Rowland's Method for the Concave Grating. 91 



other respects the conditions are similar bnt reversed. Apart 

 from signs, for the stationary grating 



, r — x 

 a = a — 3 — 



and for the rotating grating 



r 



= a -•— 

 r —; 



The correction for shift loses the factor ih/f— 1) and becomes 



tx / 1 1 \ 



6 ~ ~r~Wl—x'/r % Vn'—x'/r*)' 



As intimated, it is negative for the rotating grating and posi- 

 tive for the stationary grating. It is eliminated in the mean 

 values. 



6. Data. Single Zens Behind the Grating. — An example 

 of the results will suffice. Different parts of the spectrum 

 require focusing. 



Grating Line 2a;' Shift 2a: 



Stationary D^ 118-40 +-13 118-53 



Rotating Z> 2 118-65 —-13 .118-52 



The values of 2a?, remembering that a centimeter scale was 

 used, are again surprisingly good. The shift is computed by 

 the above equation. It may be eliminated in the mean of the 

 two methods. The lens L' may be more easily and firmly 

 fixed than L. 



7. Collimator Method. — The objection to the above single- 

 lens methods is the fact that the whole spectrum is not in 

 sharp focus at once. Their advantage is the simplicity of the 

 means employed. If a lens at L' and at L are used together, 

 the former as a collimator (achromatic) and with a focal dis- 

 tance of about 50 cm , and the latter (focal distance to be large, 

 say 150 cm ) as the objective of a telescope, all the above diffi- 

 culties disappear and the magnification may be made even 

 excessively large. The whole spectrum is brilliantly in focus 

 at once and the corrections for the shift of lines due to the 

 plates of the grating vanish. Both methods for stationary and 

 rotating gratings give identical results. The adjustments are 

 easy and certain, for with sunlight (or lamplight in the dark) 

 the image of the slit may be reflected back from the plate of 

 the grating on the plane of the slit itself, while at the same 

 time the transmitted image may be equally sharply adjusted 

 on the focal plane of the eye-piece. It is, therefore, merely 

 necessary to place the plane of spectra horizontal. Clearly a' 

 and a" are all infinite. 



