I909-] SIMILAR TO ROWLAND'S METHOD. 171 



where a' is the distance between grating and sht for the diffraction 

 corresponding to x. Hence the focal distance of the grating re- 

 garded as a concave lens is /' = ar-/x'. For the fixed grating and 

 a given color, it frequently happens that the undeviated ray and 

 the diffracted rays of the same color are simultaneously in focus, 

 though this does not follow from the equation. 



Again for the rotating grating, Fig. 3, if a" is the distance be- 

 tween slit and grating 



so that its focal distance is 



r^ — x' 



f" = a 



x" 



It follows also that a' X a" =^a-. For a = 80 cm. and sodium light, 

 the adjustment showed roughly /' = 650 cm., /" = 57o, the be- 

 havior being that of weak concave lenses. The same = 80 cm. 

 and sodium light showed furthermore a'^91 and a" ^70.3. 



Finally there is a correction needed for the lateral shift of rays, 

 due to the fact that the grating film is enclosed between two moder- 

 ately thick plates of glass (total thickness ^ = .99 cm.) of the index 

 of refraction n. This shift thus amounts to 



eJ^ ^1^ ' Y ~ 



r V v/ 1 - x'jr'' v'n'- - x^jr'' J « 



But since this shift is on the rear side of the lens L, its effect on 

 the eye-piece beyond will be (if / is the principal focal distance and 

 b the conjugate focal distance between lens and eye-piece, remem- 

 bering that the shift must be resolved parallel to the scale ss) 



where the correction c is to be added to 2x, and is positive for the 

 rotating grating and negative for the stationary grating. 



Hence in the mean values of 2.r for stationary and rotating 

 grating the effect of e is eliminated. For a given lens at a fixed 

 distance from the eye-piece {h/j — i) is constant. 



