OF ARTS AND SCIENCES. 285 



In the wave-length equation A = e sin 6; c represents the mean dis- 

 tance between the lines of the grating. A certain number of isolated 

 errors may occur in the ruling, which may entirely escape detection 

 under the spectroscope. For example, one of the provisional gratings, 



ruled with the machine built for the writer at the Waltham Watch 

 Factory, has errors of spacing which are easily measurable, and yet 

 the grating will show 7 and possibly 10 lines between b r and b 2 , not- 

 withstanding the fact that it is ruled upon commercial plate glass 

 without finish. 



Angstrom, in his investigations, found the distance between the 

 extreme lines of the different gratings employed in terms of the 

 Meter of the Archives ; and the value of c was found by dividing 

 the entire distance by the number of spaces. I cannot find that he 

 made any investigation, either of the accidental or the systematic 

 errors of the gratings. I am aware that it is commonly asserted that 

 it is impossible for systematic errors of appreciable magnitude to exist 

 in a grating which shows the solar lines sharply defined; but there are 

 many evidences that not only isolated accidental errors, but periodic, 

 errors of a small but measurable magnitude, are not incompatible with 

 apparently perfect definition. Since the periodic error of a screw may 

 undergo considerable variations in value through a change of tempera- 

 ture, especially if- this change is abrupt and violent, it does not seem 

 possible to overcome them entirely, except by a rigid investigation 

 immediately preceding the ruling of a given grating, and by the appli- 

 cation of the corrections derived, during the process of ruling. It is 

 without doubt true that the mean interval between the ruled lines can 

 be expressed with a far greater degree of accuracy than any given 

 space can be measured under the microscope ; but I believe it to be 

 possible to measure the errors of lines widely separated when there is 

 no evidence of their existence in the appearance of the solar lines. 

 Even the best gratings which have thus far been produced show traces 

 of systematic error when they are examined with monochromatic 

 light. 



Briefly, then, whenever the yard with its subdivisions is adopted as 

 the measure of length, the unit to which all measures must be referred 

 is the Bronze bar deposited in the "Strong Room" of Old Palace 

 Yard, London, known as the "Imperial Yard No. 1." It has been 

 shown that all attempts to express the length of the Imperial Yard in 

 terms of a natural unit have been abandoned. 



Wherever the metric system has been adopted, either by legal enact- 

 ment or by actual use in the absence of delinite legislation, the plati- 



