﻿184 
  On 
  Measuring 
  the 
  Torsional 
  Angle 
  of 
  a 
  Rotating 
  Shaft 
  fyc. 
  

  

  are 
  known. 
  Thus, 
  suppose 
  E 
  to 
  denote 
  the 
  HP 
  transmitted, 
  

   N 
  the 
  number 
  of 
  rotations 
  of 
  the 
  shaft 
  per 
  minute, 
  the 
  work 
  

   done 
  per 
  minute 
  in 
  inch-lbs. 
  is 
  12 
  x 
  33000 
  X 
  E 
  ; 
  and 
  this 
  equals 
  

   the 
  twisting 
  moment 
  T 
  in 
  statical 
  inch-lbs., 
  multiplied 
  by 
  the 
  

   angular 
  motion 
  of 
  the 
  shaft 
  27rN 
  per 
  minute, 
  i. 
  e. 
  

  

  2ttNT=12x 
  33000 
  xE, 
  

  

  2ttNT 
  

  

  E 
  = 
  

  

  12x33000* 
  

  

  To 
  find 
  E, 
  N 
  and 
  T 
  must 
  be 
  known. 
  When 
  variation 
  in 
  

   rotation 
  is 
  but 
  slight, 
  N 
  may 
  be 
  found 
  by 
  means 
  of 
  a 
  counter 
  

   such 
  as 
  that 
  of 
  Harding, 
  T 
  then 
  remains 
  to 
  be 
  determined. 
  

   In 
  1894, 
  May 
  2nd, 
  the 
  writer 
  of 
  this 
  paper 
  exhibited 
  at 
  the 
  

   Royal 
  Society 
  several 
  models 
  of 
  ergometers, 
  which 
  showed 
  

   how 
  the 
  torsion 
  of 
  a 
  rotating 
  shaft 
  might 
  be 
  measured 
  by 
  

   mechanical 
  and 
  optical 
  methods, 
  and 
  a 
  description 
  was 
  given 
  

   in 
  a 
  pamphlet 
  entitled 
  " 
  A 
  Torsion 
  Ergometer 
  or 
  Work- 
  

   Measuring 
  Machine 
  ; 
  " 
  a 
  rotostat 
  was 
  also 
  exhibited, 
  in 
  which 
  

   an 
  inverting 
  prism 
  rotated 
  in 
  front 
  of 
  the 
  index 
  of 
  the 
  

   ergometer, 
  brought 
  it 
  to 
  rest, 
  and 
  made 
  an 
  easy 
  reading 
  

   possible 
  although 
  the 
  shaft 
  of 
  the 
  machine 
  might 
  be 
  

   making 
  any 
  number 
  of 
  revolutions 
  per 
  minute. 
  The 
  author 
  

   has 
  been 
  subsequently 
  informed 
  that 
  a 
  similar 
  device 
  was 
  

   •used 
  by 
  Lord 
  Rayleigh 
  for 
  blending 
  colours. 
  [Reprint 
  of 
  

   some 
  Optical 
  Papers. 
  Lord 
  Rayleigh, 
  1883.] 
  At 
  the 
  time 
  

   of 
  devising 
  the 
  rotostat 
  the 
  author 
  did 
  not 
  know 
  that 
  a 
  

   rotated 
  inverting 
  prism 
  had 
  been 
  so 
  used 
  for 
  blending 
  colours 
  

   or 
  similar 
  purpose. 
  

  

  Since 
  1894 
  the 
  problem 
  of 
  measuring 
  the 
  torsion 
  of 
  a 
  very 
  

   long 
  shaft 
  arose, 
  the 
  shaft 
  being 
  used 
  to 
  drive 
  a 
  dynamo, 
  

   and 
  also 
  the 
  torsion 
  of 
  a 
  solenoidal 
  spiral 
  spring 
  used 
  as 
  a 
  

   flexible 
  shaft 
  to 
  drive 
  screw-propellers 
  of 
  different 
  forms, 
  in 
  

   water, 
  at 
  different 
  depths. 
  

  

  While 
  the 
  apparatus 
  required 
  is 
  of 
  a 
  simple 
  character 
  the 
  

   results 
  obtained 
  are 
  sufficient 
  and 
  reliable. 
  

  

  The 
  method 
  is 
  as 
  follows 
  (see 
  diagram) 
  : 
  — 
  Two 
  disks 
  of 
  insu- 
  

   lating 
  material 
  A, 
  C 
  are 
  fixed 
  at 
  the 
  ends 
  of 
  the 
  shaft, 
  the 
  bear- 
  

   ings 
  of 
  which 
  are 
  not 
  shown, 
  narrow 
  slips 
  of 
  copper 
  H, 
  K 
  are 
  

   attached 
  to 
  the 
  disks 
  at 
  their 
  circumferences, 
  and 
  to 
  the 
  shaft. 
  

   Two 
  brushes 
  D, 
  E 
  (single 
  flat 
  wires 
  answer 
  well), 
  press 
  on 
  the 
  

   edge 
  of 
  the 
  disks, 
  the 
  brushes 
  are 
  connected 
  to 
  an 
  electric 
  

   circuit, 
  including 
  a 
  battery 
  B, 
  and 
  a 
  telephone 
  T. 
  Then 
  

   when 
  H 
  and 
  K 
  are 
  in 
  the 
  same 
  plane, 
  at 
  each 
  revolution 
  of 
  

   the 
  shaft 
  a 
  click 
  is 
  heard 
  in 
  the 
  telephone 
  ; 
  but 
  if 
  while 
  the 
  

   shaft 
  is 
  rotating 
  the 
  disk 
  C 
  has 
  an 
  angular 
  advance 
  on 
  the 
  

  

  