362 Mr. Louis Bell on the Absolute 



and nature of the abnormal portion. It will have for its maxi- 

 mum value 2(s— s'), where s'is the varying grating-space, in 

 the case when the change in the spacing is so local and sudden 

 as to produce no effect at all on the spectrum ; and will be 

 variously modified by the considerations now to be mentioned. 

 If we could always assume that the abnormal portion of the 

 grating produced no effect on the spectrum, the elimination of 

 errors of ruling w r ould thus become comparatively simple. 

 But in practice it is not very uncommon to find gratings in 

 which there are several portions where the spacing is abnormal, 

 in one case perhaps producing no effect, in a second producing 

 false lines, and in a third causing a faint shading off of the 

 lines. For an abnormal portion w r ill produce no effect, a 

 slight shading, or reduplicated lines, according to its extent 

 and the amount of its variation from the normal. 



The following experiment wall readily show the law r s which 

 govern these errors of ruling. Place a rather bad grating — 

 unfortunately only too easily obtained — on the spectrometer, 

 and setting the cross-hairs carefully on a prominent line, 

 gradually cover the grating with a bit of paper, slowly moving 

 it along from one end. In very few cases will the line stay 

 upon the cross-hairs. A typical succession of changes in the 

 spectrum is as follows: Perhaps no change is observed until 

 two-thirds of the grating has been covered. Then a faint 

 shading appears on one side of the line, gro vs stronger as 

 more and more of the grating is covered, and finally is 

 terminated by a faint line. Then this line grow T s stronger till 

 the original line appears double and finally disappears, leaving 

 the displaced line due to the abnormal grating-space. This 

 description, I regret to say, is from the examination of a 

 grating which had been used for the determination of absolute 

 wave-lengths.* This case is exceptionally complete, but even 

 with a very good grating minute displacements can usually 

 be noticed. 



When the abnormal portion is sufficiently extensive to pro- 

 duce a faint shading along one side of the lines when the full 

 aperture of the grating is used, the effect of the error on the 

 resulting wave-length may be in part eliminated by the fact 

 that the shading would displace the apparent centre of the 

 line and hence slightly change the observed angle of deviation. 

 For this reason a grating so affected would be likely to give 

 results varying with the order of spectrum used, since the 

 appearance of the line would vary somewhat with the illumi- 

 nation. It is at once apparent, however, that no combination 



* Not by the author it is almost needless to add. 



