﻿120 
  On 
  the 
  Multiplication 
  of 
  Definite 
  Integrals. 
  [Dec. 
  10, 
  

  

  siderable 
  density, 
  in 
  which 
  the 
  testing-tube 
  has 
  to 
  rotate 
  ; 
  and 
  in 
  cal- 
  

   culating 
  the 
  degree 
  of 
  force 
  which 
  exists 
  in 
  the 
  blood, 
  as 
  shown 
  by 
  the 
  

   rapidity 
  of 
  the 
  movements 
  of 
  the 
  tube 
  under 
  the 
  influence 
  of 
  the 
  magnet, 
  

   allowance 
  must 
  be 
  made 
  for 
  the 
  resistance 
  from 
  this 
  source 
  that 
  has 
  to 
  

   be 
  overcome 
  : 
  consequently 
  any 
  fibrin 
  that 
  has 
  not 
  been 
  removed 
  must, 
  

   in 
  the 
  same 
  degree 
  in 
  which 
  it 
  increases 
  the 
  viscidity 
  and 
  density 
  of 
  the 
  

   fluid, 
  increase 
  the 
  resistance 
  to 
  the 
  movements 
  of 
  the 
  tube, 
  and 
  so 
  inter- 
  

   fere 
  with 
  the 
  manifestation 
  of 
  results. 
  

  

  2nd. 
  By 
  preserving 
  the 
  blood 
  from 
  contact 
  with 
  the 
  atmosphere 
  any 
  

   change 
  in 
  its 
  physical 
  character 
  from 
  such 
  source 
  is 
  prevented. 
  

  

  3rd. 
  And 
  for 
  the 
  reason 
  that 
  the 
  paramagnetic 
  force 
  in 
  arterial 
  blood 
  

   must 
  depend 
  upon 
  the 
  amount 
  of 
  oxygen 
  it 
  contains, 
  and 
  the 
  diamag- 
  

   netic 
  force 
  in 
  venous 
  blood 
  upon 
  carbonic 
  acid, 
  it 
  is 
  evident 
  that 
  the 
  force 
  

   in 
  the 
  testing-tube 
  as 
  opposed 
  to 
  the 
  force 
  in 
  the 
  suspending 
  medium 
  

   must 
  be 
  very 
  little, 
  whilst 
  the 
  mechanical 
  resistance 
  afforded 
  by 
  such 
  

   medium 
  must 
  be 
  considerable. 
  It 
  is 
  therefore 
  essential 
  that 
  the 
  battery- 
  

   force 
  should 
  be 
  of 
  sufficient 
  power 
  to 
  develop 
  these 
  forces 
  to 
  the 
  greatest 
  

   possible 
  extent. 
  

  

  Addendum. 
  

  

  Since 
  writing 
  the 
  foregoing 
  paper, 
  in 
  repeating 
  the 
  experiments, 
  it 
  has 
  

   been 
  found 
  that, 
  for 
  the 
  due 
  performance 
  of 
  them, 
  the 
  blood 
  should 
  be 
  

   maintained 
  as 
  nearly 
  as 
  possible 
  at 
  its 
  natural 
  temperature. 
  To 
  effect 
  

   this 
  the 
  shape 
  of 
  the 
  vessel 
  (Xo. 
  2) 
  has 
  been 
  altered, 
  and 
  it 
  is 
  immersed 
  

   in 
  a 
  water-bath, 
  the 
  heat 
  of 
  which 
  is 
  sustained 
  by 
  a 
  spirit-lamp, 
  its 
  tem- 
  

   perature, 
  and 
  also 
  that 
  of 
  the 
  blood, 
  being 
  regulated 
  by 
  thermometers 
  

   placed 
  in 
  each 
  vessel. 
  

  

  VI. 
  " 
  On 
  the 
  Multiplication 
  of 
  Definite 
  Integrals." 
  

   By 
  W. 
  H. 
  L. 
  Russell, 
  F.R.S. 
  Received 
  October 
  28, 
  1874. 
  

  

  The 
  definite 
  integral 
  f 
  1 
  1 
  l 
  J?dxdy 
  may 
  be 
  considered 
  geometrically 
  

  

  as 
  the 
  integral 
  1 
  P 
  dx 
  dy 
  extended 
  over 
  an 
  area 
  bounded 
  by 
  the 
  straight 
  

   lines 
  whose 
  equations 
  are 
  

  

  *=#i 
  S 
  *=y 
  . 
  y=«* 
  u= 
  x 
  o- 
  

  

  Xow 
  conceive 
  the 
  axes 
  transformed 
  through 
  an 
  angle 
  of 
  45°, 
  so 
  that 
  

  

  o?= 
  — 
  i_ 
  — 
  _ZL_ 
  5 
  y= 
  -f 
  ; 
  then 
  the 
  equations 
  to 
  the 
  four 
  straight 
  

  

  V2 
  V2' 
  V2 
  V2 
  

  

  lines 
  become 
  

  

  J-— 
  71 
  -i, 
  * 
  - 
  71 
  -ii 
  JL+ 
  77 
  -r 
  * 
  4- 
  71 
  —v 
  • 
  

  

  V2 
  72 
  Jv 
  VI 
  V? 
  ** 
  V2 
  71 
  ~ 
  v 
  7! 
  + 
  7! 
  °' 
  

  

  