﻿348 
  OLDHAM: 
  GREAT 
  EARTHQUAKE 
  OF 
  1897. 
  

  

  The 
  defect 
  in 
  theory 
  underlying 
  these 
  equations 
  is 
  the 
  supposition 
  that 
  the 
  

   impulse 
  is 
  Instantaneous, 
  it 
  is 
  assumed 
  to 
  act 
  for 
  an 
  infinitely 
  short 
  time 
  over 
  an 
  

   infinitely 
  short 
  distance. 
  

  

  The 
  next 
  attempt 
  to 
  utilise 
  overturned 
  pillars 
  and 
  columns 
  as 
  seismometers 
  

   looked 
  to 
  them 
  as 
  measures 
  not 
  of 
  the 
  maximum 
  velocity, 
  but 
  of 
  the 
  maximum 
  

   acceleration 
  of 
  the 
  wave-particle. 
  This 
  is 
  due 
  to 
  Mr. 
  C. 
  D. 
  West, 
  by 
  whom 
  

   the 
  argument 
  is 
  stated 
  as 
  follows 
  1 
  :— 
  - 
  

  

  " 
  Let 
  the 
  surface 
  of 
  the 
  earth 
  at 
  any 
  instant 
  be 
  undergoing 
  an 
  acceleration 
  

  

  of 
  velocity 
  of 
  / 
  feet 
  per 
  sec. 
  per 
  sec. 
  Let 
  

  

  M 
  be 
  the 
  mass 
  of 
  the 
  column 
  (see. 
  fig. 
  43) 
  

  

  P 
  resting 
  on 
  the 
  ground, 
  y 
  the 
  height 
  of 
  its 
  

  

  -> 
  centre 
  of 
  gravity, 
  and 
  x 
  its 
  horizontal 
  

  

  y 
  distance 
  from 
  the 
  edge 
  round 
  which 
  it 
  

   may 
  be 
  supposed 
  to 
  turn. 
  

  

  00 
  

   4yy 
  "Then 
  the 
  inertia 
  of 
  the 
  column 
  is 
  

  

  equivalent 
  to 
  a 
  force 
  

   F*g- 
  43. 
  F=Mf 
  

  

  acting 
  horizontally 
  through 
  its 
  centre 
  of 
  gravity 
  and 
  tending 
  to 
  overturn 
  

   the 
  column, 
  the 
  overturning 
  moment 
  being 
  

  

  F 
  y 
  — 
  Mfy 
  

  

  This 
  moment 
  is 
  opposed 
  by 
  the 
  moment 
  or 
  the 
  weight 
  of 
  the 
  column, 
  W 
  x, 
  and 
  

   therefore 
  when 
  the 
  column 
  is 
  on 
  the 
  point 
  of 
  overturning 
  

  

  W 
  

   W 
  x 
  = 
  F 
  y 
  = 
  MFy 
  = 
  — 
  -f 
  >'. 
  

  

  X 
  

  

  = 
  

  

  g 
  

  

  ■• 
  /= 
  

  

  - 
  g 
  

  

  X 
  

  

  y 
  

  

  (II) 
  

  

  "If/ 
  exceeds 
  this 
  value 
  the 
  column 
  may 
  go 
  over, 
  if 
  less 
  the 
  column 
  may 
  

   stand." 
  

  

  This 
  formula 
  recognizes 
  facts 
  as 
  they 
  are 
  more 
  than 
  (I) 
  and 
  in 
  Prof. 
  Milne's 
  

   experimental 
  investigations 
  it 
  gave 
  results 
  in 
  somewhat 
  close 
  agreement 
  with 
  

   the 
  actual, 
  but 
  where 
  the 
  period 
  was 
  about 
  i| 
  to 
  2 
  seconds, 
  there 
  were 
  many 
  wide 
  

   divergencies 
  ; 
  the 
  calculated 
  acceleration 
  being 
  in 
  excess 
  of 
  the 
  actual. 
  2 
  

  

  The 
  formula, 
  it 
  will 
  be 
  seen, 
  takes 
  no 
  account 
  of 
  the 
  amplitude, 
  or 
  of 
  the 
  

   range 
  of 
  motion, 
  i.e., 
  double 
  amplitude, 
  of 
  the 
  wave-particle, 
  and 
  Prof. 
  Omori 
  

   points 
  out 
  that 
  the 
  column 
  will 
  only 
  overturn 
  towards 
  the 
  direction 
  from 
  which 
  the 
  

   impulse 
  comes 
  when 
  its 
  rotation 
  is 
  sufficient 
  to 
  bring 
  the 
  centre 
  of 
  gravity 
  over 
  the 
  

   edge 
  on 
  which 
  it 
  turns. 
  3 
  

  

  1 
  Journ. 
  Seismol. 
  Soc, 
  Japan. 
  VIII, 
  35 
  (1885). 
  

  

  2 
  Seismol. 
  Journ., 
  Japan, 
  XVII, 
  74 
  (1893). 
  

  

  3 
  Seismol. 
  Journ., 
  Japan, 
  XVII, 
  p. 
  120 
  (1893). 
  

  

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  348 
  ) 
  

  

  