372 ' Dr. Gv J. Stoney on a Supposed Proof 



cone of dispersion, and becomes that sheaf of innumerable 

 radiations which produce the well-known diffraction effects. 

 That they form a very complex system and are infinite in 

 number may be seen from the considerations in the subjoined 

 footnote*. 



Let us now tarn to the events that would arise if the dis- 

 turbance %—f(yt—z)+f(vt-\rz) were maintained throughout 

 the disk-like region of space. Here a highly complex 

 sheaf of radiations almost identical with that described 

 in the last paragraph would be emitted forwards by tho 

 disturbance in the disk, and an exactly similar one back- 

 wards. What Theorem A tells us is that these two complex 

 systems of radiations can be resolved into innumerable undu- 

 lations, each of perfectly uniform plane waves, each of infinite 

 extent laterally, and each advancing in its own direction 

 through space without undergoing change. Further, that 

 if all of these were made to cross the disk, they by their 

 mutual interference would unite to produce within that small 

 portion of space the extremely simple motion represented by 

 %=f(vt—z) -\-f(yt-\-z), while everywhere else in space, whether 

 in the plane of the disk or outside it, they by their inter- 

 ference develop not that motion, but the radiations which 

 emanate from it t- This is information of importance. It is 

 a true analysis of events that are really going on. 



Contrast this with the kinematical information supplied by 

 Theorem B, viz. : — The motion within the disk represented 



by 



H=f(vt-z)+f(H + z) 

 can be forciblv resolved into two mathematical series, the 



* The innumerable direct and diffracted undulations which advance 

 from the opening in the screen and which are furnished by Theorem A, 

 could be each concentrated into a point by an aplanatic lens of infinite 

 aperture placed in front of the opening in the screen so as to receive all 

 the light which emerges from it. In practice the lens need not be of 

 infinite aperture, since the same resultant effect is produced by a lens 

 whose aperture is somewhat larger than the opening in the screen. This 

 furnishes as the image of the star a spurious disk surrounded by rings. 

 Accordingly every point of this complex image is the concentration of 

 one of the undulations of uniform plane waves of infinite extent laterally, 

 which are furnished by Theorem A. 



| Along with the radiations which converging upon the disk would 

 produce in it the motion g=f(rt— z)-\-f{vt-\-z). In fact, each infinite 

 undulation necessarily consists of a moiety of the undulation flowing in 

 towards the region of disturbance, of a small portion travelling across it, 

 and of the rest travelling past or from it. But practically the presence 

 of the inflowing portions causes no inconvenience, because in the appli- 

 cations of the theorem the radiations that are outward bound, and those 

 inward bound, are easily discriminated. 



