﻿350 
  OLDHAM: 
  GREAT 
  EARTHQUAKE 
  OF 
  1 
  897. 
  

  

  h. 
  The 
  perpendicular 
  height 
  of 
  the 
  centre 
  of 
  gravity 
  above 
  the 
  base 
  of 
  fracture. 
  

  

  F 
  The 
  coefficient 
  of 
  dynamic 
  cohesion, 
  or 
  the 
  force 
  upon 
  the 
  unit 
  of 
  surface 
  

   of 
  the 
  material 
  fractured, 
  which, 
  when 
  suddenly 
  applied, 
  is 
  sufficient 
  to 
  

   produce 
  fracture. 
  

  

  A. 
  The 
  area 
  of 
  the 
  fracture 
  in 
  such 
  units. 
  

  

  k. 
  The 
  radius 
  of 
  gyration 
  of 
  the 
  plane 
  of 
  fracture 
  round 
  the 
  edge. 
  

  

  fi 
  The 
  width 
  of 
  the 
  fractured 
  surface. 
  

  

  In 
  practice 
  the 
  value 
  of 
  F 
  cannot 
  be 
  directly 
  determined, 
  but 
  as 
  it 
  is 
  taken 
  as 
  

   half 
  of 
  the 
  breaking 
  strain 
  under 
  a 
  load 
  gradually 
  applied, 
  which 
  may 
  be 
  

   represented 
  by 
  F, 
  the 
  formula 
  becomes 
  

  

  s, 
  FA 
  k 
  * 
  

  

  V 
  = 
  gX 
  VW 
  X 
  hJ 
  

  

  or 
  substituting 
  2 
  x 
  for 
  fi 
  and_y 
  for 
  h 
  to 
  bring 
  the 
  symbols 
  into 
  uniformity 
  .with 
  

  

  previous 
  formulae 
  

  

  F 
  A 
  

   V=g 
  X 
  V 
  * 
  A 
  X 
  k 
  2 
  

  

  or, 
  since 
  

  

  W 
  = 
  2 
  y 
  A 
  w 
  

  

  where 
  v> 
  is 
  the 
  weight 
  per 
  unit 
  volume, 
  

  

  V 
  = 
  g 
  x 
  -= 
  ~ 
  x 
  k 
  2 
  

  

  8 
  to 
  %,y* 
  

  

  L 
  L2 
  

  

  = 
  g 
  SVy-> 
  Xk 
  

  

  Where 
  L 
  is 
  the 
  modulus 
  of 
  cohesion, 
  or 
  length 
  of 
  a 
  column 
  whose 
  weight 
  is 
  

   just 
  sufficient 
  to 
  cause 
  fracture, 
  

  

  It 
  must 
  be 
  noticed 
  that 
  this 
  V 
  is 
  not 
  v 
  or 
  the 
  maximum 
  velocity 
  of 
  wave- 
  

   particle, 
  but 
  the 
  velocity 
  which 
  if 
  suddenly 
  applied 
  would 
  cause 
  fracture, 
  or, 
  

   in 
  other 
  words 
  the 
  acceleration, 
  hence 
  we 
  may 
  write 
  the 
  formula 
  

  

  FA 
  , 
  s 
  F 
  Z 
  

  

  f 
  ~ 
  ^Wyx 
  g 
  8nxy 
  2 
  ~~ 
  g 
  Wx~y~i 
  

  

  For 
  a 
  wall 
  or 
  rectangular 
  column 
  

  

  *» 
  = 
  £L 
  == 
  4 
  * 
  2 
  

  

  3 
  3 
  

  

  hence 
  

  

  r 
  F 
  A 
  x 
  F 
  x 
  L 
  x 
  

  

  f 
  = 
  g 
  JWy 
  =s 
  T^? 
  =*6f 
  < 
  1Vl 
  > 
  

  

  For 
  a 
  solid 
  cylinder 
  

  

  hence 
  

  

  ( 
  350 
  ) 
  

  

  k 
  2 
  = 
  -^ 
  /3 
  2 
  = 
  -1 
  x 
  2 
  

   16 
  4 
  

  

  f= 
  „5^Ax 
  tj^ 
  = 
  SJl? 
  (lV2) 
  

  

  ' 
  g 
  i6Wy 
  g 
  32 
  to/ 
  g 
  32y> 
  {L 
  V 
  2) 
  

  

  