102 ON A Tx\BLE OF STANDAED WAVE LENGTHS OP THE SPECTRAL LINES. 
To obtain llic priinni-j standards by means of overlapping spectra, I have used 
<rratlii<'s with from 3,000 up to 20,000 lines to the inch, and from 13 to 211 feet 
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focus. The (irst series made with the 13-foot grating by Mr. Koyl in 1882 was 
found nuitc acciuatc enouprh, and I have since made personally a long series 
with <Tratinn-s of 2U feet focus which is much more accurate. These long focus 
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s liad from 7,000 to' 20,000 lines to the inch, and were ruled on two dividing 
crn'-ines, while the 13-foot one had a less number, possibly 3,000. There are two 
il errors to ^niard ao^ainst in this method, the first peculiar to the method 
prmcipal 
of coincidences, and the second to any method where gratings are used.* 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 spectrum. 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 spherical aberration of the lenses or concave grating, 
to affect the measurement of relative wave length.! 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, 5th, and Gth. Coincidences up to the 12th were, 
observed by Mr. Koyl with the 13-foot concave, and probably have some 
errors of this nature. 
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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 groat confidence in the value of most of them. Indeed, no process of 
angular measurement could approach the accuracy of this one. 
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. 
t 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 believe to be the principal causes of the great errors ia 
relative and absolute wave lengths in Vogel's tables, as the gratings he used, made by Wandschaft, were full 
of errors of all kinds. ^ ^ J 
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