﻿On 
  a 
  Certain 
  Development 
  in 
  BesseVs 
  Functions. 
  947 
  

  

  are 
  correct 
  to 
  within 
  0*2 
  A.E. 
  I 
  have 
  calculated 
  the 
  wave- 
  

   lengths 
  from 
  the 
  formula 
  given 
  in 
  Kayser's 
  ' 
  Spectroscopy,' 
  

   vol. 
  ii. 
  page 
  521, 
  for 
  several 
  of 
  the 
  lines, 
  and 
  found 
  very 
  

   good 
  agreement 
  with 
  the 
  observed 
  values. 
  As 
  soon 
  as 
  more 
  

   accurate 
  values 
  have 
  been 
  found 
  with 
  a 
  large 
  quartz 
  spectro- 
  

   graph, 
  a 
  more 
  careful 
  comparison 
  will 
  be 
  made. 
  These 
  

   results 
  I 
  hope 
  to 
  be 
  able 
  to 
  publish 
  in 
  the 
  forthcoming 
  

   number 
  of 
  the 
  ' 
  Astrophysical 
  Journal.' 
  The 
  line 
  for 
  which 
  

   w 
  = 
  4 
  is 
  not 
  shown 
  in 
  the 
  photograph. 
  At 
  the 
  density 
  

   employed 
  in 
  making 
  this 
  exposure 
  it 
  was 
  found 
  to 
  be 
  

   bordered 
  on 
  each 
  side 
  with 
  what 
  appeared 
  to 
  be 
  a 
  channelled 
  

   spectrum, 
  precisely 
  as 
  are 
  the 
  D 
  lines, 
  for 
  which 
  n 
  = 
  3. 
  A 
  

   faint 
  indication 
  of 
  a 
  channelled 
  spectrum 
  also 
  appeared 
  about 
  

   the 
  line 
  for 
  which 
  n 
  = 
  5, 
  in 
  some 
  of 
  the 
  negatives 
  made 
  with 
  

   still 
  greater 
  vapour-density. 
  I 
  have 
  already 
  shown 
  that 
  the 
  

   channelled 
  spectrum 
  in 
  the 
  green 
  and 
  blue 
  region 
  is 
  con- 
  

   nected 
  in 
  some 
  way 
  with 
  the 
  D 
  lines, 
  for 
  the 
  D 
  lines 
  appear 
  

   in 
  the 
  fluorescence 
  spectrum 
  when 
  the 
  vapour 
  is 
  stimulated 
  

   by 
  blue-green 
  light 
  which 
  is 
  absorbed 
  by 
  the 
  channelled 
  

   spectrum. 
  The 
  fact 
  that 
  the 
  other 
  members 
  of 
  the 
  principal 
  

   series 
  are 
  also 
  accompanied 
  by 
  channelled 
  spectra 
  is 
  very 
  

   significant. 
  

  

  At 
  the 
  present 
  time 
  I 
  am 
  making 
  efforts 
  to 
  find 
  some 
  way 
  

   of 
  making 
  the 
  higher 
  frequency 
  members 
  of 
  the 
  principal 
  

   series 
  appear 
  in 
  the 
  emission 
  spectrum, 
  but 
  thus 
  far 
  have 
  not, 
  

   found 
  the 
  proper 
  conditions. 
  

  

  LXXXIL 
  On 
  a 
  Certain 
  Development 
  in 
  BesseVs 
  Functions. 
  

  

  To 
  the 
  Editors 
  of 
  tlw 
  Philosophical 
  Magazine. 
  

   Gentlemen, 
  — 
  

  

  IN 
  a 
  numerical 
  calculation 
  of 
  the 
  torsion 
  of 
  a 
  circular 
  

   cylinder 
  under 
  shearing 
  forces 
  distributed 
  arbitrarily 
  

   over 
  the 
  ends, 
  there 
  has 
  come 
  to 
  notice 
  an 
  apparent 
  over- 
  

   sight 
  in 
  the 
  usual 
  method 
  of 
  determining 
  the 
  coefficients 
  in 
  

   certain 
  series 
  of 
  BessePs 
  functions. 
  The 
  formulas 
  used 
  in 
  the 
  

   computation 
  are 
  given 
  by 
  Chree 
  (Trans. 
  Camb. 
  Phil. 
  Soc. 
  

   vol. 
  xiv., 
  1889, 
  p. 
  366), 
  who 
  finds 
  that 
  in 
  a 
  cylinder 
  the 
  dis- 
  

   placement 
  (y) 
  perpendicular 
  to 
  the 
  radius 
  and 
  axis, 
  if 
  it 
  is 
  

   independent 
  of 
  the 
  angle, 
  must 
  satisfy 
  the 
  equation 
  

  

  "dr 
  2 
  r 
  ~dr 
  r 
  2 
  - 
  "dz 
  2 
  

  

  3Q2 
  

  

  