THE RAINBOW DUE TO A CIRCULAR SOURCE 'OF LIGHT. 3 



In our calculation we did not take the mme numerical values 

 for z that Pernter took. Thus in our values given above which 

 were found by interpolation, there are probably öinall errors in 

 the last figures. 



So far as we are aware, the various calculations are as yet 

 limited to cases which, strictly speaking, hold only for a point 

 source of light. These considerations have led us to undertake 

 the following investigation. It may therefore, be looked upon 

 as an extension of Aii'y's theory to the case in which the source 

 of light is circular, namely, when the apparent diameter of the 

 sun is taken into account. 



Next, let us consider the experimental side. Miller'^^ and 

 Pulfrich^"' verified Airy's theory in the special case of two 

 dimensions with a cylindrical stream of water (or glass rod), 

 and a straight slit as the source of light. But a question sug-, 

 gests itself in connexion with the problem of the circular source 

 of light — if we take account of the breadth of the slit, assum- 

 ing its length to be infinite, what difference will occur ? This 

 question must be answered. 



In the following, we shall start by briefly stating Airy's 

 theory, and then proceeding to find difierences when the source 

 of light is replaced by a small circular disk ; and after some 

 additional notes on the two-dimensional case, the colours of the 

 rainbow due to the sun are calculated in two cases, which may 

 be taken as illustrations of the difference between the point and 

 the circular source ; and lastly experimental results will be 

 discussed. 



(1) Tr.-ms. failli). I'liil. Sor. VII. p. 277 (,lb41). 



[2) Wied. Anil. XXXlll. i». 194 (1888). 



