﻿PREFACE, 
  vVt 
  

  

  backward, 
  movement, 
  if 
  the 
  dividing 
  line 
  is 
  horizontal, 
  and 
  one 
  of 
  upward, 
  and 
  on© 
  

   of 
  downward, 
  movement 
  if 
  the 
  dividing 
  line 
  is 
  vertical. 
  Moreover, 
  by 
  the 
  inter- 
  

   section 
  of 
  these 
  two 
  dividing 
  lines 
  we 
  get 
  four 
  semiphases 
  in 
  which 
  the 
  motion 
  tg 
  

   (i) 
  upward 
  and 
  forward, 
  (2) 
  downward 
  and 
  forward, 
  (3) 
  downward 
  and 
  backward, 
  

   (4) 
  upward 
  and 
  backwards, 
  thus 
  completing 
  the 
  cycle. 
  

  

  8. 
  Waves 
  of 
  the 
  kind 
  now 
  being 
  dealt 
  with 
  are 
  known 
  as 
  gravitational 
  waves, 
  

   as 
  in 
  them 
  the 
  moving 
  force 
  is 
  the 
  attraction 
  of 
  the 
  earth. 
  The 
  water 
  which 
  has 
  

   been 
  raised 
  above 
  its 
  normal 
  level 
  in 
  a 
  wave, 
  is 
  brought 
  back 
  by 
  gravitation 
  and 
  

   communicates 
  the 
  energy 
  so 
  developed 
  to 
  the 
  water 
  in 
  front, 
  by 
  which 
  it 
  is 
  

   raised 
  above 
  its 
  normal 
  level, 
  only 
  to 
  fall 
  back 
  and 
  cause 
  the 
  rise 
  of 
  fresh 
  

   water 
  m 
  front. 
  In 
  other 
  words, 
  it 
  is 
  the 
  weight 
  of 
  the 
  water 
  in 
  a 
  wave 
  which 
  

   causes 
  it 
  to 
  sink, 
  and 
  in 
  doing 
  so 
  to 
  make 
  the 
  water 
  in 
  front 
  rise 
  as 
  the 
  continua- 
  

   tion 
  of 
  the 
  same 
  wave. 
  

  

  9. 
  Elastic 
  waves. 
  — 
  Besides 
  gravitational 
  waves 
  there 
  are 
  other 
  molecular 
  

   movements 
  which, 
  by 
  analogy, 
  are 
  called 
  waves, 
  and, 
  being 
  propagated 
  in 
  virtue 
  of 
  

   the 
  elasticity 
  of 
  the 
  substance 
  through 
  which 
  they 
  travel, 
  are 
  called 
  elastic 
  waves. 
  

  

  The 
  elasticity 
  of 
  a 
  piece 
  of 
  indiarubber 
  or 
  cane 
  is 
  familiar 
  enough; 
  in 
  the 
  

   sense 
  used 
  here 
  it 
  may 
  be 
  defined 
  as 
  the 
  capacity, 
  possessed 
  by 
  all 
  substances 
  to 
  a 
  

   greater 
  or 
  less 
  extent, 
  of 
  recovering 
  their 
  original 
  bulk 
  or 
  shape, 
  if 
  these 
  are 
  

   altered 
  by 
  the 
  action 
  of 
  an 
  external 
  force. 
  It 
  is 
  of 
  two 
  kinds, 
  one, 
  common 
  to 
  both 
  

   solids 
  and 
  fluids, 
  is 
  the 
  power 
  of 
  recovering 
  the 
  original 
  volume, 
  which 
  has 
  been 
  

   altered 
  by 
  change 
  of 
  pressure, 
  when 
  the 
  original 
  pressure 
  is 
  resumed. 
  The 
  measure 
  

   of 
  this 
  is 
  the 
  bulk 
  modulus 
  of 
  the 
  substance. 
  The 
  other 
  kind 
  of 
  elasticity 
  can 
  only 
  

   be 
  possessed 
  by 
  solids, 
  and 
  is 
  the 
  power 
  of 
  recovering 
  the 
  original 
  form, 
  if 
  this 
  is 
  

   changed 
  by 
  the 
  action 
  of 
  an 
  external 
  force, 
  when 
  the 
  force 
  is 
  removed. 
  The 
  

   measure 
  of 
  this 
  is 
  known 
  as 
  the 
  rigidity 
  of 
  the 
  substance. 
  

