REVERSED AND NON-REVERSED SPECTRA. 41 



(position g'i, N path larger) ; and if the motion is continuous in one direction, 

 #'2, g', g'i, the path-difference will pass through zero. No doubt the angle 

 <p is rarely quite zero, so that this variable should be entered as an essential 

 part of the problem. The resulting conditions are complicated, as there are 

 now two angles of incidence and diffraction and it will therefore be considered 

 later ( 28). It is obvious, however, that if for a stationary grating G', 

 figure 26, the angle <p is changed from negative to positive values, through 

 zero, the effect must be about the same as results from fore-and-aft motion. 

 In both cases excess of optical path is converted into deficiency, and vice versa. 

 Hence, as has been already stated, the effects both of the fore-and-aft motion 

 and of the rotation of the grating G' around a vertical axis parallel to its 

 face conform to the interference fringes of figure 21, a to e. 



It is common, moreover, if a concave grating is used (with parallel rays) 

 at G', to find the two sodium doublets due to reflection from M and N ap- 

 proaching and receding from each other in the field of view of the ocular 

 when the grating G' is subjected to fore-and-aft motion. This means that 

 although the axes of incident rays are parallel in two positions, whenever i 

 varies (as it must for a concave grating and fore-and-aft motion), the diffracted 

 rays from M and N do not converge in the same focus in which they originally 

 converged, but converge in distinct foci. For if sin i sin 6 = \/D or cos idi = 

 cos 8d6, suppose that for a given i, 8 = 0; then cosidi = dd. But the devia- 

 tion, 5, of the diffracted ray from its original direction is now di+dQ, or 



5 = di(i +cos i} = zdi cos 2 1/2 



Similarly, the principal focal distance p', for varying i, is not quite constant. 

 From Rowland's equation, if parallel rays impinge at an angle i and are 

 diffracted at an angle 8 = 0, 



f = R = R 



I+COS i 2 COS 2 2/2 



If 2 = 20, then cos 2 2/2 = .976, and p' = R/2, nearly but not quite. 



I have not examined into the case further, as both the sodium doublets 

 are distinctly seen if the ocular follows them (fore and aft), and the lateral 

 displacement of doublets is of minor interest. 



With the plane reflecting grating this discrepancy can not enter, since for 

 parallel rays the angles of incidence remain the same throughout the fore-and- 

 aft motion, and therefore the angles of diffraction would also be identical. 



Two outstanding difficulties of adjustment have still to be mentioned, 

 though their effect will be discussed more fully in the next chapter. These 

 refer to the rotation of the grating G', around a vertical axis and around a 

 horizontal axis, in its own plane or parallel to it. The rotation around the 

 vertical axis was taken up in a restricted way above, in figure 13, Chapter II. 

 The effect (rotation of G') is to change the inclination of the fringes passing 

 from inclination to the left through zero to inclination towards the right. 

 The effect is thus similar to the fore-and-aft motion, as shown in figure 2 1 . 



