﻿490 
  Mr. 
  R. 
  F. 
  Gwyther 
  : 
  A 
  Doctrine 
  

  

  is 
  " 
  better 
  to 
  base 
  the 
  reduction 
  of 
  the 
  observations 
  on 
  known 
  

   measurements 
  rather 
  than 
  on 
  assumptions 
  as 
  to 
  the 
  ratio 
  of 
  

   impedance 
  to 
  resistance," 
  unless 
  the 
  known 
  measurements 
  

   are 
  of 
  some 
  magnitude 
  on 
  which 
  the 
  observed 
  phenomena 
  

   depend. 
  In 
  the 
  case 
  in 
  point, 
  no 
  uncertainty 
  as 
  to 
  the 
  exact 
  

   wave-form 
  can 
  be 
  regarded 
  as 
  a 
  legitimate 
  excuse 
  for 
  

   neglecting 
  the 
  fact 
  that 
  one 
  is 
  dealing 
  with 
  an 
  alternating 
  

   or 
  pulsating 
  current. 
  

  

  Yours 
  truly, 
  

   31st 
  January, 
  1918. 
  p 
  ttt 
  n 
  xt, 
  , 
  

  

  South 
  Kensington. 
  G 
  ' 
  ^ 
  ' 
  °' 
  H 
  ° 
  WE 
  ' 
  

  

  LVITI. 
  A 
  Doctrine 
  on 
  Material 
  Stresses. 
  

   By 
  R. 
  F. 
  Gwyther*. 
  

  

  IT 
  is 
  intended 
  to 
  provide 
  a 
  reasoned 
  basis 
  for 
  a 
  theory 
  of 
  

   stresses, 
  applicable 
  in 
  the 
  first 
  case 
  to 
  a 
  body 
  which 
  

   satisfies 
  the 
  geometrical 
  conditions 
  for 
  acting 
  as 
  a 
  Rio-id 
  

   Body 
  (not 
  being 
  in 
  a 
  state 
  of 
  constraint), 
  but 
  which 
  shall 
  be 
  

   capable 
  of 
  extension 
  to 
  Elastic 
  Bodies 
  or 
  to 
  other 
  approxi- 
  

   mations 
  to 
  Natural 
  Bodies, 
  without 
  introducing 
  the 
  fiction 
  of 
  

   an 
  " 
  undisturbed 
  " 
  condition 
  in 
  which 
  the 
  body 
  is 
  assumed 
  

   to 
  be 
  free 
  from 
  stress. 
  The 
  doctrine, 
  for 
  the 
  development 
  

   of 
  which 
  the 
  several 
  stages 
  are 
  indicated 
  below, 
  is 
  the 
  outcome 
  

   of 
  a 
  series 
  of 
  papers 
  on 
  the 
  " 
  Specification 
  ol 
  Stress/' 
  pub- 
  

   lished 
  by 
  the 
  Manchester 
  Literary 
  and 
  Philosophical 
  Society 
  f, 
  

   but 
  it 
  cannot 
  be 
  described 
  as 
  the 
  motive 
  of 
  the 
  papers, 
  since 
  

   it 
  has 
  formulated 
  itself 
  during 
  the 
  progress 
  of 
  the 
  series. 
  

  

  The 
  body 
  contemplated 
  is 
  not 
  supposed 
  to 
  be 
  crystalline, 
  

   fibrous, 
  or 
  annealed, 
  and 
  not 
  to 
  be 
  subject 
  to 
  any 
  special 
  

   conditions 
  either 
  locally 
  or 
  at 
  the 
  surface. 
  The 
  body 
  mav, 
  

   in 
  the 
  first 
  instance, 
  be 
  regarded 
  as 
  either 
  at 
  rest 
  or 
  in 
  

   motion 
  under 
  the 
  geometrical 
  conditions 
  which 
  define 
  rigidity, 
  

   and 
  any 
  modification 
  of 
  those 
  geometrical 
  conditions, 
  such 
  as 
  

   elastic 
  modifications, 
  are 
  to 
  be 
  deduced 
  from 
  the 
  stresses 
  in 
  

   the 
  initial 
  instance, 
  and 
  from 
  such 
  definitions 
  as 
  may 
  prove 
  

   necessary 
  in 
  the 
  sequel. 
  

  

  The 
  stages 
  by 
  which 
  the 
  theory 
  is 
  developed 
  are 
  stated 
  

   below. 
  No 
  analytical 
  expressions 
  are 
  used, 
  but 
  reference 
  is 
  

   made 
  to 
  such 
  analytical 
  expressions 
  at 
  all 
  the 
  stages. 
  This 
  is 
  

   inevitable, 
  since 
  the 
  question 
  is, 
  at 
  this 
  stage, 
  an 
  analytical 
  

   question. 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  t 
  Manchester 
  Memoirs, 
  No. 
  10, 
  vol.lvi. 
  (1912), 
  No. 
  5, 
  vol. 
  lvii. 
  (1913), 
  

   No. 
  5, 
  vol. 
  lviii. 
  (1914), 
  No. 
  14, 
  vol. 
  lx. 
  (1916), 
  No. 
  1, 
  vol 
  lxii. 
  (1917). 
  ' 
  

  

  