REVERSED AND NON-REVERSED SPECTRA. 



39 



G. It is necessary to consider the three positions of the reflecting grating G'; 

 viz, G', G\, and G' 2 . In the symmetrical position G', the pencils whose axes 

 are n and n' meet at a and are both diffracted along r. In the position G', 

 they are separately diffracted at b and b f in the direction r\ and r\, and they 

 would not interfere but for the objective of the telescope, or, in the other 

 case, of the concave mirror of the grating. In the position G' z , finally, the 

 pencils n and n' are separately diffracted at c and c' into r 2 and r' 2 and again 

 brought to interference by the lens or concave mirror, as specified. 



Now it is true that the rays na and n'a (position G'}, though parallel in a 

 horizontal plane, are not quite collimated in a vertical plane. The pencils 

 are symmetrically oblique to a central horizontal ray in the vertical plane, 

 and their optical paths should therefore differ. But fringes, if producible in 

 this way here, have nothing to do with the rotation of the grating in its own 

 plane and may here be disregarded, to be considered later. 



fJL 



* 

 t--$ 



gr< 



To take the rotation of the fringes first, it is interesting to note in passing 

 that the interferences obtained by rotation around a normal axis recall the 

 common phenomenon observed when two picket fences cross each other at a 

 small angle tp. It may therefore be worth while to briefly examine the rela- 

 tions here involved (fig. 27) where S' and 5 are two corresponding pickets of 

 the grating at an angle <p and the normals D' and D are the respective grating 

 spaces. The intersections of the groups of lines S' and S make the representa- 

 tive parallelogram of the figure (5 taken vertical), of which B is the large 

 and B' the small diagonal. The angles indicated in the figure are x-{-y = ip 

 and x'+y'+<p= 180. As the bright band in these interferences is the locus 

 of the corners in the successive parallelograms, B is the distance between 

 two bright bands, while B', making an angle y r with 5, is the direction of 

 these parallel interference bands relative to the vertical. Let the free ends 

 of D and D' be joined by the line E' ; and if D is prolonged to the left and the 

 intercept is D in length, let this be joined with the end of D' by E. Then the 

 triangle DED' and S'BS, DE'D' and S'B'S, may be shown to be similar by 

 aid of the following equations : 



r"i- r~ir\r T->/ T-> r-/ t~> U *-* Sin X 



SD=o D u sin <p = h sin x o sin <p = B sin y ~F7 = 75 ~^~ 



S B sin y 



