﻿APR. 
  4, 
  1922 
  HERSEY 
  ; 
  PROPERTIES 
  OF 
  MATTER 
  171 
  

  

  phenomenon 
  which 
  exhibits 
  the 
  desired 
  property 
  of 
  matter 
  Q. 
  This 
  

   can 
  be 
  done 
  by 
  the 
  Il-theorem 
  method^ 
  and 
  requires 
  first 
  of 
  all 
  a 
  

   complete 
  list 
  of 
  the 
  physical 
  quantities 
  which 
  would 
  influence 
  the 
  

   phenomenon 
  if 
  they 
  were 
  to 
  vary. 
  Solve 
  this 
  equation 
  for 
  Q 
  and 
  let 
  

   the 
  result 
  be 
  written 
  

  

  Q^X-^{Y,Z,..) 
  (12) 
  

  

  in 
  which 
  Q/X, 
  Y 
  , 
  Z, 
  .... 
  are 
  dimensionless 
  variables, 
  ^ 
  being 
  an 
  

   unknown 
  function. 
  

  

  2. 
  The 
  experimental 
  facilities 
  must 
  now 
  be 
  so 
  arranged 
  that 
  all 
  

   dimensionless 
  variables 
  other 
  than 
  QIX 
  and 
  F, 
  for 
  example 
  Z 
  (if 
  

   any 
  such 
  appear), 
  shall 
  be 
  kept 
  constant. 
  Under 
  these 
  conditions 
  

   (12) 
  reduces 
  to 
  

  

  Q=AXr). 
  (13) 
  

  

  3. 
  If 
  any 
  of 
  the 
  individual 
  physical 
  quantities 
  entering 
  the 
  di- 
  

   mensional 
  factor 
  X 
  or 
  the 
  dimensionless 
  argument 
  Y 
  are 
  known 
  to 
  

   be 
  constant 
  during 
  the 
  experiment, 
  they 
  can 
  be 
  left 
  out, 
  so 
  that 
  X 
  

   and 
  Y 
  degenerate 
  respectively 
  into 
  the 
  dimensional 
  factors 
  % 
  and 
  y, 
  

   and 
  (13) 
  takes 
  on 
  the 
  more 
  simple 
  form 
  

  

  Q=^</>(>0. 
  (14) 
  

  

  Equation 
  14 
  could 
  have 
  been 
  deduced 
  at 
  the 
  start 
  in 
  place 
  of 
  (12) 
  by 
  

   utilizing 
  Buckingham's 
  recent 
  method 
  of 
  suppressed 
  dimensions.^ 
  

  

  4. 
  Take 
  observations 
  of 
  the 
  phenomenon 
  in 
  question 
  when 
  the 
  

   apparatus 
  is 
  supplied 
  with 
  a 
  standard 
  sample, 
  for 
  which 
  Q 
  (whether 
  

   numerically 
  known 
  or 
  not) 
  may 
  be 
  written 
  Qo 
  . 
  Denote 
  the 
  values 
  

   of 
  X 
  and 
  y 
  which 
  prevail 
  during 
  this 
  experiment 
  by 
  Xo 
  and 
  jo, 
  respec- 
  

   tively. 
  

  

  5. 
  Proceed 
  next 
  to 
  observe 
  the 
  same 
  phenomenon 
  with 
  the 
  new 
  

   sample, 
  for 
  which 
  Q 
  is 
  constant 
  but 
  unknown. 
  It 
  will 
  be 
  sufficient 
  

   to 
  confine 
  the 
  experimental 
  variation 
  of 
  x 
  to 
  that 
  vicinity 
  for 
  which 
  

   the 
  resulting 
  value 
  of 
  y 
  is 
  found 
  by 
  trial 
  to 
  be 
  of 
  the 
  same 
  order 
  of 
  

   magnitude 
  as 
  To 
  . 
  

  

  6. 
  Plot 
  the 
  observed 
  data 
  on 
  coordinate 
  paper 
  with 
  y 
  lyo 
  as 
  ordinate 
  

   against 
  xjxo 
  as 
  abscissa. 
  Let 
  the 
  abscissa 
  of 
  point 
  P 
  where 
  the 
  experi- 
  

   mental 
  curve 
  crosses 
  the 
  line 
  y 
  lyo 
  = 
  1 
  , 
  be 
  denoted 
  by 
  X\lxo 
  . 
  This 
  

   point 
  represents 
  a 
  fictitious 
  case 
  of 
  dynamical 
  (or 
  physical) 
  similarity, 
  

  

  3 
  E. 
  Buckingham, 
  This 
  Journal 
  4: 
  347-353. 
  1914. 
  Phys. 
  Rev. 
  4: 
  345-376. 
  1914. 
  

   Trans. 
  Am. 
  Soc. 
  Mech. 
  Eng. 
  37: 
  263-296. 
  1915. 
  

  

  * 
  E. 
  Buckingham. 
  Notes 
  on 
  the 
  method 
  of 
  dimensions. 
  Phil. 
  Mag. 
  42: 
  696-719, 
  § 
  11. 
  

   1921. 
  

  

  