THE RAINEOW DUE TO A CIRCULAR SOURCE OF LTOHT. 9 



and similarly for V, 



_^ const, r -Iz ^ J C . 2~ ^ , ,7. 

 V.= — i I cos — -o, (l.r I SIR — ,-0., rA-j= V, . 



Afj J À J ?. ' 



— 00 — X 



Thus, for a spherical drop 

 and for a circular cylinder 



Of coui-se, if we leave ;. out of consideration, we may take as 

 the expression for V, and V, 



Vc=const. j cos~^diflx , ¥3=001151. j sin ~^-^^(Ix = , 



— =0 —00 



as Airy, o^ being small compared with o,. 



Airy's theory holds good only when 6'^ is negligibly small, 

 in other cases the theory must be essentially modified. If T is 

 not negligible, then we have to take into account the dependency 

 of the intensitv of lis-ht on the angles of reflections and refrac- 

 tions, namely the effect of polarization as indicated by Mascart 

 and Lorenz ; on the other hand the form of the wave front must 

 be modified by adding a term of X^. Thus some of Peruter's 

 calculation for large values of 6 can not be regarded as exact. 



4. Extension of Airy's theory to that of a 

 circular source. 



Passing now to the case of a circular source of uniform 

 intensity, the apparent diameter of the source 2tl> will he sup- 

 posed so small that we can neglect (p"' compared with 'I>, and 

 confine our attention to the neighborhood of the minimum 



