6 ART. 3. — AICHI AND TANAKADATE : THEORY OF 



M = l -0.0347//--. tan 0=0.0694;/-^; .- - 



or, approximately, 



It must be remarked that both expansions only represent 

 f(xß) for Hy-O. But for ft<0, f{xß) being a function having no 

 characteristic ])roperty, it is at once seen that no important dif- 

 ference appears between a point and a circular source. In the 

 following discussion the places where ^<0 are therefore excluded. 



3. Remarks on Airy's theory. 



In his paper, Airy contined the value of 6 weithin 2°, but 

 he did not exactly determine the limit of approximation in his 

 theory. Also he did not discuss the dependency of the intensity 

 of the rainbow on the wave length of light. Pernter applied^^' 

 Airy's theory for 6 ^IQ'^ not only to determine the positions of 

 maxima and minim;i, but also to ^calculate the amount of inten- 

 sity, and he said^-' that t) might be 20° or 80°. Mascart took^'^' 

 as the value of A of (8„) at first 





and then modified"*' it to the form of (o„) taking account of 

 dimension. 



We shall have to examine these points in detail,' before 

 proceeding to our discussion. First, in the ecjuation (2), there 

 was neglected the term of x^ compared with .t\ Ditiërentiate (2) 

 with respect of x and 



(]) Wien. Sitz. Ber. CVI. 2a, Tab. I, II (1897). 



C-i) ,, „ „ ('XIV. 2aj p. H (1905). 



(:V) Traité (l'Oi.li(iue.s I. p. ;594 (Copenliagen, 1889j. 



(4) „ „ ill. p. 437 ( „ 1893). 



