191-'] FOR A CONCAVE GRATING. 563 



Finally as to the definition. Kayser^- gives for the greatest 

 permissible length of a grating used in the customary position — i. e., 

 the length when the difiference in phase between the extreme rays 

 amounts to tt — the expression 



= 2p\ 



2e cot <i> 



m 



and the same formula holds for the autocollimating position. Com- 

 paring the same order of spectra we see that as </> is less in the 

 second case (and therefore cot </> greater) the limiting length of 

 grating would be greater ; so that a given grating will be farther 

 from this limiting value and hence will have better definition. The 

 grating is in fact in the position of minimum deviation, and the 

 aberration is equally divided between the incident and diffracted 

 beams and is therefore a minimum. 



To sum up : the mounting here described differs from the usual 

 mounting for a concave grating by employing the principle of auto- 

 collimation. It possesses the advantages of the Rowland mount- 

 ing of having all spectra automatically in focus, but differs from 

 it in having greater compactness, convenience and rigidity. The 

 adjustments are easier and the necessity of a dark room is avoided. 

 The definition in the same order is somewhat greater, and twice 

 as many orders may be observed. The deviations of the spectrum 

 from the normal type are small and may be accurately allowed for. 

 The instrument may be readily adapted to work in astronomical 

 spectrography. 



Randal Morgan Laboratory of Physics, 

 University of Pennsylvania. 



" H. Kayser, " Handbuch der Spectroscopic," I., 458. 



