MICHELSON. — THE ECHELON SPECTROSCOPE. 115 



dO 



d\/\ 



|_^' ^ dXjs s 



For the majority of optical glasses b varies between 0.5 and 1.0. 



The expression II. measures the dispersion of the echelon. To obtain 



tlie resolving power, put e = dk/k for the limit. For this limiting value 



the ano'le 6 will be k/n s, where n is the number of elements ; hence 



n s p= the effective diameter of the observing telescope. Substituting 



these values, we find 



A. 



e = 



biit' 



III. 



To obtain the angular distance between the spectra, differentiate I. for 

 m ; we find 



dm s ' 



or, putting d m = unity, 



de^=^. IV. 



The quantity dk/k = E corresponding to this is found by substitut- 

 ing this value of c^^ in II., whence 



Hence the limit of resolution is the 7iih part of the distance between 

 the spectra. 



This fact is evidently a rather serious objection to this form of spectro- 

 scope. Thus, in observing the effect of increasing density on the breadth 

 of the sodium lines, if the broadening be of the order of k/bt the two 

 contiguous spectra (of the same line) will overlap. As a particular case, 

 let us take t — 7 mm., JiJ = 17 Joo- It will be impossible to examine lines 

 whose breadth is greater than the fourteenth part of the distance between 

 the D Hues. It is evidently advantageous to make t as small as possible. 



Now the resolving power, which may be defined by - is proportional 



to the product 71 1. Consequently in order to increase it as much as 

 possible it is necessary to use thick plates, or to increase their number. 

 But in consequence of the losses hj the successive reflections, experience 

 shows that this number is limited to from 20 to 35 plates, any excess not 

 contributing in any important degree to the efficiency. 



I have constructed three echelons, the thickness of the plates being 



