Rowland's Method for the Concave Grating. 89 



3. Adjustments. — The first general test which places slit, 

 grating and its spectra and the two positions of the eye-piece 

 in one plane, is preferably made with a narrow beam of sun- 

 light, though lamplight suffices in the dark. Thereafter let 

 the slit be focused with the eye-piece on the right marking the 

 position of the slit ; next focus the slit for the eye-piece on the 

 left ; then place the slit midway between these positions and 

 now focus by slowly rotating the grating. The slit will then 

 be found in focus for both positions and the grating, which acts 

 as a concave lens counteracting Z, will be symmetrical with 

 respect to both positions. 



Let the grating be thus adjusted when fixed normally to the 

 slide B or parallel to A. Then for the first order of the 

 spectra the wave-length \ = d sin 0, where d is the grating 

 space and 6 the angle of diffraction. The angle of incidence i 

 is zero. 



Again let the grating, adjusted for symmetry, be free to 

 rotate with the rod ab. Then 6 is zero and \ = d sin i. 



In both cases however if 2x be the distance apart of the car- 

 riage C, measured on the scale ss, for the effective length of 

 rod ab=r between axis and axis, 



\=dx/r or (d/2r) 8x, 



so that in either case A. and x are proportional quantities. 



The whole spectrum is not however clearly in focus at one 

 time, though the focusing by aid of the rod hh is not difficult. 

 For extreme positions a pulley adjustment operating on the ends 

 of h is a convenience, the cords running around the slide AA. 

 In fact if the slit is in focus when the eye-piece is at the cen- 

 ter (0=0, i=0) at a distance a from the grating, then for the 

 fixed grating, fig. 4, 



r* 

 a =a— , 



r~ — x 



where a' is the distance between grating and slit for the dif- 

 fraction corresponding to x. Hence the focal distance of the 

 grating regarded as a concave lens is f'=ar*/x 2 . For the fixed 

 grating and a given color, it frequently happens that the 

 undeviated raj 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 

 between slit and grating 



„ r 2 — £C 2 



a =a , 



r 



so that its focal distance is 



, r 2 — x 2 



