﻿ROTATION 
  OF 
  PILLARS. 
  2ig 
  

  

  each 
  may 
  make 
  an 
  angle 
  of 
  J 
  with 
  the 
  central 
  line, 
  and 
  cut 
  the 
  

   points 
  A 
  and 
  B, 
  respectively, 
  we 
  have 
  an 
  isosceles 
  triangle, 
  whose 
  

   apical 
  angle 
  is, 
  and 
  whose 
  two 
  equal 
  sides 
  are 
  radii 
  of 
  the 
  circle 
  in 
  

   which 
  the 
  centre 
  of 
  gravity 
  may 
  be 
  assumed 
  to 
  have 
  moved, 
  to 
  

   enable 
  it 
  to 
  pass 
  from 
  its 
  old 
  to 
  its 
  new 
  position, 
  while 
  turning 
  

   through 
  the 
  angle 
  A 
  C 
  B 
  = 
  0. 
  If 
  this 
  radius 
  be 
  represented 
  by 
  r, 
  and 
  

   the 
  distance 
  A 
  B 
  by 
  d^ 
  then 
  

  

  d 
  . 
  6 
  

  

  f=--=-sin 
  - 
  

  

  2 
  2 
  

  

  According 
  to 
  Mallet's 
  theory, 
  r 
  should 
  equal 
  the 
  distance 
  of 
  the 
  

   centre 
  of 
  gravity 
  from 
  the 
  point 
  or 
  edge 
  on 
  which 
  the 
  object 
  rotated, 
  

   that 
  is 
  to 
  say 
  it 
  should 
  be 
  equal 
  to, 
  or 
  lie 
  somewhere 
  between, 
  the 
  

   semidiameter 
  and 
  semidiagonal, 
  and 
  should 
  not 
  materially 
  differ 
  from 
  

   them 
  in 
  excess 
  or 
  defect. 
  

  

  In 
  applying 
  this 
  test 
  it 
  will 
  be 
  necessary 
  to 
  reject 
  those 
  cases 
  where 
  

   the 
  apparent 
  shifting 
  of 
  the 
  centre 
  of 
  gravity 
  and 
  the 
  angle 
  of 
  rotation 
  

   are 
  both 
  small. 
  Neither 
  can 
  be 
  measured 
  with 
  very 
  great 
  accuracy, 
  

   and 
  when 
  either 
  is 
  small 
  a 
  very 
  slight 
  absolute 
  error 
  would 
  be 
  a 
  very 
  

   large 
  one 
  proportionately, 
  and 
  lead 
  to 
  great 
  errors 
  in 
  the 
  result. 
  

   Applying 
  the 
  test 
  to 
  those 
  cases 
  where 
  it 
  may 
  be 
  expected 
  to 
  give 
  a 
  

   reasonably 
  accurate 
  result, 
  we 
  have, 
  in 
  the 
  case 
  of 
  Inglis' 
  monument 
  

   at 
  Chhatak, 
  ^=27*8 
  in., 
  while 
  the 
  semidiameter 
  is 
  52 
  in. 
  In 
  the 
  case 
  

   of 
  the 
  monument 
  No. 
  2 
  on 
  Plate 
  XXI, 
  fig. 
  1, 
  r=3 
  in., 
  while 
  the 
  semi- 
  

   diameter 
  is 
  g 
  in. 
  In 
  the 
  case 
  of 
  the 
  W 
  pillar 
  E 
  gate, 
  and 
  the 
  E 
  pillar 
  

   W 
  gate 
  of 
  the 
  telegraph 
  signallers' 
  quarters 
  at 
  Gauhati 
  r 
  =5 
  in. 
  

   and 
  24 
  in. 
  respectively, 
  while 
  the 
  semidiameter 
  is 
  \2\ 
  in. 
  in 
  both 
  

   cases. 
  

  

  From 
  this 
  it 
  will 
  be 
  seen 
  that 
  there 
  is 
  no 
  correspondence 
  between 
  

   the 
  calculated 
  radius 
  of 
  revolution 
  and 
  that 
  required 
  by 
  the 
  theory. 
  

  

  Mallet's 
  first 
  theory, 
  though 
  undoubtedly 
  an 
  explanation, 
  is 
  insuffi- 
  

   cient 
  as 
  it 
  does 
  not 
  account 
  for 
  the 
  fact 
  that 
  a 
  number 
  of 
  similar 
  objects 
  

   are 
  similarly 
  rotated 
  in 
  the 
  same 
  neighbourhood 
  ; 
  nor 
  does 
  it 
  seem 
  

   probable 
  that 
  there 
  would 
  be 
  so 
  great 
  a 
  divergence 
  between 
  the 
  

   positions 
  of 
  the 
  centre 
  of 
  gravity 
  and 
  the 
  centre 
  of 
  resistance, 
  and 
  what 
  

  

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