﻿340 
  Mr. 
  C. 
  Kinsley 
  on 
  the 
  Determination 
  of 
  

  

  Tubes 
  3 
  cm. 
  and 
  larger 
  do 
  not 
  need 
  any 
  tubes 
  

   leading 
  to 
  the 
  ear. 
  Use 
  tubes 
  with 
  smooth 
  

   inside 
  surface, 
  such 
  as 
  glass 
  or 
  drawn 
  brass. 
  

  

  In 
  most 
  alternating 
  current 
  work 
  it 
  has 
  been 
  

   found 
  by 
  numerous 
  observers 
  * 
  that 
  the 
  E.M.F. 
  

   and 
  current 
  may 
  be 
  considered 
  a 
  simple 
  function 
  

   of 
  the 
  number 
  of 
  alternations 
  : 
  

  

  2 
  = 
  I 
  1 
  sinc&£ 
  

  

  where 
  i 
  = 
  instantaneous 
  value 
  of 
  current, 
  

   I 
  x 
  = 
  maximum 
  value 
  of 
  current, 
  

   G) 
  = 
  27m, 
  

   £ 
  = 
  time 
  since 
  the 
  current 
  was 
  zero. 
  

  

  This 
  is 
  substantially 
  true 
  under 
  normal 
  working 
  

   conditions, 
  and 
  may 
  be 
  assumed 
  for 
  alternating 
  

   current 
  computations. 
  

  

  The 
  actual 
  curve, 
  however, 
  may 
  be 
  strictly 
  con- 
  

   sidered 
  as 
  the 
  resultant 
  of 
  many 
  pure 
  sine-curves 
  

   whose 
  periods 
  are 
  multiples 
  of 
  the 
  first 
  harmonic 
  : 
  

  

  ^IiSino^ 
  + 
  Ljsin 
  2co(t 
  + 
  a) 
  +I 
  3 
  sin 
  3(o(t 
  + 
  b) 
  -f 
  <fec. 
  

  

  where 
  t, 
  co, 
  and 
  t 
  are 
  as 
  already 
  used, 
  

   Ij 
  is 
  the 
  maximum 
  value 
  of 
  the 
  first 
  harmonic, 
  

  

  1 
  

  

  second 
  

   third 
  

  

  „ 
  „ 
  „ 
  ,, 
  ^vv,ixu 
  „ 
  

  

  I3 
  » 
  v 
  » 
  » 
  third 
  „ 
  

  

  a 
  and 
  b 
  are 
  the 
  differences 
  between 
  the 
  values 
  

   of 
  t 
  for 
  the 
  fundamental 
  and 
  the 
  corresponding 
  

   values 
  for 
  the 
  overtones. 
  

  

  As 
  is 
  stated 
  above, 
  all 
  terms 
  but 
  the 
  first 
  term 
  

   are 
  usually 
  neglected. 
  

  

  The 
  telephone 
  diaphragm 
  will 
  therefore 
  give 
  a 
  

   composite 
  note 
  containing 
  not 
  only 
  the 
  funda- 
  

   mental 
  but 
  all 
  the 
  higher 
  harmonics 
  that 
  may 
  be 
  

   present 
  +. 
  

  

  A 
  quantitive 
  determination 
  of 
  the 
  harmonics 
  

   present 
  has 
  not 
  yet 
  been 
  made, 
  and 
  for 
  the 
  present 
  

  

  * 
  Reasons 
  for 
  considering 
  the 
  above 
  equation 
  correct 
  : 
  

   S. 
  P. 
  Thompson, 
  ' 
  Dynamo 
  Electric 
  Machinery,' 
  5th 
  edition, 
  

   p. 
  553 
  ; 
  Rodes, 
  Elect. 
  Rev. 
  vol. 
  xxxix. 
  p. 
  845 
  ; 
  Bedell, 
  ' 
  The 
  

   Principles 
  of 
  the 
  Transformer,' 
  p. 
  59. 
  Curves 
  determined 
  

   from 
  machines 
  — 
  among 
  others 
  : 
  Bedell, 
  Miller, 
  and 
  Wagner, 
  

   Am. 
  Hist. 
  Elect. 
  Eng. 
  vol. 
  x. 
  p. 
  500 
  ; 
  Fleming, 
  J. 
  A., 
  Elect. 
  

   Rev. 
  vol. 
  xxxix. 
  pp. 
  91, 
  122, 
  &c. 
  

  

  t 
  Dr. 
  Steinmetz, 
  in 
  ' 
  Theory 
  and 
  Calculation 
  of 
  Altern- 
  

   ating 
  Current 
  Phenomena,' 
  finds 
  that 
  only 
  the 
  odd 
  

   harmonics 
  need 
  be 
  considered. 
  Houston 
  and 
  Kennelly, 
  Elect. 
  

   World, 
  vol. 
  xxiii. 
  p. 
  35, 
  are 
  of 
  the 
  same 
  opinion. 
  

  

  Resonance 
  

   Tube. 
  

  

  