OBJECT-GLASS WITH A TRIANGULAR APERTURE. 



4;J9 



Since this expression for Z is the sum of two squares, Z can never 

 = 0, and therefore the six rays cannot be interrupted by a perfectly 

 black band or ring. Perhaps, however, there may be a ring of light of 

 such feeble intensity, interrupting the rays, as to appear like a black 

 band cutting off the rays from the central part in the maimer described 

 by Sir J. Herschel. To ascertain if this be the case, let us find the value 

 of m which gives Z a minimum. By differentiation we obtain 



cLZ 





m cos 



2 / 



2 . 

 — 7=sm 

 \/3 



'^)l 



The only factor in this expression which can be equated to zero, 

 for the purpose of finding the maximum and minimum values of Z, 

 being an exact square, Z. admits neither of a maximum nor minimum, 

 but decreases perpetually from the centre of the screen, as the fol- 

 lowing Table will shew. 



In this Table the central brightness ( = -^ «' j is taken as unity. 



