﻿Pressure-integral 
  as 
  Kinetic 
  Potential 
  439 
  

  

  no 
  term 
  in 
  energy 
  involving 
  ^ 
  and 
  to 
  jointly, 
  and 
  if 
  we 
  use 
  

  

  for 
  the 
  energies 
  belonging 
  to 
  cyclic 
  and 
  acyclic 
  motions 
  

   respectively, 
  (5) 
  is 
  

  

  >> 
  

  

  • 
  (6) 
  

  

  or 
  with 
  

  

  p 
  + 
  ^r^rf 
  T 
  = 
  T-K+T 
  = 
  L; 
  

  

  where 
  T 
  is 
  a 
  quadratic 
  in 
  velocities, 
  K 
  in 
  the 
  constants 
  of 
  

   circulation, 
  and 
  I 
  is 
  a 
  bilinear 
  function 
  of 
  these 
  quantities. 
  

   As 
  L 
  is 
  Kelvin's 
  kinetic 
  potential 
  the 
  question 
  before 
  us 
  now 
  

  

  is, 
  what 
  is 
  the 
  effect 
  of 
  the 
  term 
  -j- 
  1 
  pcf> 
  dr 
  on 
  the 
  dynamical 
  

   position. 
  " 
  

  

  § 
  2. 
  If 
  L 
  is 
  a 
  function 
  of 
  coordinates 
  6 
  and 
  the 
  time- 
  

  

  rates 
  6... 
  0, 
  its 
  time-rate 
  or 
  whole 
  rate 
  of 
  increment 
  can 
  

   be 
  expressed 
  as 
  a 
  sum 
  of 
  terms 
  6 
  © 
  , 
  together 
  with 
  the 
  time- 
  

   rate 
  of 
  a 
  function 
  derivable 
  from 
  L. 
  It 
  is 
  sufficient 
  to 
  write 
  

   a 
  single 
  variable. 
  In 
  

  

  the 
  first 
  term 
  has 
  the 
  required 
  form, 
  and 
  subsequent 
  terms 
  

   are 
  

  

  6 
  w 
  -dtl 
  e 
  w 
  dt^e] 
  + 
  cie-^B' 
  

  

  c+«3L 
  _ 
  d_ 
  r<»>9L 
  ^d 
  BL 
  „_, 
  ^ 
  BL1 
  

  

  

  