MICHELSON. — THE ECHELON SPECTROSCOPE. 115 



d6 



dk/k 



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 

 the resolving power, put e — dk/k for the limit. For this limitiug value 

 the ariirle will be kin s, where n is the number of elements; hence 

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

 these values, we find 



e = -£-. HI- 



bnt 



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



m ; we find 



d$ X . , ' . 



- — = - ; or, putting dm = unity, 



UL ill o 



d6 1 = X . IV. 



s 



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

 ing this value of dO in II., whence 



Hence the limit of resolution is the nth 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., JEJ = T7 J (J - . It will be impossible to examine lines 

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

 the 1) lines. 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 n t. Consequently in order to increase it as much as 

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

 But iu consequence of the losses by 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 



