256 Mr. Louis Bell on the Absolute 



ruled in Dec. 1887, at a constant temperature of 17 0, 2 C. It 

 contains 40,000 spaces within the same dimensions as III., is 

 equal to it in definition, and but very little inferior in regularity 

 of ruling. It has very nearly the same focus on both sides 

 of the normal, and the ruling is wonderfully even and perfect. 



It should be noted that these four gratings are widely 

 diverse, being ruled at different temperatures and under 

 different conditions. I. and II. were ruled to widely diverse 

 grating-spaces on different parts of the screw ; 111. was on 

 speculum metal and with more than six times the ruled sur- 

 face of I. or II. ; and finally IV. was ruled to a new grating- 

 space on a new dividing-engine. These differences may not 

 favour close agreement in the experimental results, but they 

 certainly serve to eliminate anything like systematic errors 

 due to the gratings. 



The above gives a general view of the gratings employed; 

 but some further details will be mentioned in the second part 

 of this paper in connexion with the determination of the 

 grating-spaces. 



On the Standards of Length. 



Very many of the discrepancies in the determinations of 

 absolute wave-lengths are the direct result of uncertainty in 

 the standard of length employed. The cases of Angstrom 

 and Van der Willigen have been already alluded to; and the 

 same source of error is common to all other determinations. 

 It seems, therefore, desirable to give at some length the 

 various comparisons on which the wave-length as given by 

 my experiments is based. Reserving for the present the 

 actual measurement of the gratings, which is a compara- 

 tively simple matter, I will therefore discuss the standards 

 directly employed, their relations to the Metre des Archives 

 as found by various comparisons, and finally the changes 

 which have taken place in those relations since they were 

 first determined. 



The standards with which the gratings have been directly 

 compared are two double decimetres on speculum metal, 

 designated respectively S a x and S a 2 . They were graduated 

 and compared by Prof. W. A. Rogers in 1885. The bar S x 

 is 23 cm. long, and bears near its edge the double decimeter 

 S a 1? subdivided to centimetres. The defining lines are less 

 than 1 /* in width and beautifully sharp and distinct. IS 2 is 

 27 cm. long, and is graduated in the same way, with lines of 

 the same width. Both standards are of the same speculum 

 metal, and are of very nearly the same mass, while the 

 surfaces and graduation leave little to be desired. The 



