
  

   the 
  test 
  sample 
  would 
  be 
  sufficient. 
  In 
  practice 
  two 
  or 
  more 
  experi- 
  

   ments 
  should 
  be 
  made 
  and 
  the 
  observed 
  values 
  of 
  R 
  plotted 
  as 
  ordinate 
  

   against 
  v- 
  as 
  abscissa. 
  Draw 
  a 
  straight 
  line 
  from 
  the 
  origin 
  through 
  

   the 
  point 
  whose 
  coordinates 
  are 
  Ro 
  and 
  Vo 
  -. 
  Suppose 
  this 
  line 
  inter- 
  

   sects 
  the 
  empirical 
  curv^e 
  for 
  the 
  test 
  sample 
  in 
  some 
  point 
  P. 
  Then 
  

   the 
  condition 
  for 
  dynamical 
  similarity 
  (Eq. 
  4) 
  is 
  exactly 
  realized 
  at 
  

   the 
  point 
  P, 
  although 
  this 
  is 
  a 
  fictitious 
  point 
  and 
  not 
  a 
  real 
  observa- 
  

   tion. 
  Therefore, 
  the 
  abscissa 
  i', 
  of 
  the 
  point 
  P 
  satisfies 
  Equation 
  5 
  

   and 
  is 
  to 
  be 
  substituted 
  for 
  v 
  in 
  that 
  equation 
  when 
  using 
  it 
  as 
  a 
  work- 
  

   ing 
  formula. 
  

  

  If 
  the 
  size 
  of 
  the 
  body 
  which 
  is 
  towed 
  through 
  a 
  fluid, 
  or 
  the 
  density 
  

   of 
  the 
  fluid, 
  are 
  not 
  constant. 
  Equation 
  2 
  can 
  be 
  employed 
  instead 
  of 
  

   Equation 
  3, 
  and 
  for 
  this 
  purpose 
  Equation 
  2 
  may 
  be 
  rewritten 
  

  

  ti 
  = 
  x 
  \p{y) 
  (6) 
  

  

  in 
  which 
  x 
  denotes 
  Dvp 
  while 
  y 
  stands 
  for 
  the 
  dimensionless 
  variable 
  

   R/p 
  D-v~. 
  Using 
  subscript 
  zero 
  hereafter 
  to 
  refer 
  to 
  the 
  standard 
  

   substance, 
  Equation 
  G 
  gives 
  for 
  the 
  standard 
  viscosity 
  

  

  Mo 
  =Xo\p(yo) 
  (7) 
  

  

  Now 
  plot 
  experimental 
  values 
  of 
  .1' 
  j'o 
  as 
  ordinate, 
  against 
  x/Xo 
  as 
  

   abscissa, 
  and 
  call 
  rci/r^o 
  the 
  abscissa 
  of 
  the 
  point 
  where 
  the 
  empirical 
  

   curve 
  crosses 
  the 
  horizontal 
  straight 
  line 
  j/j'o 
  = 
  1. 
  Dividing 
  (6) 
  by 
  

   (7) 
  the 
  final 
  formula 
  becomes 
  

  

  ^ 
  = 
  2^ 
  (8) 
  

  

  Mo 
  Xo 
  

  

  of 
  which 
  (5) 
  above 
  may 
  be 
  considered 
  a 
  special 
  case. 
  

  

  Thermal 
  conductivity. 
  — 
  Let 
  it 
  be 
  required 
  to 
  determine 
  relative 
  

   thermal 
  conductivity 
  X/Xo 
  by 
  successive 
  observations 
  of 
  the 
  tempera- 
  

   ture 
  rise 
  A 
  on 
  the 
  sample 
  under 
  test 
  and 
  on 
  a 
  standard 
  sample 
  which 
  

   is 
  geometrically 
  similar 
  to 
  it. 
  When 
  the 
  steady 
  state 
  has 
  been 
  reached, 
  

   the 
  heat 
  input 
  H 
  will 
  be 
  just 
  equal 
  to 
  the 
  heat 
  carried 
  off 
  from 
  the 
  

   exterior 
  of 
  the 
  sample 
  by 
  the 
  convective 
  action 
  of 
  some 
  cooling 
  agent 
  

   such 
  as 
  a 
  vigorously 
  stirred 
  water 
  bath. 
  If 
  the 
  specific 
  heat 
  of 
  this 
  

  

  