26 



Transactions of the Society. 



surface of the cone A At?. It seems, therefore, an obvious plan to. 

 compute diffraction, not from the internal surfaces AC A and AjCA,,. 

 but from the external surface A A v. Upon this, which is believed to he 

 a new problem, the following suggestions are offered with great humility, 

 and in the hope that the problem itself, having been suggested for dis- 

 cussion, will receive the attention of some mathematician better qualified 

 than the present writer to deal with it. 



In the following diagram (fig. 22) let A. . .A represent the wave- 

 front occupying the aperture, and let A At? be the dioptric beam. Also 

 let the dark wedge cut out of the cone A A v be a part of the sur- 

 face of the cone directed towards the point t^ taken anywhere upon the- 

 focal plane. 



It is manifest that we need not for the purpose of reckoning the- 

 illumination at vi consider the radiation from other parts of the conical 



Fig. 22. 



Fio. 23. 



surface which are directed towards other parts of the focal plane. Thi& 

 follows at once from the symmetry of the figure. Furthermore, let p 

 be the radial distance in the focal plane of the point n x from the true- 

 focus v, and let E = the semidiameter of the aperture. Let F = the 

 optical distance from the aperture to the focal point v. Also, let S S be an 

 element of surface taken anywhere upon the radiant wedge, and from the 

 centre point of 8 S draw the straight line joining that point to the point t/, . 

 Lastly, to complete the diagram, from the point t^ draw a perpen- 

 dicular upon the conical surface, and let the angle between these two 

 lines, drawn from the point n x to the conical surface, be a. Also, let 

 the distance, measured on the surface of the cone, between the point 

 where the perpendicular meets the conical surface and the central point 

 of 8 S, be called D. It will be convenient to show these last mentioned 

 magnitudes by another diagram (fig. 23), in which the angle a may 



