JOURNAL OF THE COLLEÖE OF 30TENCE, IMPERIAL UNIVERSITY, 

 TOKYO, JAPAN. 



Vol. XXI., ARTICLE 3. 



Theory of the Rainbow due to a Circular 

 Source of light. 



By 

 K. Aichi <-tiid T. Tanakadate. 



Wdli Ö jj/ati's. 



1. Introduction. 



From the time of Descartes, many theories of the rainbow 

 have been proposed, but Airy'^^ was the first to establish a satis- 

 factory theory on the nndulatory theory of light. Airy's equation 

 of the meridian section of the emergent wave-surface immedi- 

 ately after leaving the surface of the raindrop {y—ax''), was, 

 however, formed with reference to the tangent and normal to 

 the curve at the point of inflexion, based on geometrical optics. 

 This point in Airy's theory was afterwards developed in detail 

 by Boitel,'- Larmor,'"' and especially by Mascart^^^ and L. 

 Lorenz.'"'^ But all the above investigations were based on the 

 assumption of a point source of light, and for the actual case 



(1) Trans. Camb. Phil. Soc. VI. p. .379 (1838); VIII. p. 595 (1848). 



(2) Compt. Kend. May 28, 1888; Phil. Ma^. XXVI. p. 2.39 il888). 



(3) Proc. Camb. Phil. Soc. VI. p. 283 (1888). 



(4) Traité d'Optique, I. p. 382 (1889) ; III. p. 430 (1893). 



(5) Œuvres Scientifiques, I. p. 405 (Copenhagen, 1898). 



