﻿644 
  Prof. 
  S. 
  B. 
  McLaren 
  on 
  a 
  

  

  Let 
  dr 
  be 
  an 
  element 
  of 
  length 
  moving 
  with 
  the 
  fluid 
  

  

  ^ 
  (/>u 
  di) 
  = 
  ^7 
  (p\L)dY 
  + 
  pu 
  du, 
  

  

  -jp 
  (pu 
  dx) 
  = 
  —c 
  2 
  dp 
  -f 
  ud 
  (pu) 
  + 
  pu 
  du 
  (by 
  8) 
  . 
  

  

  So 
  ^ 
  r 
  (pudr)=d(pu>-p 
  C 
  *) 
  (9) 
  

  

  And 
  if 
  the 
  integral 
  be 
  taken 
  round 
  any 
  closed 
  curve 
  

  

  Thus 
  if 
  the 
  integral 
  expression 
  

  

  J 
  pudr 
  

  

  is 
  initially 
  zero 
  round 
  all 
  closed 
  circuits,, 
  it 
  remains 
  per- 
  

   manently 
  zero. 
  In 
  that 
  case 
  

  

  Curl 
  /on 
  = 
  

  

  • 
  (10) 
  

  

  But 
  (8) 
  may 
  also 
  be 
  written 
  

  

  

  j 
  t 
  (pu) 
  + 
  c 
  2 
  Vp 
  - 
  [n 
  Curl 
  pu] 
  = 
  0. 
  . 
  

  

  • 
  (11) 
  

  

  In 
  case 
  (10) 
  holds 
  (11) 
  becomes 
  

  

  

  |(pu) 
  + 
  cVp=0 
  

  

  • 
  (12) 
  

  

  And 
  (10) 
  and 
  (12) 
  are 
  then 
  equivalent 
  to 
  

  

  

  W7- 
  dJ 
  

  

  • 
  (13) 
  

  

  With 
  the 
  equation 
  (4) 
  of 
  continuity 
  (13) 
  gives 
  

  

  

  (vs-i^y-o, 
  . 
  . 
  . 
  

  

  • 
  (W) 
  

  

  and 
  (13) 
  may 
  also 
  be 
  written 
  

  

  ^(pudr—pcdct) 
  = 
  (15) 
  

  

  Any 
  disturbance 
  in 
  the 
  motion 
  will 
  according 
  to 
  (14) 
  be 
  

   propagated 
  with 
  the 
  velocity 
  of 
  light. 
  

  

  