402 CARNEGIE INSTITUTION OF WASHINGTON. 



direction. About two years ago I was able to make a fresh beginning, 

 and I inclose the titles of four articles pubUshed recently, and send 

 copies of these articles under separate cover. I may add that I have 

 nearly ready for publication articles on the ultra-violet spectra of 

 krypton and xenon, and that R. L. Sebastian, working with me, is 

 completing an article on the absorption spectra of the mono-derivatives 

 of benzene, all this work having been accomplished with the quartz 

 spectrograph secured with the aid of the grant. Reports on these 

 researches were made at the meeting of the Physical Society held here 

 August 5, 1915, and abstracts will shortly be published in the Physical 

 Review. 



Michelson, A. A., University of Chicago, Chicago, Illinois. Ruling and per- 

 formance oj a ten-inch diffraction grating. (For previous reports see Year 

 Books Nos. 2 and 3.) 



The principal element in the efficiency of any spectroscopic apphance 

 is its resolving power — that is, the power to separate spectral Unes. 

 The Umit 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 Une of sodium 



its limit of resolution will be — ^^5^ or approximately 0.001, and 



the resolving power is called 1,000. 



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 30,000. This limit was equaled if not surpassed by the excel- 

 lent 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 milUmeter. These were superseded by the 

 superb gratings of Rowland, with something over 100,000 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 = mn, in which n is the total 

 number of Unes and m is the order of the spectnmi. An equivalent 



expression is furnished by jR = ^ (sin i -f sin 0), where I is the total 



length of the ruled surface, X the wave-length of the light, i the angle 

 of incidence, and 6 the angle of diffraction. The maximum resolving 

 power which a grating can have is that corresponding to i and 6, each 



21 

 equal to 90°, which gives R=y~'' *^^* ^^» twice the number of light- 

 waves in the entire length of the ruled surface. This shows that 

 neither the closeness of the rulings nor the total number determines 

 this theoretical limit and emphasizes the importance of a large ruled 

 space. 



