48 Mr. W. Baily on a Theorem 



value of 6 for which r is infinite. Then 



0=55*4 



c d 

 and the equation to the curve may be written 



-.cos 2 0=cos0— cos0 (2) 



In fig. 1, G is the diffraction-grating and G N its normal ; 

 Fig.l. 



and the angle N G S is equal to (f>. The curves marked L l7 L 2 

 are traced from equation (2). G S is parallel to one asymptote 

 to the curve, so that if a source of light (say a star) is at an 

 infinite distance on the corresponding branch of the curve it 

 lies in the direction G 8 ; and the foci of its diffracted light 

 lie on the curves Lj, L 2 . The foci of reflected light will lie on 

 the oval marked L 1? and the foci of transmitted light will lie 

 on the branches marked L 2 . 



Let F l5 F 2 be the points at which these curves cut the 

 normal to the grating, and let GF 1 =/d 1 and GF 2 =/o 2 . The 

 points F 1? F 2 I will call the normal foci ; F 2 is the normal 

 focus for reflected light, and F 2 for transmitted light. 



