﻿Rotation 
  of 
  Electric 
  Discharge, 
  537 
  

  

  Experimental 
  Determination 
  of 
  the 
  Relation 
  between 
  

   Pressure 
  and 
  Angular 
  Velocity, 
  Sfc. 
  

  

  19. 
  If 
  a 
  magnet- 
  pole 
  of 
  strength 
  m 
  acts 
  on 
  a 
  movable 
  

   and 
  flexible 
  wire 
  carrying 
  current 
  £, 
  the 
  energy 
  of 
  motion 
  

   of 
  such 
  a 
  wire 
  is 
  mi£l, 
  where 
  H 
  is 
  the 
  solid 
  angle 
  subtended 
  

   at 
  the 
  pole 
  by 
  the 
  area 
  described 
  by 
  the 
  wire. 
  

  

  Moreover, 
  if 
  <f> 
  be 
  the 
  angular 
  displacement 
  of 
  the 
  wire 
  

  

  12 
  = 
  (cos 
  1 
  — 
  cos 
  2 
  )<t>i 
  

  

  where 
  X 
  and 
  2 
  are 
  the 
  angles 
  made 
  by 
  the 
  bounding 
  radii 
  

   of 
  the 
  wire, 
  to 
  the 
  pole, 
  with 
  the 
  axis 
  of 
  the 
  magnet. 
  

   .*. 
  the 
  moment 
  of 
  couple 
  acting 
  on 
  the 
  wire 
  

  

  = 
  mi 
  (cos 
  #x 
  — 
  cos 
  2 
  ) 
  . 
  

  

  If, 
  instead 
  of 
  a 
  single 
  pole, 
  we 
  have 
  a 
  distribution 
  of 
  

   magnetism 
  and 
  p 
  is 
  the 
  linear 
  density 
  of 
  magnetism, 
  the 
  

   moment 
  

  

  •= 
  i\p 
  civ 
  (cos 
  1 
  — 
  cos 
  2 
  ) 
  . 
  

  

  In 
  the 
  case 
  of 
  an 
  electromagnet 
  as 
  in 
  fig. 
  1, 
  and 
  a 
  flexible 
  

   wire 
  extending 
  between 
  the 
  electrodes 
  of 
  the 
  discharge-tube 
  

   of 
  fig. 
  1, 
  it 
  is 
  

  

  nearly, 
  

  

  s 
  

  

  — 
  2 
  

  

  (a=the 
  radius 
  of 
  the 
  ring, 
  being 
  small), 
  if 
  m 
  is 
  the 
  total 
  

   magnetic 
  strength 
  and 
  I 
  the 
  length 
  of 
  the 
  iron 
  rod 
  above 
  the 
  

   ring. 
  

  

  Here 
  p 
  has 
  been 
  taken 
  to 
  be 
  constant. 
  This 
  is 
  found 
  to 
  

   be 
  the 
  case, 
  both 
  as 
  the 
  result 
  of 
  theory 
  and 
  experiment 
  

   (" 
  Experimental 
  Determination 
  of 
  Magnetic 
  Induction," 
  Phil. 
  

   Mag. 
  Jan. 
  1908). 
  

  

  20. 
  Assuming 
  that 
  the 
  " 
  band 
  " 
  discharge 
  can 
  be 
  replaced 
  

   by 
  such 
  a 
  wire 
  (and 
  experiments 
  justify 
  the 
  assumption), 
  the 
  

   equation 
  of 
  motion 
  of 
  the 
  discharge 
  will 
  be 
  of 
  the 
  form 
  

  

  Io) 
  = 
  § 
  mi 
  — 
  jtt 
  ( 
  A 
  1 
  + 
  A 
  2 
  )rnds 
  i 
  

  

  where 
  I 
  is 
  the 
  moment 
  of 
  inertia 
  of 
  the 
  discharge 
  about 
  the 
  

   axis 
  of 
  rotation 
  j 
  

  

  ay 
  = 
  angular 
  velocity 
  ; 
  

  

  