﻿APPENDIX 
  C. 
  

  

  349 
  

  

  But 
  the 
  impulse 
  may 
  be 
  assumed 
  to 
  be 
  imparted 
  at 
  the 
  centre 
  of 
  percussion 
  

   P 
  (fig. 
  44) 
  whose 
  distance 
  from 
  the 
  base 
  is 
  

  

  4 
  W+f) 
  

  

  that 
  is 
  to 
  say 
  when 
  

  

  ia 
  O 
  A 
  . 
  . 
  

  

  -Q-p 
  -~q~q 
  approximately 
  

  

  2 
  a 
  being 
  the 
  double 
  amplitude, 
  or 
  range 
  of 
  motion 
  of 
  the 
  

   edge 
  A, 
  hence 
  

  

  A 
  

   2a 
  =0~G 
  X 
  

  

  OP=^ 
  

  

  4(* 
  2 
  + 
  y 
  2 
  ) 
  

  

  y 
  3y 
  

  

  = 
  4 
  x 
  (x* 
  + 
  y 
  2 
  ) 
  

   3> 
  

   In 
  the 
  same 
  p^per 
  Prof. 
  Omori 
  suggests 
  that, 
  where 
  the 
  

   amplitude 
  is 
  greater 
  than 
  this 
  and 
  the 
  period 
  a 
  long 
  one, 
  

   the 
  pillar 
  will, 
  during 
  the 
  forward 
  semiphase 
  of 
  the 
  wave, 
  

   acquire 
  a 
  velocity 
  of 
  movement 
  equal 
  to 
  that 
  of 
  the 
  wave 
  

   particle, 
  and 
  on 
  the 
  backward 
  semiphase 
  setting 
  in, 
  this 
  

   velocity 
  may 
  be 
  regarded 
  as 
  having 
  been 
  suddenly 
  imparted 
  

   at 
  the 
  centre 
  of 
  gravity 
  of 
  the 
  pillar. 
  Equating 
  this 
  with 
  the 
  work 
  required 
  to 
  

   turn 
  the 
  pillar 
  till 
  the 
  centre 
  of 
  gravity 
  comes 
  over 
  the 
  edge 
  on 
  which 
  it 
  turns, 
  he 
  

   gives, 
  for 
  a 
  pillar 
  of 
  rectangular 
  section— 
  1 
  

  

  F'g. 
  44- 
  

  

  v 
  = 
  / 
  Sgy/x*+y*{i-cos 
  

   V 
  3 
  cos 
  - 
  * 
  <P 
  

  

  or 
  

  

  J 
  

  

  e 
  v 
  (t 
  — 
  cos 
  <t>) 
  

  

  3 
  cos* 
  «/> 
  

  

  This 
  formula, 
  however, 
  though 
  different 
  in 
  form, 
  is 
  identical 
  with 
  Prof. 
  Haughton's 
  

   formula 
  (I, 
  1) 
  for 
  tha 
  overthrow 
  of 
  a 
  rectangular 
  pillar. 
  

  

  Besides 
  pillars 
  that 
  have 
  been 
  overthrown 
  it 
  will 
  be 
  found 
  that 
  others 
  have 
  

   been 
  broken 
  across 
  but 
  not 
  overthrown. 
  For 
  determining 
  the 
  velocity 
  of 
  wave- 
  

   particle 
  from 
  this, 
  only 
  one 
  formula 
  has 
  been 
  proposed, 
  though 
  its 
  form 
  nuy 
  

   be 
  modified. 
  This 
  is 
  the 
  one 
  given 
  by 
  Mallet 
  — 
  2 
  

  

  

  

  

  V 
  : 
  

  

  s 
  W 
  

  

  X 
  

  

  k 
  2 
  

   h(i 
  

  

  where 
  

  

  

  

  

  

  

  

  Wis 
  

  

  the 
  

  

  weight 
  of 
  the 
  

  

  mass 
  

  

  broken 
  off 
  

  

  

  

  1 
  Journ. 
  Seismol. 
  Soc, 
  Japan, 
  XVIII, 
  121 
  (1893). 
  

   3 
  Great 
  Neapolitan 
  Earthquake, 
  I. 
  141. 
  

  

  ( 
  349 
  ) 
  

  

  