﻿292 
  Mr. 
  H. 
  J. 
  E. 
  Beth 
  on 
  the 
  Oscillations 
  

  

  Fig. 
  7. 
  q 
  = 
  -co 
  . 
  

  

  _ 
  _i 
  

  

  

  \q. 
  Circle 
  £=J. 
  

  

  — 
  J</ 
  < 
  r 
  < 
  0. 
  Two 
  circles 
  with 
  as 
  centre. 
  

  

  r 
  = 
  0. 
  Circle 
  £ 
  = 
  1, 
  isolated 
  point 
  f=0. 
  

  

  Fig. 
  8. 
  -co 
  <</<(). 
  

  

  r=— 
  1(^ 
  — 
  1). 
  Isolated 
  points 
  f=J, 
  sin 
  = 
  0. 
  

  

  — 
  \q<r< 
  —1(^—1). 
  A 
  curve 
  to 
  the 
  right 
  and 
  a 
  curve 
  to 
  

  

  the 
  left 
  o£ 
  0. 
  

   r=— 
  \q. 
  Curve 
  with 
  double 
  points 
  in 
  £ 
  = 
  ^, 
  

   cos 
  = 
  0. 
  

   0<r< 
  —\q. 
  Two 
  curves 
  surrounding 
  0. 
  

  

  r 
  = 
  0. 
  Circle 
  £ 
  = 
  1, 
  isolated 
  point 
  f 
  = 
  0. 
  

  

  Fig. 
  9. 
  = 
  0. 
  

  

  r 
  = 
  ^. 
  Isolated 
  points 
  %=h, 
  sin 
  = 
  0. 
  

   0<r<^. 
  A 
  curve 
  to 
  the 
  right 
  and 
  a 
  curve 
  

   to 
  the 
  left 
  of 
  0. 
  

   r 
  = 
  0. 
  Circle 
  £ 
  = 
  1, 
  isolated 
  point 
  £ 
  = 
  0. 
  

  

  Fig. 
  10. 
  0<q<l. 
  

  

  r=—~\(q 
  — 
  l). 
  Isolated 
  points 
  £=2> 
  sm 
  = 
  0- 
  

   0<r< 
  — 
  -\(q~ 
  1). 
  A 
  curve 
  to 
  the 
  right 
  and 
  a 
  curve 
  

   to 
  the 
  left 
  of 
  0. 
  

   r 
  = 
  0. 
  Two 
  straight 
  lines 
  passing 
  through 
  0. 
  

  

  — 
  4<7<? 
  J 
  <0. 
  A 
  curve 
  below 
  and 
  a 
  curve 
  above 
  O. 
  

  

  r= 
  —\q. 
  Isolated 
  points 
  £=2, 
  cos 
  = 
  0. 
  

  

  Fig. 
  11. 
  0=1. 
  

  

  f 
  = 
  0. 
  Origin 
  of 
  angles, 
  circle 
  f=l. 
  

  

  — 
  J<y«0' 
  <0. 
  A 
  curve 
  below 
  and 
  a 
  curve 
  above 
  O. 
  

  

  r=—\q. 
  Isolated 
  points 
  f=^, 
  cos 
  = 
  0. 
  

  

  Fig. 
  12. 
  l<q<yo. 
  

  

  r 
  = 
  0. 
  Isolated 
  point 
  f=0, 
  circle 
  f=l. 
  

   — 
  1(^ 
  — 
  1) 
  < 
  7'< 
  0. 
  Two 
  curves 
  surrounding 
  0. 
  

  

  r= 
  — 
  1(^—1). 
  Curve 
  with 
  double 
  points 
  in 
  £=J, 
  

   sin 
  = 
  0. 
  

  

  — 
  \q<r< 
  —\(q— 
  1). 
  A 
  curve 
  below 
  and 
  a 
  curve 
  above 
  0. 
  

   \q. 
  Isolated 
  points 
  £=is 
  cos 
  = 
  0. 
  

  

  

  Fig. 
  13. 
  q=co 
  . 
  

  

  The 
  same 
  as 
  for 
  # 
  = 
  — 
  co 
  . 
  

  

  