MICHELSON. — THE ECHELON SPECTROSCOPE. 117 



on the thickness of the plates — which for mechanical reasons cannot 

 well be reduced below 5 or G mm. — it is desirable to look to other 

 means for obviating the difficulty, among which may be mentioned the 

 use of a liquid instead of air. 



In this case Formula II. becomes 



d$ /|~1 . . d(n — mi)~I t 



= c 



'P ( \ \ d ^ ~ ^ 1 



dX/X s L/i,! d X J s 



and Formula IV. becomes 



d$_ _ _X^ 

 dm [i l s 



Repeating the same operations as in the former case, we find : 



X 

 n c t 



and E — —. 



ct 



The limit of resolution is still the n'th part of the distance between 

 the spectra, but both are increased in the ratio bjc. 



Suppose for instance the liquid is water. Neglecting dispersion the 

 factor would be 8.55. Hence the distance between the spectra will be 

 increased in this proportion, but the limit of resolution will also be 

 multiplied by this factor. But as there is now a surface water-glass 

 which reflects the light, the loss due to this reflection will be very much 

 less, so that it will be possible to employ a greater number of elements, 

 thus restoring the resolving power. At the same time the degree of 

 accuracy necessary in working the plates is 3.55 times less than before. 



For many radiations the absorption due to thicknesses of the order 

 of 50 cm. of glass would be a very serious objection to the employ- 

 ment of the transmission echelon. I have attempted, therefore, to 

 carry out the original idea of a reflecting echelon, and it may be of 

 interest to indicate in a general way how it is hoped the problem may be 

 solved. 



Among the various processes which have suggested themselves the 

 following appear the most promising. 



In the first a number of plates (20 to 30), of equal thickness, are 

 fastened together as in Figure 5, and the surfaces A and B are ground 

 and polished plane and parallel. They are then separated and placed on 

 an inclined plane surface, as indicated in Figure G. 



