258 Prof. H. A. Rowland on the Relative Wave-lengths 



wave-length 5790. In order to place the scale correctly on 

 this map, I have found it necessary to measure the relative 

 wave-lengths of the spectrum and to reduce them to absolute 

 wave-lengths by some more modern determination. I have 

 not yet entirely finished the work ; but as my map of the 

 spectrum is now being published, Q and as all observers so far 

 seem to accept the measures of Angstrom, I have decided 

 that a table of my results would be of value. For as they 

 stand now, they have at least ten times the accuracy of any 

 other determination. This great accuracy arises from the use 

 of the concave grating, which reduces the problem of relative 

 wave-lengths to the measure of the coincidences of the lines 

 in the different spectra by a micrometer. 



The instrument which I have employed has concave gratings 

 5 or 6 inches in diameter, having either 7200 or 14,400 lines 

 to the inch and a radius of 21 ft. 6 in. By my method of 

 mounting, the spectrum is normal where measured, and thus 

 it is possible to use a micrometer with a range of 5 inches. 

 The spectrum keeps in focus everywhere, and the constant of 

 the micrometer remains unchanged except for slight variations 

 due to imperfections in the workmanship. The micrometer 

 has no errors of run or period exceeding 20 1 000 inch. The 

 probable error of a single setting on a good clear line is 

 about 20P00 °f tne wave-length. 1" of arc is about '0012 inch. 

 The D line in the second spectrum is *17 inch or 4*4 millim. 

 wide. Determinations of relative wave-length of good lines 

 seldom differ 1 in 500,000 from each other, and never exceed 

 1 in 100,000, even with different gratings. This is, of course, 

 for the principal standard lines, and the chance of error is 

 greater at the extremities of the spectrum. The interpolation 

 of lines was made by running the micrometer over the whole 

 spectrum, 5 inches at a time, and adding the readings together 

 so as to include any distance, even the whole spectrum. The 

 wave-length is calculated for a fixed micrometer constant, and 

 then corrected so as to coincide everywhere very nearly with 

 the standards. I suppose the probable error of the relative de- 

 terminations with the weight 1 in my table to be not far from 

 1 in 500,000. Angstrom thinks his standard lines have an 

 accuracy of about 1 in 50,000, and ordinary lines much less. 

 As to the absolute measure, it is now well determined that 

 Angstrom's figures are too small by about 1 part in 6000. 

 This rests, first, on the determinations of Peirce made for the 

 U.S. Coast Survey with Rutherford's gratings, and not yet 

 completely published ; secondly, on an error made by Tresca in 

 the length of the standard meter used by Angstrom*, which 

 * Sur le Spectre du Fer, Thal^n. 



