﻿434 
  Prof. 
  C. 
  H. 
  Lees 
  on 
  Vascliy's 
  or 
  PiranVs 
  Method 
  

  

  ci'i, 
  X2, 
  -%, 
  &c., 
  respectively, 
  then 
  if 
  we 
  write 
  down 
  the 
  Electro- 
  

   kinetic 
  Energy 
  

  

  T 
  = 
  XiWi;2 
  + 
  2M„M„,urA,, 
  . 
  . 
  . 
  (1) 
  

  

  the 
  Dissipation 
  Function 
  

  

  D 
  = 
  XiR.^^, 
  (2) 
  

  

  and 
  the 
  Electrostatic 
  Energy 
  

  

  V 
  = 
  Xi|^, 
  (3) 
  

  

  the 
  equations 
  for 
  the 
  flow 
  of 
  electricity 
  through 
  the 
  various 
  

   branches 
  of 
  the 
  network 
  may 
  be 
  written 
  in 
  the 
  form 
  : 
  

  

  l/^\ 
  + 
  ^+^=0 
  (4) 
  

  

  In 
  this 
  equation 
  there 
  is 
  no 
  reference 
  , 
  to 
  electromotive 
  

   forces 
  due 
  to 
  cells 
  or 
  other 
  causes 
  present 
  in 
  the 
  system. 
  To 
  

   extend 
  the 
  method 
  to 
  cover 
  such 
  cases, 
  we 
  make 
  use 
  of 
  a 
  

   device 
  well 
  known 
  to 
  readers 
  of 
  Heaviside 
  *, 
  that 
  is 
  we 
  

   consider 
  a 
  constant 
  electromotive 
  force 
  E 
  as 
  due 
  to 
  the 
  

   presence 
  of 
  a 
  condenser 
  of 
  large 
  capacity 
  K 
  possessing 
  an 
  

   initial 
  charge 
  X=EK. 
  The 
  Electrostatic 
  Energy 
  of 
  such 
  

   a 
  condenser 
  when 
  it 
  has 
  given 
  up 
  a 
  finite 
  quantity 
  of 
  electricity 
  

   ic 
  is 
  equal 
  to 
  ^(X 
  — 
  xYjKj 
  i. 
  e. 
  to 
  ^KW 
  — 
  '^x 
  since 
  x\'X. 
  is 
  small. 
  

   As 
  we 
  are 
  only 
  concerned 
  with 
  changes 
  of 
  Energy, 
  the 
  term 
  

   contributed 
  to 
  the 
  Electrostatic 
  Energy 
  by 
  the 
  cell 
  reduces 
  

   to 
  — 
  Ea;. 
  The 
  extended 
  form 
  of 
  the 
  Electrostatic 
  Energy 
  

   becomes 
  therefore 
  

  

  V 
  == 
  SK/K,. 
  - 
  2E 
  A 
  (3') 
  

  

  Although 
  in 
  stating 
  these 
  propositions 
  it 
  has 
  been 
  con- 
  

   venient 
  to 
  take 
  a 
  simple 
  symbol 
  for 
  the 
  quantity 
  of 
  electricity 
  

   which 
  has 
  flowed 
  through 
  each 
  branch 
  of 
  the 
  network, 
  it 
  is 
  

   more 
  convenient 
  in 
  applying 
  the 
  method 
  to 
  the 
  solution 
  of 
  

   a 
  problem 
  to 
  follow 
  Maxwell's 
  plan 
  of 
  assigning 
  a 
  simple 
  

   symbol 
  to 
  the 
  quantity 
  which 
  has 
  flowed 
  round 
  a 
  mesh 
  of 
  

   the 
  network. 
  Kirchhofl'^s 
  first 
  law 
  for 
  the 
  distribution 
  of 
  

   currents 
  in 
  networks, 
  i. 
  e. 
  that 
  the 
  currents 
  leaving 
  a 
  node 
  

   have 
  a 
  sum 
  equal 
  to 
  zero, 
  is 
  then 
  fulfilled 
  automatically. 
  

  

  The 
  following 
  figure 
  gives 
  the 
  arrangement 
  of 
  the 
  circuit 
  

  

  * 
  See 
  for 
  example, 
  0. 
  Heaviside, 
  Electrical 
  Papers, 
  ii. 
  p. 
  216 
  (1892). 
  

  

  