﻿of 
  comparing 
  the 
  Self-Inductance 
  of 
  a 
  Coil. 
  43.^ 
  

  

  discharge 
  of 
  the 
  condenser 
  was 
  non-oscillatory. 
  In 
  the 
  June 
  

   number 
  of 
  this 
  Magazine 
  Mr. 
  E. 
  C. 
  Snow 
  * 
  completed 
  the 
  

   examination 
  by 
  dealing 
  with 
  the 
  oscillatory 
  case. 
  

  

  In 
  treating 
  the 
  problem 
  Messrs. 
  Silva 
  and 
  Snow 
  write 
  

   down 
  the 
  Kirchhoff 
  equations 
  for 
  the 
  currents 
  in 
  each 
  branch 
  

   of 
  the 
  resistance-bridge, 
  and 
  from 
  them 
  deduce 
  a 
  differential 
  

   equation 
  of 
  the 
  third 
  order 
  for 
  the 
  current 
  through 
  the 
  

   galvanometer. 
  This 
  equation 
  they 
  solve 
  and 
  find 
  the 
  quantity 
  

   of 
  electricity 
  discharged 
  through 
  the 
  galvanometer 
  by 
  in- 
  

   tegrating 
  the 
  expression 
  for 
  the 
  current 
  as 
  a 
  function 
  of 
  the 
  

   time 
  betw^een 
  the 
  limits 
  and 
  oo 
  . 
  On 
  equating 
  this 
  quantity 
  

   to 
  zero, 
  there 
  results 
  the 
  well-known 
  equation 
  for 
  the 
  method 
  

   L 
  = 
  K?'^. 
  The 
  investigations 
  are 
  therefore 
  very 
  detailed, 
  and 
  if 
  

   the 
  object 
  were 
  to 
  determine, 
  for 
  example, 
  the 
  time 
  which 
  must 
  

   elapse 
  before 
  the 
  quantity 
  of 
  electricity 
  which 
  has 
  passed 
  

   through 
  the 
  galvanometer 
  amounts 
  to 
  say 
  '999 
  of 
  its 
  final 
  

   value 
  (a 
  question 
  which 
  might 
  arise 
  in 
  connexion 
  with 
  the 
  

   condition 
  that 
  the 
  discharge 
  must 
  have 
  passed 
  through 
  the 
  

   galvanometer 
  before 
  its 
  moving 
  part 
  has 
  moved 
  appreciably) 
  

   such 
  detail 
  would 
  be 
  unavoidable. 
  But 
  if 
  we 
  start, 
  as 
  do 
  

   Messrs. 
  Silva 
  and 
  Snow, 
  with 
  the 
  assumptions 
  that 
  the 
  

   galvanometer 
  satisfies 
  the 
  above 
  condition, 
  and 
  that 
  the 
  

   needle 
  starts 
  from 
  a 
  symmetrical 
  position 
  t, 
  the 
  investigation 
  

   may 
  be 
  simplified 
  considerably. 
  

  

  The 
  method 
  of 
  using 
  the 
  Electro-Kinetic 
  Energy 
  and 
  

   Rayleigh^s 
  Dissipation 
  Function 
  % 
  for 
  the 
  treatment 
  of 
  

   problems 
  of 
  this 
  kind, 
  first 
  introduced 
  by 
  Maxwell 
  §, 
  and 
  

   extended 
  by 
  Fleming 
  || 
  and 
  Niven 
  If, 
  has 
  proved 
  so 
  powerful,, 
  

   and 
  it 
  is 
  so 
  much 
  in 
  keeping 
  with 
  modern 
  dynamical 
  

   methods 
  ** 
  that 
  a 
  brief 
  statement 
  of 
  it 
  may 
  not 
  be 
  out 
  of 
  

   place 
  here. 
  

  

  If 
  a 
  netv/ork 
  of 
  conductors 
  consist 
  of 
  branches 
  having 
  

   resistances 
  Ri, 
  R25 
  ^s? 
  &c., 
  self-inductances 
  Lj, 
  L2, 
  L3, 
  &c., 
  

   mutual 
  inductances 
  Mio, 
  M23, 
  M34, 
  &c., 
  and 
  capacities 
  Kj, 
  K2, 
  

   K3, 
  &c., 
  and 
  if 
  the 
  quantities 
  of 
  electricity 
  which 
  have 
  

   flowed 
  through 
  the 
  various 
  branches 
  up 
  to 
  a 
  given 
  time 
  t 
  are 
  

  

  * 
  E. 
  C. 
  Snow, 
  Phil. 
  Mag. 
  vol. 
  xvii. 
  p. 
  849 
  (1909). 
  

  

  t 
  See 
  Russell, 
  Phil. 
  Mag. 
  vol. 
  xii. 
  p. 
  202 
  (1906). 
  

  

  X 
  Lord 
  Rayleigh, 
  Proc. 
  Lond. 
  Math. 
  Soc. 
  iv. 
  p. 
  357 
  (1873), 
  aud 
  

   Scientific 
  Papers, 
  i. 
  p. 
  176. 
  

  

  § 
  Clerk 
  Maxwell, 
  'Electricity 
  and 
  Magnetism,' 
  2nd 
  edit. 
  vol. 
  ii. 
  p. 
  365 
  

   (1881). 
  

  

  II 
  J. 
  A. 
  Fleming, 
  Phil. 
  Mag. 
  vol. 
  xx. 
  p. 
  242 
  (1885). 
  

  

  % 
  J. 
  C. 
  Niven, 
  Phil. 
  Mag. 
  vol. 
  xxiv. 
  p. 
  225 
  (1887). 
  

  

  ** 
  See 
  E. 
  T. 
  Whittaker, 
  'Analytical 
  Dynamics,' 
  pp. 
  226, 
  228 
  (1904). 
  

  

  