358 L.Bell — Absolute Wave-length of Light. 



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 space is so local and sudden as 

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

 ously 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 would 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 will 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 will readily show the laws 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, gradu- 

 ally 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 spec- 

 trum 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, grows stronger as more and 

 more of the grating is covered, and finally is terminated by a 

 faint line. Then this line grows 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-length.* 

 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 center 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 

 of the results from different orders of spectra can possibly 

 eliminate the class of errors we are discussing, since the alge- 



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



