﻿Steady 
  Flow 
  of 
  an 
  Incompressible 
  Viscous 
  Fluid. 
  35 
  

  

  A 
  fair 
  estimate 
  of 
  the 
  actual 
  increase 
  of 
  the 
  earth's 
  tem- 
  

   perature 
  due 
  to 
  " 
  trapping 
  ^^ 
  has 
  been 
  made. 
  Imagine 
  a 
  

   perfectly 
  " 
  black 
  '' 
  and 
  rapidly 
  rotating 
  planet 
  of 
  the 
  earth's 
  

   dimensions, 
  situated 
  beyond 
  the 
  orbit 
  of 
  the 
  earth 
  at 
  such 
  a 
  

   distance 
  from 
  ihe 
  sun 
  that 
  the 
  radiation 
  absorbed 
  by 
  it 
  would 
  

   be 
  equal 
  to 
  that 
  available 
  to 
  be 
  absorbed 
  by 
  the 
  earth, 
  allowinor 
  

   for 
  the 
  reflexion 
  of 
  clouds, 
  et 
  cetera. 
  Such 
  a 
  planet 
  would 
  

   assume 
  the 
  temperature 
  of 
  — 
  17° 
  C, 
  whereas 
  the 
  real 
  earth 
  

   has 
  a 
  mean 
  temperature 
  of 
  +14° 
  C. 
  * 
  The 
  difference, 
  

   31° 
  C, 
  is 
  attributable 
  to 
  three 
  causes 
  : 
  — 
  (1) 
  The 
  imperfect 
  

   "blackness'' 
  of 
  the 
  earth. 
  (2) 
  The 
  "blanket 
  effect 
  '' 
  of 
  the 
  

   atmosphere. 
  (3) 
  The 
  warming 
  of 
  the 
  earth's 
  surface 
  by 
  

   radio-active 
  substances 
  and 
  internal 
  heat. 
  Remembering 
  

   that 
  the 
  earth 
  is 
  mainly 
  water 
  covered, 
  it 
  must 
  be 
  almost 
  

   " 
  perfectly 
  black 
  " 
  for 
  long-wave 
  rays. 
  I 
  myself 
  regard 
  the 
  

   comhiction 
  of 
  internal 
  heat 
  and 
  that 
  of 
  radio-active 
  substances 
  

   as 
  negligible. 
  This 
  would 
  leave 
  the 
  full 
  31° 
  as 
  due 
  to 
  the 
  

   " 
  blanket 
  efft^ct." 
  

  

  If 
  there 
  were 
  no 
  water 
  on 
  the 
  earth, 
  the 
  emissive 
  power 
  of 
  

   its 
  surface 
  for 
  long-wave 
  rays 
  would 
  be 
  less. 
  Also, 
  on 
  

   account 
  of 
  the 
  absence 
  of 
  clouds, 
  its 
  absorption 
  of 
  solar 
  rays 
  

   would 
  be 
  greater. 
  The 
  two 
  differences 
  vvould 
  perhaps 
  more 
  

   than 
  counterbalance 
  the 
  loss 
  of 
  tlie 
  " 
  blanketing 
  effect," 
  so 
  

   that 
  the 
  mean 
  temperature 
  of 
  the 
  earth 
  without 
  water 
  would 
  

   perhaps 
  be 
  rather 
  higher 
  than 
  now, 
  but 
  much 
  less 
  uniform, 
  

   ranging 
  from 
  above 
  present 
  temperatures 
  by 
  day 
  to 
  far 
  below 
  

   0° 
  C. 
  by 
  night. 
  

  

  YI. 
  On 
  the 
  Steady 
  Flow 
  of 
  an 
  Incompressible 
  Viscous 
  Fluid 
  

   through 
  a 
  Circular 
  Tube 
  with 
  (j)Liformltj 
  Converging 
  

   Boundaries. 
  By 
  A. 
  H. 
  Gibson, 
  M.Sct 
  Lecturer 
  in 
  

   Ilgdraulics 
  in 
  the 
  Mancliester 
  University 
  '\ 
  . 
  

  

  rpHE 
  general 
  equations 
  of 
  motion 
  for 
  the 
  three-dimensional 
  

   J- 
  flow 
  of 
  an 
  incompressible 
  viscous 
  fluid 
  are 
  % 
  : 
  — 
  

  

  dp 
  ^"d-it 
  l)'!' 
  ^2?^ 
  13- 
  r 
  "^u 
  B// 
  "dii 
  "duX 
  

  

  -Zc 
  =-^ 
  \^? 
  + 
  s? 
  + 
  -b?] 
  + 
  y 
  V'§i. 
  +^- 
  bi; 
  +'"Bi 
  + 
  9< 
  / 
  

  

  -rf^ 
  =-'^ 
  15? 
  + 
  5? 
  + 
  -S?^I 
  + 
  ^ 
  i 
  "B.. 
  +''b^-*-'^9l-*- 
  BFJ 
  

  

  * 
  Annals, 
  Astrophysical 
  Ob 
  ervatory, 
  vol. 
  ii. 
  p. 
  175. 
  

   t 
  Communicated 
  by 
  the 
  Authin'. 
  

   X 
  ' 
  Hvdraulicf," 
  Gibaun, 
  p. 
  Do. 
  

  

  D 
  2 
  

  

  