﻿204 
  Prof. 
  Barton 
  and 
  Miss 
  Browning 
  on 
  

  

  analogy 
  should 
  explain 
  or 
  render 
  easier 
  that 
  of 
  the 
  electrical 
  

   case. 
  In 
  its 
  mathematical 
  aspect 
  the 
  electrical 
  case 
  is 
  prob- 
  

   ably 
  simpler 
  than 
  that 
  o£ 
  any 
  mechanical 
  model 
  yet 
  put 
  

   forward. 
  

  

  The 
  utility 
  of 
  the 
  mechanical 
  analogies 
  given 
  in 
  the 
  

   October 
  paper 
  lies 
  in 
  their 
  power 
  to 
  give 
  with 
  such 
  simple 
  

   apparatus 
  actual 
  traces 
  of 
  the 
  vibrations 
  in 
  question, 
  and 
  

   that 
  under 
  the 
  most 
  various 
  conditions 
  as 
  to 
  masses 
  of 
  bobs, 
  

   lengths 
  of 
  the 
  separate 
  pendulums, 
  and 
  looseness 
  or 
  closeness 
  

   of 
  their 
  coupling. 
  And 
  these 
  advantages 
  can 
  be 
  reaped 
  by 
  

   students 
  who 
  are 
  too 
  weak 
  to 
  assimilate 
  the 
  mathematics 
  

   either 
  of 
  the 
  original 
  problem 
  or 
  its 
  analogies, 
  though 
  for 
  

   completeness' 
  sake 
  the 
  equations 
  of 
  both 
  were 
  naturally 
  

   included 
  in 
  the 
  paper. 
  

  

  There 
  is 
  also 
  another 
  aspect 
  of 
  the 
  matter. 
  For 
  it 
  may 
  

   be 
  hoped 
  that 
  the 
  study 
  of 
  these 
  mechanical 
  models 
  may 
  

   throw 
  some 
  light 
  on 
  the 
  hidden 
  mechanism 
  of 
  the 
  electro- 
  

   magnetic 
  phenomena. 
  

  

  3. 
  Equations 
  (27) 
  and 
  (28) 
  of 
  the 
  October 
  paper 
  for 
  the 
  

   double-cord 
  pendulum 
  were 
  in 
  the 
  form 
  

  

  d 
  2 
  y 
  P 
  + 
  Q+/3Q 
  v 
  g 
  13 
  PQ 
  g 
  1 
  

   r 
  dt> 
  + 
  (l 
  + 
  /3)(P 
  + 
  Q) 
  r 
  / 
  ?/ 
  ~ 
  i-f/tp 
  + 
  q: 
  I 
  >\ 
  

  

  d 
  2 
  z 
  P-J-/3P 
  + 
  Q 
  g_ 
  £_ 
  PQ 
  9 
  I 
  " 
  (1) 
  

  

  H 
  dt 
  2 
  + 
  (l 
  + 
  i3)(F 
  + 
  Q) 
  H 
  r~ 
  l 
  + 
  Z^P 
  + 
  QT^j 
  

  

  Prof. 
  Plummer 
  prefers 
  the 
  form 
  

  

  dt 
  2 
  ' 
  v 
  ™* 
  J 
  ™dt> 
  

  

  (P 
  + 
  Q+/8Q)g+(P4Q)^- 
  1 
  2=-/9pJ 
  ; 
  J 
  

  

  (2) 
  

  

  and 
  adds 
  "the 
  analogy 
  is 
  now 
  exact." 
  Is 
  not 
  this 
  too 
  much 
  

   to 
  claim 
  ? 
  As 
  to 
  the 
  occurrence 
  of 
  the 
  variables 
  and 
  their 
  

   derivatives 
  the 
  equations 
  (2) 
  do 
  indeed 
  present 
  a 
  formal 
  

   agreement 
  with 
  those 
  for 
  the 
  electrical 
  circuits, 
  viz., 
  

  

  u 
  dt 
  2 
  + 
  R- 
  M 
  ^ 
  2 
  ' 
  

   ^d 
  2 
  z 
  z 
  ^d 
  2 
  y 
  

  

  (3) 
  

  

  Hence 
  in 
  a 
  certain 
  restricted 
  mathematical 
  sense 
  the 
  analogy 
  

   is 
  exact. 
  But 
  this 
  exactness 
  of 
  analogy 
  does 
  not 
  extend 
  to 
  

  

  