II. — On the Diffraction Rings for a Circular Opening ; 

 and on the Limit of Resolving Power. 



(Being a rejoinder to Mr. Nelson.) 

 By Alfred W. Porter, B.Sc. 



(Read November 20, 1907.) 



There are two different though related questions connected with 

 Mr. Nelson's reply to the paper by Mr. Everitt and myself. The 

 first is, what is the size of the first dark diffraction ring for 

 the case calculated by Airy and others ? and the second is, what is 

 the ultimate resolving power of a telescope for a close double star ? 

 I do not mean to say that these questions are explicitly stated, but 

 Mr. Nelson confuses them both in his original paper and in his 

 reply to our criticism. 



What I wish to make perfectly clear, first of all, is that our 

 short paper referred only to the former of these questions, viz. the 

 radius of the first dark diffraction ring. Airy's calculation of this 

 radius was for the case of a point source of light : and as a physicist 

 I feel somewhat perturbed that a calculation which was free from 

 any obvious flaw should be called into question. It was with the 

 object of testing the calculation that our measurements were made, 

 with the result that we obtained a practically complete experi- 

 mental verification of the theoretical value. Hence, whatever may 

 be the explanation of Mr. Nelson's data, this explanation is not to 

 be found in incorrectness in the theoretical calculation. 



Now this was the only point dealt with in our paper. Mr. 

 Nelson in his reply forces upon us a consideration of the second 

 question, viz. that of the ultimate resolving power. 



It is very difficult to gather the exact mode in which his 

 experiments were made. From his paper we (and others) con- 

 cluded that he moved his stars till the first dark rings came 

 into contact. From his reply, we gather that his two stars were 

 moved to such a distance that they just failed to be seen as two. 

 But this latter does not give one a measure of the first dark ring, as 

 he seems to claim ! Mr. Nelson does not appear to realise that his 

 two star images may be so near as to overlap, and yet show a dark 

 line separating them. I believe that this last fact is at the bottom 

 of the confusion in his statements. 



When the two stars are a distance apart corresponding to the 



b 2 



