﻿-202 
  

  

  Mr. 
  James 
  Walker 
  on 
  

  

  The 
  ratio 
  o£ 
  the 
  axes 
  of 
  the 
  elliptic 
  vibrations 
  may 
  be 
  

   easily 
  determined 
  from 
  the 
  formula 
  

  

  tan2 
  7= 
  tan 
  (u-^O) 
  tan 
  (a 
  + 
  R-6') 
  

  

  which 
  in 
  this 
  case 
  reduces 
  to 
  the 
  simple 
  form 
  

  

  tan 
  7 
  = 
  ± 
  tan 
  (6 
  + 
  a) 
  tan 
  (6 
  — 
  a), 
  

  

  the 
  sign 
  to 
  be 
  attributed 
  to 
  tan 
  7 
  being 
  determined 
  from 
  that 
  

   of 
  sin 
  27. 
  

  

  The 
  following 
  table 
  gives 
  the 
  principal 
  changes 
  relating 
  to 
  

   this 
  case. 
  

  

  Table 
  III.— 
  cos^ 
  2a 
  = 
  tan^ 
  2/3. 
  

   < 
  a 
  < 
  7r/4. 
  

  

  

  tanE. 
  

  

  tan 
  2(0 
  -a). 
  

  

  e. 
  

  

  tan 
  y. 
  

  

  1. 
  

  

  

  

  

  

  a 
  

  

  

  

  2. 
  

  

  cot 
  2a 
  

  

  cot 
  2a 
  

  

  TT 
  

  

  4 
  

  

  1 
  

  

  3. 
  

  

  -cot 
  2a 
  

  

  00 
  

  

  TT 
  

  

  tan(|+2a) 
  

  

  4- 
  

  

  -tan 
  2a 
  

  

  — 
  tan 
  4a 
  

  

  TT 
  

  

  "2~" 
  

  

  00 
  

  

  5. 
  

  

  sin 
  2rt 
  cos 
  2a 
  

   l 
  + 
  cos^2a 
  

  

  — 
  tan 
  2a 
  

  

  TT 
  

  

  — 
  cot2a 
  

  

  6. 
  

  

  

  

  

  

  TT 
  

  

  2+« 
  

  

  CO 
  

  

  

  

  7r/4 
  < 
  a 
  < 
  

  

  7r/2. 
  

  

  

  

  tanR. 
  

  

  tan 
  2(0 
  -a) 
  

  

  e. 
  

  

  tan 
  y. 
  

  

  1. 
  

  

  

  

  

  

  a 
  

  

  4 
  

  

  2. 
  

  

  sin 
  2a 
  cos 
  2a 
  

   r+^os2 
  2a" 
  

  

  -tan 
  2a 
  

  

  TT 
  

  

  cot^a 
  

  

  3. 
  

  

  - 
  tan 
  2a 
  

  

  —tan 
  4a 
  

  

  Tt 
  — 
  a 
  

  

  

  

  4. 
  

  

  — 
  cot 
  2a 
  

  

  00 
  

  

  i+" 
  

  

  -tan(- 
  + 
  2a) 
  

  

  5. 
  

  

  cot 
  2a 
  

  

  cot 
  2a 
  

  

  4 
  

  

  -1 
  

  

  G. 
  

  

  

  

  

  

  -;+" 
  

  

  — 
  CO 
  

  

  