﻿the 
  Frequency 
  of 
  Alternating 
  Currents. 
  343 
  

  

  Computation 
  of 
  the 
  Tables. 
  

  

  We 
  have 
  seen 
  that 
  

  

  Y 
  t 
  = 
  An, 
  

  

  and 
  so 
  we 
  must 
  know 
  the 
  velocity 
  of 
  sound 
  in 
  air 
  in 
  the 
  tube. 
  

   According 
  to 
  Kirchhoff's 
  * 
  equation 
  

  

  where 
  V 
  = 
  the 
  velocity 
  of 
  sound 
  in 
  the 
  tube 
  at 
  0° 
  temp, 
  and 
  

   vapour-pressure. 
  

   a 
  = 
  the 
  velocity 
  of 
  sound 
  in 
  free 
  air 
  at 
  0° 
  temp, 
  and 
  

  

  vapour-pressure. 
  

   y 
  = 
  a 
  constant 
  depending 
  on 
  the 
  inside 
  surface 
  of 
  

   the 
  tube. 
  

  

  Use 
  a 
  = 
  330'9, 
  y 
  = 
  «00799. 
  

  

  The 
  equation 
  has 
  been 
  experimentally 
  established 
  and 
  the 
  

   constants 
  gotten 
  by 
  Dr. 
  Low 
  f. 
  

  

  The 
  velocities 
  for 
  any 
  atmospheric 
  condition 
  can 
  be 
  gotten 
  

   from 
  the 
  equation 
  

  

  SB 
  

  

  where 
  a= 
  '003665, 
  

  

  p 
  = 
  vapour-pressure, 
  

   B 
  = 
  barometric 
  pressure. 
  

  

  The 
  length 
  of 
  the 
  tube, 
  plus 
  correction 
  for 
  open 
  end, 
  will 
  

   thus 
  be 
  

  

  8B 
  

  

  ^~*fczhJ^ii 
  

  

  8B 
  

  

  r 
  ±n 
  

  

  In 
  this 
  equation 
  the 
  constants 
  known 
  are 
  

  

  a 
  = 
  330*9 
  metres 
  per 
  sec, 
  

   ^ 
  = 
  •00799, 
  

   « 
  = 
  -003665; 
  

  

  * 
  Pogg. 
  Ann. 
  vol. 
  cxxxiv. 
  p. 
  177. 
  

   t 
  Dr. 
  Low, 
  Phil. 
  Mag. 
  Sept. 
  1894. 
  

  

  