Counting the Rulings of a Diffraction Grating. 715 



Most of Nobert's gratings, however, were small and inaccu- 

 rately ruled, they all gave very imperfect definition and 

 showed numerous " ghosts/' There does not seem to have 

 been any special trouble in ruling lines as close together as 

 need be ; for example Nobert, who jealously guarded his 

 machine and methods as a trade secret, succeeded in ruling 

 as many as 100,000 lines to the inch. The real difficulty 

 was to secure uniformity of spacing. 



It was about forty years ago that Rutherfurd, a New York 

 lawyer, by attention to the accuracy of the feeding-screw of 

 his ruling machine, was able to make a great advance in the 

 art of ruling gratings. The best of Rutherfurd's gratings, 

 however, were still faulty in respect of uniformity of spacing, 

 and his larger gratings are not satisfactory. 



As is well known, Rowland's success at Baltimore in 

 ruling gratings was largely attendant on the success of his 

 method to secure perfection in his feeding-screw. As at 

 present made, the Rowland gratings are usually ruled with 

 10,000, 14,438, or 20,000 lines to the inch. Practically all 

 are on speculum metal (c. 7 Cu, 3 Sn) which, permitting a 

 high polish, yields gratings of great brilliance and definition, 

 and being soft is not severe on the ruling diamond. On the 

 other hand, speculum metal is not a simple alloy — a state of 

 things which tends to local heterogeneity — it is heavy (which 

 necessitates thick and rather massive gratings to prevent 

 distortion), and further it has a considerable thermal coeffi- 

 cient of expansion (19*3 xlO -6 ) — a fact which introduces 

 some uncertainty into the certified grating-space for those 

 gratings whose temperature of ruling is unknown. 



A determination of the grating-space involves (1) the 

 measurement at a known temperature of the overall length 

 of a selected number of rulings, (2) the counting of those 

 rulings. The first part presents no difficulty for the modern 

 comparator fitted with suitable high-power micrometer 

 microscopes. It was to carry out what threatened to be a 

 hopelessly tedious and fatiguing task in the counting of the 

 rulings that the following method was employed in the case 

 of a plane Rowland gr;iting about 8 cms. long on speculum 

 metal, belonging to Mr. J. W. Grifford, and for which 

 ignorance of the ruling temperature made the certified value 

 (14,438 lines to the inch) not so certain as was required. 



With some of Rowland's gratings every fiftieth and 

 hundredth rulings are differentiated by being shorter and 

 longer than the rest. Others have all the rulings the same 

 length ; this was the case with Mr. Gifford's grating. 



