﻿90 
  A 
  New 
  Harmonic 
  Analyser. 
  

  

  Table 
  {continued). 
  

  

  11 
  - 
  6-0 
  - 
  6-0 
  0-0 
  

  

  12 
  0-0 
  0-0 
  00 
  

  

  13 
  4-0 
  5-0 
  -1-0 
  

  

  14 
  - 
  2-0 
  0-0 
  -2-0 
  

  

  15 
  - 
  4-0 
  - 
  4-5 
  0-5 
  

  

  16 
  0-5 
  0-0 
  0-5 
  

  

  17 
  3-5 
  4-0 
  -0-5 
  

  

  18 
  - 
  1-0 
  0-0 
  -1-0 
  

  

  19 
  - 
  3-5 
  - 
  30 
  -0-5 
  

  

  20 
  0-0 
  0-0 
  0-0 
  

  

  The 
  average 
  error 
  is 
  only 
  *65 
  of 
  one 
  per 
  cent, 
  of 
  the 
  value 
  

   of 
  the 
  oreatest 
  term. 
  

  

  Another 
  illustration 
  is 
  given 
  in 
  curve 
  No. 
  27 
  (PL 
  XVIII.) 
  , 
  

   in 
  which 
  

  

  <M^) 
  = 
  

  

  -a2x 
  2 
  

  

  For 
  a 
  = 
  l 
  the 
  following 
  are 
  the 
  values 
  of 
  the 
  coefficients 
  of 
  

   the 
  first 
  twelve 
  terms 
  of 
  the 
  equivalent 
  Fourier 
  series 
  : 
  — 
  

  

  i 
  

  

  0-02*2 
  cog 
  ^ 
  ^ 
  

  

  n. 
  Obs. 
  Calc. 
  A. 
  

  

  100 
  100 
  

  

  1 
  97-5 
  96 
  1-5 
  

  

  2 
  , 
  88 
  86 
  2 
  

  

  3 
  73-5 
  70 
  3-5 
  

  

  4 
  56 
  54 
  2 
  

  

  5 
  40 
  38 
  2 
  

  

  6 
  26-5 
  25 
  1-5 
  

  

  7 
  16-5 
  15 
  1-5 
  

  

  8 
  9-5 
  8 
  1-5 
  

  

  9 
  5-5 
  4-5 
  1 
  

  

  10 
  3 
  2 
  1 
  

  

  11 
  1 
  10 
  

  

  12 
  0-5 
  -0-5 
  

  

  Here 
  the 
  average 
  error 
  is 
  somewhat 
  greater, 
  being 
  1*5 
  

   per 
  cent, 
  of 
  the 
  value 
  of 
  the 
  greatest 
  term, 
  but 
  by 
  a 
  suitable 
  

   selection 
  of 
  the 
  constant 
  it 
  may 
  be 
  made 
  less 
  than 
  1 
  per 
  cent. 
  

  

  It 
  appears, 
  therefore, 
  that 
  the 
  machine 
  is 
  capable 
  of 
  effecting 
  

   the 
  integration 
  \ 
  <f>(x) 
  cos 
  hx 
  dx 
  with 
  an 
  accuracy 
  comparable 
  

   with 
  that 
  of 
  other 
  integrating 
  machines 
  ; 
  and 
  while 
  it 
  is 
  

   scarcely 
  hoped 
  that 
  it 
  will 
  be 
  used 
  for 
  this 
  purpose 
  where 
  

  

  