﻿106 
  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  M. 
  Lame's 
  equations 
  differ 
  from 
  these 
  only 
  in 
  assuming 
  that 
  /jl 
  = 
  ^m. 
  If 
  this 
  

  

  assumption 
  be 
  correct, 
  then 
  the 
  coefficients 
  /m, 
  m, 
  and 
  /x„ 
  may 
  be 
  found 
  from 
  two 
  

   of 
  these 
  equations 
  ; 
  but 
  since 
  one 
  of 
  these 
  equations 
  may 
  be 
  derived 
  from 
  the 
  other 
  

   two, 
  the 
  three 
  coefficients 
  cannot 
  be 
  found 
  when 
  jx 
  is 
  supposed 
  independent 
  of 
  m. 
  

   In 
  Equations 
  (39.), 
  the 
  quantities 
  which 
  may 
  be 
  varied 
  at 
  pleasure 
  are 
  h 
  l 
  and 
  h 
  2 
  , 
  

   and 
  the 
  quantities 
  which 
  may 
  be 
  deduced 
  from 
  the 
  apparent 
  compressions 
  are, 
  

  

  ?1 
  \fx 
  + 
  2 
  m) 
  an 
  \fx 
  nj 
  

  

  jJ- 
  /V 
  2 
  

  

  therefore 
  some 
  independent 
  equation 
  between 
  these 
  quantities 
  must 
  be 
  found, 
  and 
  

   this 
  cannot 
  be 
  done 
  by 
  means 
  of 
  the 
  sphere 
  alone 
  ; 
  some 
  other 
  experiment 
  must 
  

   be 
  made 
  on 
  the 
  liquid, 
  or 
  on 
  another 
  portion 
  of 
  the 
  substance 
  of 
  which 
  the 
  vessel 
  

   is 
  made. 
  

  

  The 
  value 
  of 
  /x 
  2 
  , 
  the 
  elasticity 
  of 
  the 
  liquid, 
  may 
  be 
  previously 
  known. 
  

  

  The 
  linear 
  elasticity 
  m 
  of 
  the 
  vessel 
  may 
  be 
  found 
  by 
  twisting 
  a 
  rod 
  of 
  the 
  

   material 
  of 
  which 
  it 
  is 
  made 
  ; 
  

  

  Or, 
  the 
  value 
  of 
  E 
  may 
  be 
  found 
  by 
  the 
  elongation 
  or 
  bending 
  of 
  the 
  rod, 
  and 
  

   112 
  

   E 
  ~ 
  9 
  jj. 
  + 
  3 
  m 
  

  

  We 
  have 
  here 
  five 
  quantities, 
  which 
  may 
  be 
  determined 
  by 
  experiment. 
  

   (43.) 
  1. 
  c 
  x 
  = 
  ( 
  — 
  + 
  o~~) 
  D 
  y 
  ex 
  t 
  erna 
  l 
  pressure 
  

   (42.) 
  2. 
  c.,= 
  ( 
  J 
  equal 
  pressures 
  

  

  (31.) 
  3. 
  -^ 
  = 
  (<j£+§-) 
  b 
  y 
  elongation 
  of 
  a 
  rod. 
  

  

  (17.) 
  4. 
  m 
  by 
  twisting 
  the 
  rod. 
  

  

  5. 
  fj.. 
  2 
  the 
  elasticity 
  of 
  the 
  liquid. 
  

  

  When 
  the 
  elastic 
  sphere 
  is 
  solid, 
  the 
  internal 
  radius 
  a 
  x 
  vanishes, 
  and 
  h 
  2 
  =p 
  = 
  q, 
  

   , 
  8 
  V 
  K 
  

   and 
  ^r 
  = 
  7T 
  

  

  When 
  the 
  case 
  becomes 
  that 
  of 
  a 
  spherical 
  cavity 
  in 
  an 
  infinite 
  solid, 
  the 
  ex- 
  

   ternal 
  radius 
  a, 
  becomes 
  infinite, 
  and 
  

  

  on 
  sphere. 
  

  

  p= 
  

  

  -K 
  

  

  

  (h 
  x 
  -h 
  

  

  i) 
  

  

  

  

  q- 
  

  

  -K 
  

  

  l 
  

  

  2 
  

  

  ?HV 
  

  

  -h) 
  

  

  

  

  r 
  

  

  --\ 
  

  

  1 
  

   3// 
  

  

  1 
  a, 
  3 
  

  

  2 
  r 
  3 
  

  

  ih~ 
  

  

  K) 
  

  

  m 
  

  

  8y 
  

  

  

  1 
  

   2 
  

  

  h 
  x 
  — 
  h 
  2 
  

   m 
  

  

  

  

  ) 
  

  

  (46.) 
  

  

  

  