﻿1875.] 
  

  

  Reduction 
  of 
  Anemograms. 
  

  

  513 
  

  

  A 
  Table 
  whose 
  data 
  belong 
  to 
  dates 
  separated 
  by 
  considerable 
  intervals 
  

   will 
  not 
  give 
  the 
  components 
  generally 
  without 
  interpolation. 
  The 
  for- 
  

   mula 
  universally 
  adopted 
  for 
  this 
  when 
  the 
  quantities 
  concerned 
  are 
  

   periodic 
  functions 
  of 
  the 
  time-angle 
  is 
  that 
  given 
  by 
  Bessel 
  — 
  - 
  

  

  U=K+A 
  cos 
  + 
  B 
  cos 
  20 
  &c, 
  +0 
  sin 
  0+P 
  sin 
  20 
  &c, 
  

   e 
  

  

  or 
  its 
  secondary 
  equivalent 
  — 
  

  

  U=K 
  + 
  K 
  sm(K 
  + 
  0) 
  + 
  Ksm(K 
  + 
  20)+ 
  &c, 
  

  

  0' 
  ' 
  n 
  n 
  

  

  where 
  is 
  the 
  hour-angle 
  from 
  midnight. 
  But 
  as 
  the 
  monthly 
  varia- 
  

   tions 
  must 
  also 
  be 
  represented, 
  the 
  coefficients 
  of 
  the 
  first 
  equation 
  must 
  

   be 
  developed 
  in 
  terms 
  of 
  <p 
  (the 
  time-angle 
  from 
  the 
  beginning 
  of 
  the 
  

   year), 
  and 
  the 
  expression 
  of 
  each 
  of 
  them 
  multiplied 
  by 
  the 
  corresponding 
  

   cosine 
  or 
  sine 
  of 
  0. 
  Bessel's 
  computation 
  of 
  the 
  coefficients 
  may 
  be 
  

   much 
  shortened 
  where, 
  as 
  in 
  the 
  cases 
  before 
  us, 
  the 
  circle 
  is 
  divided 
  

   into 
  2n 
  equal 
  parts 
  (n 
  being 
  an 
  integer), 
  and 
  the 
  first 
  term 
  of 
  the 
  series 
  

  

  = 
  or 
  for, 
  in 
  consequence 
  of 
  the 
  numerical 
  equality 
  of 
  the 
  cosine 
  and 
  

  

  sine 
  of 
  0, 
  180 
  + 
  0, 
  180 
  — 
  0, 
  and 
  360—0, 
  it 
  is 
  only 
  necessary 
  to 
  compute 
  

   for 
  the 
  first 
  quadrant. 
  Eor 
  the 
  horary 
  sets 
  this 
  labour 
  might 
  be 
  short- 
  

   ened 
  by 
  combining 
  them 
  in 
  groups 
  of 
  3 
  ; 
  and 
  the 
  formula 
  for 
  this 
  is 
  

   given, 
  but 
  it 
  is 
  not 
  quite 
  as 
  exact 
  as 
  the 
  ordinary 
  one, 
  which 
  is 
  also 
  

   given. 
  The 
  horary 
  constants 
  for 
  W 
  and 
  S, 
  computed 
  by 
  this 
  last, 
  are 
  

   given 
  in 
  Tables 
  Y. 
  and 
  VI. 
  for 
  each 
  month 
  to 
  the 
  fourth 
  order, 
  and 
  an 
  

   estimate 
  of 
  their 
  precision. 
  

  

  These 
  constants 
  are 
  then 
  developed 
  in 
  month-time, 
  for 
  which 
  the 
  

   formula 
  is 
  given.. 
  This, 
  however, 
  requires 
  a 
  correction; 
  it 
  supposes 
  

   each 
  u 
  from 
  which 
  it 
  is 
  deduced 
  to 
  belong 
  to 
  a 
  series 
  of 
  in 
  arithme- 
  

   tical 
  progression. 
  This 
  is 
  not 
  the 
  case 
  : 
  first, 
  the 
  mean 
  of 
  each 
  month 
  

   does 
  not 
  represent 
  the 
  u 
  belonging 
  to 
  the 
  middle 
  of 
  that 
  month 
  ; 
  

   secondly, 
  the 
  angular 
  distances" 
  of 
  the 
  middle 
  of 
  each 
  month 
  from 
  the 
  

   beginning 
  of 
  the 
  year 
  are 
  not 
  in 
  arithmetical 
  progression. 
  These 
  are 
  

   both 
  corrected 
  by 
  multiplying 
  the 
  constants 
  by 
  certain 
  factors. 
  The 
  

   secondary 
  constants 
  so 
  corrected 
  are 
  given 
  in 
  Table 
  VIII. 
  to 
  the 
  6th 
  

   order. 
  

  

  As 
  an 
  example 
  of 
  the 
  mode 
  of 
  trying 
  what 
  effect 
  any 
  periodical 
  agent 
  

   may 
  have 
  on 
  the 
  coordinates, 
  the 
  sun's 
  altitude 
  at 
  Armagh 
  is 
  considered. 
  

   It 
  is 
  developed 
  in 
  terms 
  of 
  0, 
  and 
  may 
  probably 
  account 
  for 
  0-27 
  of 
  the 
  

   variation 
  of 
  W 
  and 
  0*53 
  of 
  that 
  of 
  S. 
  

  

  The 
  paper 
  concludes 
  with 
  an 
  attempt 
  to 
  show 
  from 
  these 
  observations 
  

   the 
  existence 
  of 
  an 
  aerial 
  tide-current, 
  which, 
  according 
  to 
  Laplace, 
  is 
  at 
  

   its 
  maximum 
  0-195 
  mile 
  per 
  hour. 
  There 
  was 
  little 
  hope 
  of 
  detecting 
  

   so 
  small 
  a 
  quantity 
  ; 
  but 
  the 
  attempt 
  would 
  at 
  least 
  show 
  how 
  far 
  the 
  

   mean 
  of 
  a 
  large 
  number 
  of 
  observations 
  may 
  approach 
  the 
  truth. 
  When 
  

   the 
  moon 
  is 
  east 
  of 
  the 
  meridian 
  its 
  attraction 
  increases 
  W, 
  when 
  west 
  

  

  2k2 
  

  

  