﻿Coupled 
  Circuits 
  and 
  Mechanical 
  Analogies. 
  203 
  

  

  where 
  N 
  is 
  the 
  total 
  number 
  of 
  molecules 
  in 
  the 
  gas, 
  and 
  a 
  2 
  

   is 
  proportional 
  to 
  the 
  absolute 
  temperature 
  — 
  see 
  §2. 
  If 
  

   one 
  assumes 
  that 
  N 
  does 
  not 
  change 
  with 
  *, 
  then 
  (3) 
  does 
  

   not 
  follow 
  from 
  Wien's 
  assumptions, 
  but 
  instead 
  

  

  <MM) 
  = 
  5^~^ 
  (42) 
  

  

  If 
  (3) 
  be 
  replaced 
  by 
  (42) 
  and 
  the 
  argument 
  given 
  in 
  § 
  1 
  

   be 
  repeated, 
  it 
  will 
  be 
  found 
  that 
  

  

  FW= 
  x 
  i; 
  /M=£; 
  • 
  • 
  • 
  • 
  (») 
  

  

  where 
  A 
  and 
  c 
  are 
  constants. 
  

  

  Moreover 
  (43) 
  is 
  consistent 
  with 
  (40) 
  and 
  (27), 
  and 
  so 
  

   ty 
  iens 
  assumptions 
  lead 
  to 
  the 
  law 
  

  

  £(M) 
  = 
  pU~^- 
  • 
  • 
  • 
  , 
  (44) 
  

  

  Evanston, 
  Illinois, 
  

   July 
  5, 
  1917. 
  

  

  XXII. 
  Coupled 
  Circuits 
  and 
  Mechanical 
  Analogies. 
  By 
  

   E. 
  H. 
  Barton, 
  D.Sc, 
  F.R.S., 
  and 
  H. 
  M. 
  Browning, 
  

   B.Sci 
  

  

  1. 
  A 
  8 
  the 
  valuable 
  "Note 
  on 
  the 
  Action 
  of 
  Coupled 
  

   J\. 
  Circuits 
  and 
  their 
  Mechanical 
  Analogies" 
  by 
  

  

  Prof. 
  H. 
  C. 
  PlummerJ 
  seems 
  in 
  places 
  to 
  imply 
  a 
  slight 
  mis- 
  

   understanding 
  of 
  a 
  previous 
  one 
  dealing 
  with 
  the 
  same 
  

   subject, 
  a 
  brief 
  reply 
  appears 
  desirable. 
  

  

  Prof. 
  Plummer 
  regards 
  the 
  matter 
  chiefly 
  from 
  the 
  

   mathematical 
  standpoint, 
  whereas 
  the 
  authors 
  of 
  the 
  October 
  

   paper§ 
  were 
  concerned 
  chiefly 
  with 
  the 
  physical 
  phenomena 
  

   and 
  their 
  visible 
  representation 
  to 
  average 
  electrical 
  students 
  

   (see 
  pp. 
  246-7). 
  And 
  in 
  some 
  colleges 
  not 
  one 
  per 
  cent, 
  of 
  

   these 
  are 
  masters 
  of 
  the 
  problem 
  mathematically. 
  

  

  2. 
  Prof. 
  Plummer 
  expresses 
  " 
  a 
  doubt 
  whether 
  a 
  simple 
  

   electrical 
  problem 
  really 
  is 
  made 
  easier 
  for 
  the 
  average 
  

   student 
  by 
  a 
  complicated 
  mechanical 
  analogy" 
  (p. 
  510). 
  It 
  

   was 
  never 
  intended 
  that 
  the 
  mathematics 
  of 
  the 
  mechanical 
  

  

  * 
  If 
  N 
  = 
  cr(#), 
  where 
  a 
  is 
  an 
  undetermined 
  function, 
  and 
  if 
  Theorem 
  

   IV. 
  § 
  4 
  be 
  regarded 
  as 
  valid, 
  then 
  it 
  can 
  be 
  proved 
  that 
  <r(#)=a 
  const. 
  

   Wien's 
  implicit 
  assumption 
  is 
  that 
  N 
  = 
  c'0 
  32 
  , 
  where 
  c' 
  is 
  a 
  constant. 
  

  

  t 
  Communicated 
  by 
  the 
  Authors. 
  

  

  t 
  Phil. 
  Mag. 
  pp. 
  510-517, 
  vol. 
  xxxiv., 
  Dec. 
  1917. 
  

  

  § 
  Phil. 
  Mag. 
  pp. 
  246-270, 
  vol. 
  xxxiv., 
  Oct. 
  1917. 
  

  

  