THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



DECEMBER 1918. 



XLIX. On the Light emitted from a Random Distribution of 

 Luminous Sources. By Lord Rayleigh, O.M., F.R.S.* 



RECENT researches have emphasized the importance of 

 a clear comprehension of* the operation under various 

 ■conditions of a group of similar unit sources, or centres, of 

 iso-periodic vibrations, e. g. of sound or of light. The sources, 

 ■supposed to be concentrated in points, may be independently 

 excited (as probably in a soda flame), or they may be con- 

 stituted of similar small obstacles in an otherwise uniform 

 medium, dispersing plane waves incident upon them. We 

 inquire into an effect, such as the intensity, at a great 

 distance from the cloud, either in a particular direction, or 

 in the average of all directions. For convenience of calcu- 

 lation and statement we shall consider especially sonorous 

 vibrations ; but most of the results are equally applicable to 

 -electric vibrations, as in light, the additional complication 

 being merely such as arises from the vibrations being trans- 

 verse to the direction of propagation. 



If the centres, supposed to be distributed at random in a 

 region whose three dimensions are all large, are spaced 

 widely enough in relation to the wave-length (X) to act inde- 

 pendently, the question reduces itself to one formerly treatedf, 

 for it then becomes merely one of the composition of a large 



* Communicated bv the Author. 



t Phil. Yuxx. vol. x. p. 73 (1830) ; Scientific Papers, vol. i. p. 491. For 

 Another method see 'Theory of Sound,' 2nd ed. § 42a, and for a more 

 complete theory K. Pearson's Math. Contributions to the Theory of 

 .Evolution, XV, Dulau, London. 



Phil. Mag. S. 6. Vol. 36. No. 216. Dec. 1918. 2 G 



