﻿T 
  HE 
  

   LONDON, 
  EDINBURGH, 
  and 
  DUBLIN 
  

  

  PHILOSOPHICAL 
  MAGAZINE 
  

  

  AND 
  

  

  JOURNAL 
  OF 
  SCIENCE. 
  

  

  [FIFTH 
  SERIES.] 
  \ 
  

   JANUARY 
  1898. 
  

  

  I. 
  Diffraction 
  Phenomena 
  in 
  the 
  Focal 
  Plane 
  of 
  a 
  Telescope 
  

   with 
  Circular 
  Aperture, 
  due 
  to 
  a 
  Finite 
  Source 
  of 
  Light. 
  

   By 
  H. 
  Nagaoka, 
  Pigakuhakushi, 
  Professor 
  of 
  Applied 
  

   Mathematics, 
  Imperial 
  University, 
  Tokyo 
  "*. 
  

  

  THE 
  diffraction 
  of 
  a 
  circular 
  aperture 
  has 
  for 
  a 
  long 
  time 
  

   attracted 
  the 
  attention 
  of 
  physicists, 
  on 
  account 
  of 
  its 
  

   intimate 
  connexion 
  with 
  the 
  theory 
  of 
  optical 
  instruments. 
  

   For 
  a 
  point 
  source 
  of 
  light, 
  the 
  problem 
  was 
  treated 
  by 
  Airy 
  f. 
  

   Schwerd 
  %, 
  and 
  Lommel 
  § 
  ; 
  the 
  last-mentioned 
  author 
  has 
  

   brought 
  our 
  knowledge 
  of 
  the 
  subject 
  to 
  the 
  highest 
  state 
  of 
  

   perfection, 
  both 
  with 
  regard 
  to 
  Fraunhofer's 
  and 
  Fresnel's 
  

   diffraction 
  phenomena. 
  For 
  practical 
  purposes, 
  however, 
  it 
  

   is 
  necessary 
  to 
  modify 
  the 
  problem 
  slightly, 
  and 
  investigate 
  

   the 
  diffraction 
  due 
  to 
  a 
  finite 
  source 
  of 
  light. 
  In 
  connexion 
  

   with 
  the 
  resolving 
  power, 
  or 
  for 
  the 
  explanation 
  of 
  drop- 
  

   formation 
  during 
  the 
  transit 
  of 
  inferior 
  planets, 
  the 
  problem 
  

   was 
  treated 
  by 
  Lord 
  Rayleigh 
  ||, 
  Andre 
  H, 
  Struve 
  **, 
  and 
  

   Strehl 
  ||. 
  In 
  the 
  present 
  paper 
  I 
  give, 
  in 
  the 
  first 
  place, 
  a 
  

  

  * 
  Coininunicated 
  by 
  the 
  Author. 
  

  

  f 
  Airy, 
  Camb. 
  Phil. 
  Trans, 
  vol. 
  v. 
  p. 
  283 
  (1834). 
  

  

  "J" 
  Schwerd, 
  Beugungserscheinungen, 
  Mannheim 
  (1835). 
  

  

  § 
  Lommel, 
  Abhandl. 
  d 
  bayer. 
  Akad. 
  Bd. 
  xv. 
  (1884). 
  

  

  || 
  Rayleigh, 
  "Wave-Theory 
  of 
  Light, 
  Encycl. 
  Brit., 
  9th 
  edition. 
  

  

  i[ 
  Andre, 
  Annates 
  de 
  VEcole 
  nor 
  male, 
  [2] 
  torn. 
  v. 
  p. 
  275 
  (1876). 
  

  

  ** 
  Struve, 
  Me 
  moires 
  de 
  lAcademie 
  des 
  Sciences 
  de 
  St. 
  Petersbouro. 
  

   torn. 
  xxx. 
  (1882) 
  ; 
  Wied. 
  Ann. 
  Bd. 
  xvii. 
  p. 
  1008 
  (1882). 
  

  

  ft 
  Strehl, 
  Zeitschrift 
  fur 
  Instrnnientenkunde, 
  Bd. 
  xv. 
  p. 
  362 
  (1895; 
  ; 
  

   Bd. 
  xvi. 
  p. 
  257 
  (1896) 
  ; 
  Bd. 
  xvii. 
  p. 
  165 
  (1897). 
  

  

  Phil. 
  Mag. 
  S. 
  5. 
  Vol. 
  45. 
  No. 
  272. 
  Jan, 
  1898, 
  B 
  

  

  