68 0. Barus — Rotation of Interference Fringes 



sections will depend on the obliquity of the rays (axes of verti- 

 cal pencils), and will be a minimum when the center of the 

 Held of view corresponds to an axis of rays, normal to the grat- 

 ing G'G". In other words, the vertical maximum occurs under 

 conditions of complete symmetry of rays in the vertical plane. 

 If therefore e, or the virtual distance apart of the half gratings, 

 G" and OG\ is also zero, the field will show the same 

 illumination throughout. 



Therefore, to completely represent the hehavior of fringes, 

 it will he sufficient and necessary to consider that either grat- 

 ing. G'G" for instance, is capahle of rotation, not only around 

 a vertical axis through 0, but also through a horizontal axis 

 through O parallel to the grating. The last case has been 

 directly tested. But a rotation around these two axes is equiva- 

 lent to a rotation around a single oblique axis and the fringes 

 will therefore in general be arranged obliquely and parallel to 

 the oblique axis. 



Thus if <f> v and $ h is the angle of rotation of the grating 

 (always to be small) around a vertical and a horizontal axis 

 respectively, and if x is the angle of the interference fringes 

 with the horizontal edge or axis of the spectrum, 



tan x = — 



so that if <£ v = 0, «' = ; if </> h = 0, a/ = 90°. In other 

 words, for a rotation of grating around a vertical axis (parallel 

 to slit) the fringes of maximum size will be horizontal, because 

 the adjustment around the horizontal axis remains outstanding 

 and the residual fringes (large or small) are therefore parallel 

 to it. For a rotation of grating around a horizontal axis, the 

 fringes of maximum size will be vertical, for the vertical adjust- 

 ment is left incomplete. When both adjustments are made 

 a single fringe fills the whole infinite field, and this result fol- 

 lows automatically if but a single grating is used to produce 

 the fringes, as in the original method (1. c). 



3. Case of Reflecting Gratings. Homogeneous Light. — The 

 results exhibited in figure 2 for transmitting gratings are shown 

 in figures 3 and 4 for the combination of one transmitting 

 grating G and one reflecting grating G\ the adjustment used 

 in the preceding paper (1. c.) and for which the path lengths 

 of rays were computed without allowances. (Cf. figures 10, 11, 

 §8). The path differences obtained were inadmissible. It is 

 now necessary to completely modify the demonstration. 



In figure 3 the rays are shown for the case of symmetry of 

 all parts, gratings at G and G' vertical and parallel, opaque 

 mirrors at M^ and JY„ telescope or lens at T. The incident 

 ray 1 at normal incidence is diffracted and reflected into 



