﻿PREFACE. 
  XIX 
  

  

  of 
  the 
  wave-particle 
  is 
  never 
  the 
  same 
  for 
  two 
  successive 
  instants: 
  it 
  is 
  constantly 
  

   changing, 
  but 
  the 
  rate 
  of 
  change 
  is 
  not 
  constant. 
  Like 
  the 
  velocity, 
  it 
  is 
  nothing 
  

   at 
  one 
  point 
  of 
  the 
  path 
  of 
  the 
  wave-particle, 
  increases 
  to 
  a 
  maximum, 
  and 
  

   then 
  decreases 
  again, 
  being 
  zero 
  when 
  the 
  wave-particle 
  is 
  at 
  rest 
  or 
  at 
  its 
  maxi- 
  

   mum 
  velocity, 
  and 
  attaining 
  a 
  maximum 
  four 
  times 
  in 
  each 
  complete 
  wave 
  period, 
  

   at 
  positions 
  half 
  way 
  between 
  the 
  maximum 
  and 
  zero 
  velocity, 
  which 
  are 
  reached 
  

   twice 
  only 
  in 
  each 
  complete 
  undulation. 
  

  

  58. 
  As 
  it 
  is 
  important 
  that 
  there 
  should 
  be 
  a 
  clear 
  understanding 
  of 
  what 
  is 
  

   meant 
  by 
  acceleration, 
  a 
  brief 
  explanation 
  may 
  not 
  be 
  amiss. 
  Suppose 
  a 
  body, 
  

   such 
  as 
  a 
  railway 
  train, 
  is 
  standing 
  still, 
  and 
  that, 
  by 
  the 
  action 
  of 
  an 
  external 
  

   force, 
  such 
  as 
  a 
  locomotive, 
  it 
  is 
  set 
  in 
  movement, 
  and 
  that 
  at 
  the 
  end 
  of 
  the 
  first 
  

   second 
  it 
  is 
  moving 
  at 
  the 
  rate 
  of 
  one 
  foot 
  per 
  second, 
  at 
  the 
  end 
  of 
  the 
  next 
  second 
  

   at 
  the 
  rate 
  of 
  two 
  feet 
  per 
  second, 
  at 
  the 
  end 
  of 
  the 
  third 
  at 
  the 
  rate 
  of 
  three 
  feet 
  per 
  

   second 
  ; 
  then 
  the 
  acceleration 
  of 
  that 
  train 
  is 
  one 
  foot 
  per 
  second 
  per 
  second. 
  

   That 
  is 
  to 
  say, 
  at 
  the 
  end 
  of 
  each 
  second 
  its 
  velocity 
  is 
  one 
  foot 
  per 
  second 
  greater 
  

   thaaat 
  the 
  beginning. 
  

  

  59. 
  The 
  instance 
  taken 
  is 
  a 
  very 
  simple 
  one, 
  where 
  the 
  acceleration 
  is 
  supposed 
  

   to 
  remain 
  constant 
  for 
  at 
  least 
  three 
  seconds 
  ; 
  in 
  the 
  case 
  of 
  a 
  wave-particle, 
  on 
  the 
  

   other 
  hand, 
  it 
  does 
  not 
  remain 
  constant 
  for 
  two 
  successive 
  instants. 
  Just, 
  however, 
  

   as 
  it 
  is 
  possible 
  to 
  define 
  the 
  velocity 
  at 
  any 
  instant, 
  so 
  the 
  acceleration 
  at 
  any 
  

   instant 
  may 
  be 
  defined 
  as 
  being 
  so 
  many 
  feet, 
  inches 
  or 
  millimetres 
  per 
  second 
  per 
  

   second 
  ; 
  by 
  which 
  it 
  is 
  not 
  meant 
  that 
  the 
  given 
  rate 
  of 
  acceleration 
  is 
  maintained 
  

   for 
  a 
  whole 
  second, 
  or 
  for 
  any 
  finite 
  fraction 
  of 
  a 
  second, 
  but 
  that, 
  if 
  the 
  actual 
  

   rate 
  of 
  change 
  of 
  velocity 
  at 
  the 
  given 
  instant 
  were 
  maintained 
  for 
  a 
  whole 
  second, 
  

   the 
  velocity 
  would 
  at 
  the 
  end 
  of 
  it 
  be 
  so 
  many 
  feet, 
  inches 
  or 
  millimetres 
  per 
  second 
  

   greater 
  than 
  at 
  the 
  commencement. 
  

