﻿about 
  a 
  Position 
  of 
  Equilibrium. 
  319 
  

  

  £=—00. 
  r=— 
  \q. 
  The 
  envelope 
  of 
  the 
  system 
  

  

  of 
  ellipses 
  is 
  a 
  square 
  (fig. 
  

   23). 
  

   — 
  iq<r<0. 
  Two 
  systems 
  of 
  ellipses; 
  each 
  

   of 
  them 
  has 
  a 
  rectangle 
  as 
  

   envelope 
  (fig. 
  24). 
  

   r=0. 
  Periodic 
  form 
  of 
  motion 
  ; 
  

   f=0 
  or 
  1 
  continually 
  (fig. 
  

   25). 
  

  

  — 
  ao 
  <q<0. 
  r=—\(q—l). 
  Periodic 
  form 
  of 
  motion; 
  

  

  ?=£, 
  sin 
  <£ 
  = 
  (fig. 
  26). 
  

   — 
  - 
  \q<r< 
  — 
  \{q—l). 
  Two 
  systems 
  of 
  ellipses 
  (fig. 
  

  

  27). 
  

   r= 
  — 
  \q. 
  The 
  envelope 
  consists 
  of 
  two 
  

   squares 
  ; 
  asymptotic 
  form 
  of 
  

   motion 
  (fig. 
  28). 
  

   0<r<— 
  \q. 
  Two 
  systems 
  of 
  ellipses 
  (fig. 
  

   29). 
  

   r 
  = 
  0. 
  Periodic 
  form 
  of 
  motion 
  ; 
  

   f=0 
  or 
  1 
  continually 
  (fig. 
  

   30). 
  

  

  2 
  = 
  0. 
  r 
  = 
  \. 
  Periodic 
  form 
  of 
  motion 
  ; 
  

  

  ?=£, 
  sin 
  = 
  (fig. 
  31). 
  

   < 
  r< 
  J. 
  Two 
  systems 
  of 
  ellipses; 
  each 
  

   of 
  them 
  has 
  a 
  rectangle 
  as 
  

   envelope 
  (fig. 
  32). 
  

   r=0. 
  The 
  envelope 
  of 
  the 
  system 
  

   of 
  ellipses 
  is 
  a 
  square 
  (fig. 
  

   33), 
  

  

  0<<7<1. 
  r— 
  — 
  i($— 
  1). 
  Periodic 
  form 
  of 
  motion; 
  

  

  £=i 
  sin</> 
  = 
  (fig. 
  34). 
  

   0<r< 
  — 
  -J(«7~-l). 
  Two 
  systems 
  of 
  ellipses 
  (fig. 
  

   35 
  ; 
  in 
  fig. 
  35 
  r 
  has 
  a 
  very 
  

   little 
  positive 
  value). 
  

   r=0. 
  Asymptotic 
  form 
  of 
  motion 
  

   (fig. 
  36). 
  

   — 
  \q<r<0. 
  One 
  system 
  of 
  ellipses 
  (fig. 
  

  

  37 
  belongs 
  to 
  a 
  very 
  little 
  

   negative 
  value 
  of 
  r, 
  in 
  fig. 
  

  

  38 
  r 
  is 
  greater, 
  in 
  fig. 
  39 
  

   still 
  greater). 
  

  

  r= 
  — 
  \q. 
  Periodic 
  form 
  of 
  motion 
  in 
  a 
  

   circle 
  ; 
  ?=J, 
  cos<£ 
  = 
  (fig. 
  

   40). 
  

  

  