  

  10. 
  A 
  perfectly 
  elastic 
  substance 
  would 
  completely 
  recover 
  its 
  original 
  bulk 
  and 
  

   form, 
  and 
  in 
  doing 
  so 
  give 
  up 
  exactly 
  the 
  same 
  amount 
  of 
  energy 
  as 
  was 
  absorbed 
  

   in 
  producing 
  the 
  change. 
  So 
  far 
  as 
  bulk 
  is 
  concerned 
  a 
  gas 
  may 
  be 
  regarded 
  

   as 
  a 
  perfectly 
  elastic 
  substance, 
  but 
  no 
  solid 
  can 
  be 
  regarded 
  as 
  such 
  or 
  even 
  nearly 
  

   such, 
  except 
  within 
  comparatively 
  small 
  limits. 
  A 
  bar 
  of 
  iron 
  bent 
  slightly 
  will 
  

   spring 
  back 
  to 
  its 
  original 
  form, 
  but 
  if 
  bent 
  further 
  and 
  strained 
  beyond 
  the 
  limit 
  of 
  

   elasticity 
  will 
  remain 
  bent. 
  So 
  all 
  solids, 
  if 
  strained 
  within 
  their 
  limit 
  of 
  elasticity 
  

   will 
  recover 
  their 
  original 
  form, 
  but 
  if 
  strained 
  beyond 
  that 
  limit 
  will 
  either 
  remain 
  

   permanently 
  bent 
  or 
  break. 
  

  

  11. 
  Within 
  these 
  limits 
  elasticity 
  is 
  measured 
  by 
  the 
  force 
  required 
  to 
  produce 
  

   a 
  given 
  amount 
  of 
  change 
  in 
  bulk 
  or 
  shape. 
  The 
  greater 
  the 
  force 
  that 
  has 
  to 
  be 
  

   applied, 
  the 
  greater 
  that 
  which 
  the 
  substance 
  will 
  exert 
  in 
  regaining 
  its 
  original 
  

   bulk 
  or 
  shape, 
  and 
  the 
  one 
  is 
  equal 
  to 
  the 
  other. 
  Measured 
  in 
  this 
  way 
  the 
  elas- 
  

   ticity 
  of 
  steel 
  or 
  glass 
  is 
  very 
  high, 
  while 
  that 
  of 
  the 
  typical 
  elastic 
  band 
  is 
  very 
  

   small 
  ; 
  for, 
  though 
  the 
  limit 
  of 
  elasticity 
  is 
  much 
  wider, 
  the 
  force 
  required 
  to 
  

   produce 
  a 
  small 
  change 
  of 
  shape 
  is 
  much 
  smaller. 
  

  

  12. 
  Waves 
  0/ 
  elastic 
  compression. 
  — 
  Corresponding 
  to 
  the 
  two 
  kinds 
  of 
  elasticity 
  

   there 
  are 
  two 
  kinds 
  of 
  elastic 
  waves, 
  one 
  of 
  which, 
  depending 
  on 
  the 
  resistance 
  to 
  

   compression, 
  can 
  be 
  propagated 
  in 
  solids 
  and 
  fluids 
  alike. 
  This 
  form, 
  which 
  will 
  

   be 
  considered 
  first, 
  is 
  that 
  of 
  those 
  known 
  as 
  waves 
  of 
  elastic 
  compression 
  or 
  more 
  

   briefly 
  condensational 
  waves. 
  In 
  these 
  the 
  movement 
  of 
  the 
  wave-particle 
  is 
  

  

  