TABLE OF STANDARD WAVE-LENGTHS OF THE SPECTRAL LINES 549 



the inch, and from 13 to 21| feet focus. The first series made with the 

 13-foot grating by Mr. Koyl in 1882 was not found quite accurate 

 enough, and I have since made personally a long series with gratings 

 of 21| feet focus which is mnch more accurate. These long focus grat- 

 ings had from 7000 to 20,000 lines to the inch, and were ruled on two 

 dividing engines, while the 13-foot one had a less number, possibly 

 3000. There are two principal errors to guard against in this method, 

 the first peculiar to the method of coincidences, and the second to any 

 method where gratings are used. 2 The first is that, where spectra are 

 over each other and the lines therefore often on top of each other, the 

 line of one spectrum may be apparently slightly displaced by the 

 presence of one from another spectrum, although the latter may be 

 almost invisible. The use of proper absorbents obviates this difficulty. 

 The second source of error is more subtle, and arises from the diamond 

 ruling differently on different parts of the grating. It is more apt to 

 occur in concave gratings than plane ones, although few are perfectly 

 free from the error, as it is very difficult to get a diamond to rule a 

 concave grating uniformly. Looking at the grating in spectra of 

 different orders, the grating may appear uniform from end to end in 

 one, and possibly brighter at one end than the other in another spec- 

 trum. This gives a chance for any imperfection in the form of the 

 surface of the grating, or any errors in its ruling, or indeed the spheri- 

 cal aberration of the lenses or concave grating, to affect the measure- 

 ment of relative wave-length. 3 This error I have guarded against by 

 using only uniformly ruled gratings, reversing them, and using a great 

 number of them. I have also used the coincidence of only the lower 

 orders of spectra, such as the 2d, 3d, 4th, oth, and 6th. Coincidences 

 up to the 12th were, however, observed by Mr. Koyl with the 13-foot 

 concave, and probably have some errors of this nature. 



In this way I established about fifteen points in the visible spectrum 

 which served as primary standards. These were so interwoven by the 

 coincidences that I have great confidence in the value of most of them. 



2 The variation of the dispersion of the air with the thermometer and barometer 

 is probably not worth considering for the visible part of the spectrum, although it 

 might be worth investigating for the two extremities of the spectrum. 



3 The error of using gratings of variable brightness in different parts, or those 

 with imperfect ruling of any kind, I have constantly guarded against. Such I be- 

 lieve to be the principal causes of the great errors in relative and absolute wave- 

 lengths in Vogel's tables, as the gratings he used, made by Wandschaft, were full of 

 errors of all kinds. 



