﻿70 
  Prof. 
  Barton 
  and 
  Miss 
  Browning 
  on 
  

  

  y 
  and 
  z 
  vibrations 
  are 
  now 
  denoted 
  by 
  rjl 
  and 
  I 
  respectively, 
  

   the 
  droop 
  of 
  each 
  bridle 
  being 
  (31 
  as 
  before. 
  

  

  Then 
  the 
  equations 
  of 
  motion 
  of 
  the 
  pendulums 
  may 
  be 
  

   written 
  at 
  first 
  in 
  the 
  form 
  : 
  

  

  Pg 
  + 
  P<^=0, 
  (54) 
  

  

  qJ 
  + 
  Q^-0, 
  (55) 
  

  

  where 
  6 
  and 
  ^ 
  are 
  the 
  inclinations 
  of 
  the 
  suspensions 
  to 
  the 
  

   vertical. 
  

  

  But 
  we 
  have 
  also 
  

  

  n 
  y 
  — 
  Bl(0 
  , 
  , 
  Z-/3l(0 
  frnx 
  

  

  0=^— 
  and 
  ir= 
  — 
  f—, 
  . 
  . 
  . 
  (56) 
  

  

  where 
  o> 
  is 
  the 
  inclination 
  to 
  the 
  vertical 
  of 
  the 
  planes 
  of 
  

   the 
  bridles. 
  

  

  Neglecting 
  masses 
  of 
  bridles, 
  connector, 
  and 
  suspensions, 
  

   w 
  must 
  satisfy 
  

  

  Q 
  9 
  r(^-«.) 
  = 
  P 
  S 
  r(«-tf) 
  =?g(f-<o). 
  . 
  . 
  (57) 
  

  

  Then 
  (56) 
  in 
  (57) 
  gives 
  

  

  l 
  -wfSh 
  ™ 
  

  

  And 
  (58) 
  in 
  (56) 
  yields 
  

  

  (2 
  + 
  /%-/3.~ 
  (0 
  + 
  2 
  v 
  )z-fy 
  

  

  e 
  -l(0 
  + 
  /3 
  v 
  + 
  2 
  n 
  ) 
  md 
  +-l{0 
  + 
  l3 
  V 
  +2 
  V 
  )- 
  ■ 
  (59) 
  

  

  Then 
  by 
  (59), 
  equations 
  (54) 
  and 
  (55) 
  become 
  

  

  d*z 
  $ 
  + 
  2 
  v 
  3 
  _ 
  /3m 
  2 
  

  

  where 
  m 
  3 
  is 
  written 
  for 
  gjl. 
  

  

  So, 
  for 
  the 
  coupling 
  7, 
  we 
  have 
  

  

  *- 
  v 
  + 
  /w+h> 
  (62) 
  

  

  Hence, 
  for 
  77=1, 
  we 
  recover 
  the 
  original 
  relation 
  

  

  , 
  2+/3 
  , 
  • 
  • 
  • 
  

   which 
  agrees 
  with 
  (32) 
  of 
  the 
  first 
  paper. 
  

  

  (63) 
  

  

  