﻿168 
  JOURNAL 
  OF 
  THE 
  WASHINGTON 
  ACADEMY 
  OF 
  SCIENCES 
  VOL. 
  12, 
  NO. 
  7 
  

  

  was 
  in 
  fact 
  first 
  brought 
  to 
  the 
  writer's 
  attention 
  through 
  a 
  specific 
  

   instance 
  discussed 
  by 
  Dr. 
  E. 
  Buckingham'- 
  at 
  the 
  Philosophical 
  Society 
  

   of 
  Washington 
  in 
  1916 
  in 
  connection 
  with 
  the 
  subject 
  of 
  efflux 
  vis- 
  

   cosimeters. 
  

  

  When 
  attempting 
  to 
  reverse 
  the 
  principle 
  of 
  dynamical 
  similarity, 
  

   it 
  is 
  in 
  general 
  impossible 
  to 
  predetermine 
  the 
  necessary 
  conditions 
  

   because 
  the 
  resulting 
  forces 
  or 
  motions 
  cannot 
  be 
  experimentally 
  

   controlled 
  or 
  foreseen. 
  It 
  is 
  an 
  essential 
  feature 
  of 
  the 
  proposed 
  dem- 
  

   onstration 
  to 
  show 
  that 
  this 
  can 
  be 
  done 
  by 
  securing 
  fictitious 
  similarity 
  

   by 
  graphical 
  interpolation 
  among 
  two 
  or 
  more 
  experimental 
  trials 
  

   which 
  approximate, 
  but 
  do 
  not 
  exactly 
  realize, 
  the 
  conditions 
  for 
  

   similarity. 
  Before 
  treating 
  the 
  problem 
  symbolically, 
  this 
  feature 
  

   will 
  be 
  illustrated 
  by 
  concrete 
  examples. 
  

  

  Viscosity 
  measurement. 
  — 
  The 
  familiar 
  equation 
  for 
  fluid 
  resistance 
  

   due 
  to 
  Lord 
  Rayleigh 
  may 
  be 
  written 
  

  

  i?=p/)%= 
  ^(^^) 
  ' 
  (1) 
  

  

  in 
  which 
  R 
  denotes 
  the 
  resistant 
  force, 
  D 
  some 
  linear 
  dimension 
  of 
  

   the 
  body, 
  and 
  v 
  its 
  relative 
  speed 
  through 
  the 
  medium 
  of 
  density 
  p 
  

   and 
  viscosity 
  m- 
  The 
  function 
  / 
  is 
  the 
  same 
  for 
  all 
  geometrically 
  

   similar 
  bodies. 
  This 
  equation 
  can 
  be 
  solved 
  for 
  the 
  unknown 
  vis- 
  

   cosity 
  /x 
  and 
  written 
  

  

  n 
  = 
  DvpJ^~] 
  (2) 
  

  

  \pDhy 
  

  

  or, 
  when 
  D 
  and 
  p 
  are 
  constant, 
  

  

  /7?\ 
  

  

  (3) 
  

  

  Now, 
  if 
  the 
  functions 
  \p 
  or 
  (i> 
  were 
  known, 
  either 
  of 
  these 
  equations 
  

   could 
  be 
  used 
  as 
  it 
  stands 
  for 
  the 
  determination 
  of 
  absolute 
  viscosity 
  

   from 
  observations 
  on 
  the 
  resistance 
  and 
  speed. 
  But 
  for 
  the 
  purpose 
  

   of 
  relative 
  determinations, 
  the 
  form 
  of 
  the 
  function 
  need 
  not 
  be 
  known, 
  

   as 
  will 
  presently 
  appear. 
  For 
  suppose 
  that 
  the 
  apparatus, 
  when 
  sup- 
  

   plied 
  with 
  a 
  standard 
  sample 
  of 
  viscosity 
  ^o, 
  gives 
  an 
  observed 
  re- 
  

   sistance 
  Ro 
  at 
  the 
  speed 
  Vo, 
  while 
  the 
  sample 
  under 
  test 
  gives 
  some 
  

   different 
  resistance 
  i? 
  at 
  a 
  speed 
  v; 
  then 
  if 
  

  

  . 
  R 
  Ro 
  

  

  (4) 
  

  

  2 
  This 
  Journal 
  6: 
  154-155. 
  1916. 
  

  

  