  

  60. 
  It 
  is 
  important 
  that 
  the 
  distinction 
  between 
  the 
  velocity 
  or 
  rate 
  of 
  move- 
  

   ment, 
  and 
  the 
  acceleration 
  or 
  rate 
  of 
  change 
  of 
  velocity, 
  should 
  be 
  clearly 
  under- 
  

   stood. 
  It 
  is 
  possible 
  to 
  have 
  a 
  high 
  velocity 
  combined 
  with 
  a 
  low 
  acceleration, 
  or 
  

   a 
  low 
  velocity 
  with 
  a 
  high 
  acceleration, 
  the 
  two 
  being 
  quite 
  independent. 
  It 
  may 
  

   also 
  be 
  necessary 
  to 
  state 
  that 
  the 
  word 
  acceleration 
  is, 
  in 
  this 
  connection, 
  equally 
  

   applied 
  to 
  what 
  would 
  ordinarily 
  be 
  regarded 
  as 
  retardation 
  : 
  a 
  body 
  which, 
  

   moving 
  at 
  the 
  rate 
  of 
  10 
  feet 
  per 
  second, 
  slows 
  down 
  at 
  the 
  rate 
  of 
  5 
  feet 
  per 
  

   second 
  per 
  second 
  is 
  said 
  to 
  have 
  that 
  acceleration 
  equally 
  with 
  one 
  that 
  increases 
  

   its 
  speed 
  at 
  that 
  rate. 
  The 
  word 
  is 
  in 
  fact 
  used 
  as 
  equivalent 
  to 
  rate 
  of 
  change 
  

   of 
  velocity, 
  and 
  irrespective 
  of 
  whether 
  the 
  change 
  is 
  one 
  of 
  increase 
  or 
  decrease. 
  

  

  61. 
  As 
  in 
  the 
  case 
  of 
  the 
  velocity 
  of 
  wave-particle, 
  it 
  is 
  only 
  the 
  maximum 
  

   acceleration 
  whose 
  determination 
  is 
  ordinarily 
  necessary 
  or 
  attempted. 
  

  

  62. 
  The 
  intensity 
  of 
  an 
  earthquake.— 
  Besides 
  the 
  elements 
  above 
  mentioned, 
  

   to 
  which 
  numerical 
  values 
  can 
  be 
  given, 
  attempts 
  have 
  been 
  made 
  to 
  define 
  in 
  a 
  

   similar 
  manner 
  a 
  vague 
  and 
  uncertain 
  quantity 
  called 
  the 
  intensity 
  of 
  an 
  earth- 
  

   quake. 
  The 
  best 
  known 
  and 
  most 
  often 
  used 
  of 
  these 
  so-called 
  scales 
  of 
  inten- 
  

   sity 
  is 
  that 
  known 
  as 
  the 
  Rossi-Forel, 
  which, 
  because 
  it 
  is 
  so 
  frequently 
  used 
  and 
  

   because 
  in 
  the 
  absence 
  of 
  anything 
  better 
  it 
  may 
  be 
  better 
  than 
  nothing, 
  is 
  given 
  

   below. 
  Of 
  it, 
  all 
  that 
  may 
  be 
  said 
  at 
  present 
  is 
  that, 
  though 
  to 
  a 
  certain 
  extent 
  

   it 
  may 
  serve 
  for 
  the 
  comparison 
  of 
  different 
  earthquakes, 
  each 
  being 
  taken 
  at 
  its 
  

   maximum 
  intensity, 
  it 
  does 
  not 
  serve 
  as 
  a 
  scale 
  for 
  the 
  gradual 
  dying 
  out 
  of 
  a 
  

  

  