﻿36 
  Mr. 
  A. 
  H. 
  Gibson 
  on 
  the 
  Steady 
  Floio 
  of 
  an 
  

  

  where 
  yu. 
  is 
  the 
  coefficient 
  of 
  viscosity 
  ; 
  -cr 
  is 
  the 
  weight 
  o£ 
  

   unit 
  volume 
  ; 
  u, 
  v, 
  and 
  w 
  are 
  the 
  velocities 
  of 
  flow 
  in 
  

   directions 
  ^, 
  y, 
  and 
  z 
  respectively 
  ; 
  and 
  p 
  is 
  the 
  pressure 
  

   (reckoned 
  positive 
  if 
  compressive). 
  

  

  Assuming 
  that 
  in 
  a 
  circular 
  tube 
  with 
  uniformly 
  converging 
  

   boundaries 
  motion 
  takes 
  place 
  in 
  uniformly 
  converging 
  lines, 
  

   so 
  that 
  the 
  pressure 
  is 
  uniform 
  at 
  all 
  points 
  on 
  a 
  spherical 
  

   shell 
  having 
  the 
  point 
  of 
  convergence 
  as 
  centre, 
  we 
  have 
  

  

  ^ 
  = 
  0; 
  «. 
  = 
  0; 
  ^ 
  = 
  0; 
  J^ 
  = 
  ; 
  

  

  ay 
  dz 
  

  

  while 
  if 
  the 
  motion 
  is 
  steady 
  ^ 
  = 
  0, 
  so 
  that 
  in 
  the 
  latter 
  

  

  case 
  the 
  state 
  o£ 
  flux 
  along 
  the 
  tube 
  is 
  represented 
  by 
  the 
  

   single 
  equation 
  

  

  If 
  r 
  be 
  the 
  distance 
  of 
  a 
  particle 
  from 
  the 
  centre 
  of 
  the 
  

   tube 
  at 
  a 
  point 
  distant 
  ^ 
  from 
  the 
  point 
  of 
  convergence 
  

  

  and 
  the 
  equation 
  of 
  motion 
  becomes 
  

  

  while 
  if 
  the 
  angle 
  of 
  convergence 
  of 
  the 
  sides 
  is 
  small, 
  so 
  

  

  

  by^ 
  dy 
  \dy> 
  

  

  Similarly 
  

  

  _ 
  y^ 
  S^^* 
  , 
  d^* 
  r^ 
  — 
  y" 
  

  

  

  r2-02 
  

  

  ■ 
  r^ 
  

  

  