128 Dr. G. Johnstone Stoney on 



this, the definition o£ the image of L as seen in the telescope 

 will fall short of what the light that passes through lens L is 

 capable of producing ; if the aperture of the objective is re- 

 duced to so small a size that it admits the light of the spurious 

 disk only and excludes the whole of the diffraction rings, 

 then the definition will have become so bad that even the 

 outline of L cannot be seen. Moreover, we can by this 

 analysis ascertain the poor character of the image which 

 results from employing in its formation the light of the 

 spurious disk and the innermost ring only ; as also the greatly 

 improved definition, which is obtained if the aperture of the 

 objective admits the light of the central disk and of two rings ; 

 and the slightly further improvement which results from still 

 more enlarging the aperture. All these particulars are easily 

 investigated by employing the analysis into undulations of 

 flat wavelets. A full examination of phenomena of this kind 

 will be given in the next of the Flat-wavelet Resolution 

 papers. 



The same method of proof shows that when the source of 

 light is enlarged there is no necessity, such as Lord Rayleigh 

 speaks of, for any phase relation between the portions of light 

 emanating from the several luminous puncta of the source A 

 when enlarged. In fact, the phase relation which needs to 

 be present is of a totally different kind. It is the phase 

 relation which necessarily subsists between the light forming at 

 C the spurious disk of each separate punctum of the enlarged 

 A, and the light forming at the annular appendages asso- 

 ciated ivith that particular spurious disk. This is a phase 

 relationship which will prevail, however unrelated may be 

 the portions of light emanating from different puncta of A*. 

 Accordingly, it may safely be affirmed (and is fully confirmed 

 by experiment) that, without any loss of definition, the source 

 of light may be a self-luminous body. It seems necessary to 

 point this out, because an insufficient appreciation of the way 

 in which images are produced is still prevalent. 



In Lord Rayleiglr's paper, and in the present paper, the 

 simplest case, viz. where the image of a point-source A falls 



* This makes it plain, why when Lord .Rayleigh employed as the 

 source of light, light coming through a narrow slit situated at A, he 

 found that the definition of L as seen in the telescope did not suffer, " the 

 vertical parts of the circular edge (parallel to the slit) being as well 

 defined as the horizontal parts." For, in fact, the light issuing from the 

 several puncta of the slit independent!}' formed good images of L, and 

 the simultaneous presence of these independent images of L, made a re- 

 sultant brighter image and somewhat modified in other respects, but of 

 which the definition was equally good. 



