I OS 



C. Barus — Methods in Reversed and 



G. Tlh ory. — Hence the theory* of the apparatus (fig. 6) may 

 be regarded as justified. Here the rays 7, and Y' come from 

 the first grating (G transmitting) and after reflection from the 

 opaque mirrors M and iV(the former on a micrometer) impinge 

 on the second reflecting grating G', with a smaller grating- 

 space, and thereafter interfere along the line 2\ entering the 

 telescope. To treat the case the mirrors M~, etc., may be 

 rotated on the axis T normal to G' in the position J/,. G' n and 

 G' m show the reflections of G' in the mirrors JY l and M x . We 

 thus have a case resembling the interferences of thin plates 



Fig. 6. 



^S^/2" 





\ 



/ & 





'^/ 



11/ 



and if e m is the normal distance, apart of the mirrors M 1 and 

 JV,, the displacement Ae m per fringe is given by 

 A = 2A<? m cos 8 / 2 



where 8 is the angle between the rays incident and reflected at 

 the mirrors. This is the equation used above. If the mirrors 

 and the reflections of the gratings G' make angles cr/2 and a 

 with G\ the actual lengths of the rays (prolonged) before 

 meeting to interfere, terminate in e and /respectively. Let 

 the image of G' be at a normal distance e apart. Then 

 e = 2<? m cos o-/2, for the figure fd be is a parallelogram. If the 

 distance eg is called C we may also write 



X = e cos 2 + G sin 2 



since 0= 2e m sin o-/2 and the angle of diffraction # 2 =(o- + S)/2. 



* This Journal, xlii, pp. 63-73, 1916 ; cf. §3. 



