THE RULING AND PERFORMANCE OF A TEN INCH 

 DIFFRACTION GRATING. 



By a. a. MICHELSON. 



(Read April 22, 191 5.) 



The principal element in the efficiency of any spectroscopic appli- 

 ance is its resolving power — that is, the power to separate spectral 

 lines. The limit of resolution is the ratio of the smallest difference 

 of wave-length just discernible to the mean wave-length of the pair 

 or group. If a prism can just separate or resolve the double yellow 



1- r 1- • 1- • r 1 • -11 1 s8q6-=;8oo 



Ime 01 sodium its limit of resolution will be - „ or approxi- 



5893 

 mately one one thousandth, and the resolving power is called one 



thousand. 



Until Fraunhofer (1821) showed that light could be analyzed 

 into its constituent colors by diffraction gratings this analysis was 

 effected by prisms the resolving power of which has been gradually 

 increased to about thirty thousand. This limit was equalled if not 

 surpassed by the excellent gratings of Rutherford, of New York, 

 ruled by a diamond point on speculum metal, with something like 

 20,000 lines, with spacing of 500 to 1,000 lines to the millimeter. 

 These were superseded by the superb gratings of Rowland with 

 something over one hundred thousand lines, and with a resolving 

 power of 150,000.^ 



The theoretical resolving power of a grating is given as was first 

 shown by Lord Rayleigh by the formula R = m7t, in which n is the 

 total number of lines, and m the order of the spectrum. An equiva- 

 lent expression is furnished by 



i? = -(sin z-f-sin 0), 



A 



1 The 6j4 in. gratings now ruled on the Rowland engine have a much 

 higher resolving power — probably 400,000. 



PROC. AMER. PHIL. SOC. LIV. 217 J, PRINTED JULY 7, I915. 



137 



