116 



PROCEEDINGS OP THE AMERICAN ACADEMY. 



7 mm., 18 mm., and 30 mm. respectively, each containing the maximum 

 number of elements, — that is, 20 to 35, and whose theoretical resolving 

 powers are therefore of the order of 210000, 540000, and 900000, 

 respectively. In other words, they can resolve lines whose distances 

 apart is the two-hundredth, the five-hundredth, and the nine-hundredth 

 of the distance between the D lines. 



Consequently the smallest of these echelons surpasses the resolving 

 power of the best gratings, and what is even more important, it concen- 

 trates all the light in a single spectrum. 



The law of the distribution of intensities in the successive spectra is 

 readily deduced from the integral 



Hence 



rs,, 



I cosp 

 J s/2 



27r^ 



X ax. where p = — - 6. 



A 



I=A^- 



sin- TT-a 



A 



-x'^" 



This expression vanishes for = t X / s, which is also the value of dOi, 

 the distance between the spectra. 



Hence in general there are two spectra visible as indicated in Figure 4. 



Figure i. 



By slightly inclining the echelon, one of the sj^ectra is readily brought 

 to the centre of the field, while the adjacent ones are at the minima, and 

 disappear. The remaining spectra are practically invisible, except for 

 very bright lines. 



As has just been indicated, the proximity of the successive spectra of 

 one and the same line is a serious objection, and as this proximity depends 



